diff options
152 files changed, 52286 insertions, 1525 deletions
diff --git a/buch/buch.fdb_latexmk b/buch/buch.fdb_latexmk new file mode 100644 index 0000000..f134656 --- /dev/null +++ b/buch/buch.fdb_latexmk @@ -0,0 +1,537 @@ +# Fdb version 3 +["bibtex buch"] 0 "buch.aux" "buch.bbl" "buch" 0 + "buch-blx.bib" 1626975915 340 2f52f1f530ba6b5adc70fa4723f31a54 "pdflatex" + "buch.aux" 0 -1 0 "pdflatex" + "c:/texlive/2019/texmf-dist/bibtex/bst/biblatex/biblatex.bst" 1572020807 64965 69a9b5cd41a72f970d6b09ef293df7d7 "" + "chapters/references.bib" 1624097835 5138 b960dfcb0de83e9e8f8f3069c9375978 "" + "papers/clifford/references.bib" 1617288101 882 fc3a2de90065ad3355d6feb3e32d6590 "" + "papers/erdbeben/references.bib" 1626875294 2810 35c86ade2ee7ffbd8d2c17a9a69fcac8 "" + "papers/ifs/references.bib" 1624462097 3387 102d440dfef6b76edc1bfcef9286df16 "" + "papers/mceliece/references.bib" 1617288102 882 26b9bed1d376319cfdb70a05b9effc85 "" + "papers/multiplikation/references.bib" 1617288103 906 6f04b44fd8203281e79bd4b1d72d1cdf "" + "papers/punktgruppen/references.bib" 1624097835 875 c9e56ac2b002eee9bc7e364c4fbbd108 "" + "papers/reedsolomon/references.bib" 1626875294 1742 ccf87406646d84ea519c39fd92f457e5 "" + "papers/spannung/references.bib" 1624097835 1468 8a716916c129a78a71e9b15399fddd43 "" + "papers/verkehr/references.bib" 1617288104 878 e59fa309d2c6a84aa650cfdaef592901 "" + (generated) + "buch.blg" + "buch.bbl" +["makeindex buch.idx"] 0 "buch.idx" "buch.ind" "buch" 0 + "buch.idx" 0 -1 0 "pdflatex" + (generated) + "buch.ilg" + "buch.ind" +["pdflatex"] 1626975907 "c:/JB/LaTex/SeminarMatrizen/buch/buch.tex" "c:/JB/LaTex/SeminarMatrizen/buch/buch.pdf" "buch" 1626975907 + "buch.aux" 0 -1 0 "pdflatex" + "buch.bbl" 0 -1 0 "bibtex buch" + "buch.ind" 0 -1 0 "makeindex buch.idx" + "buch.tex" 1626109319 1116 8c6f673a90a3e92f548441ca71316946 "" + "c:/JB/LaTex/SeminarMatrizen/buch/buch.aux" 1626975907 9 a94a2480d3289e625eea47cd1b285758 "" + "c:/JB/LaTex/SeminarMatrizen/buch/buch.tex" 1626109319 1116 8c6f673a90a3e92f548441ca71316946 "" + "c:/texlive/2019/texmf-dist/fonts/map/fontname/texfonts.map" 1572022227 3332 103109f5612ad95229751940c61aada0 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/jknappen/ec/ecrm1000.tfm" 1572021830 3584 adb004a0c8e7c46ee66cad73671f37b4 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm" 1572021195 1296 45809c5a464d5f32c8f98ba97c1bb47f "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm" 1572037353 1020 c53143d3e3747b5c1149bd9a5ecd7b55 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxi.tfm" 1572037354 1048 a97cff5f6b833b712079817ce7a40d4c "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm" 1572037354 1056 e2202af076e43d03fc17f87e104021b0 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm" 1572037354 4572 2c370d27bbb031f7592de9d41dc8cfca "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm" 1572037354 4452 0fd0a792eaab7113e4d4f1b941ff0367 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm" 1572037354 4640 ce59980bcbe9e6236fab46d0b5212c7e "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm" 1572037354 1004 c0e991f864f31f017ea4ff9e451b76d4 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm" 1572037354 6892 772bf8e6c154137db8568fa8a47a6ceb "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xi.tfm" 1572037354 6956 cab20301c4a0fe2075f774c8a2433c5d "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm" 1572037354 6716 6d25a377562601272906e3bfe6b2817a "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xtt.tfm" 1572037354 1384 8943063000d26272532f74ca134dfecd "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/tcxr.tfm" 1572037354 1468 26982ed5d4aefc6c98ed466c7d6869d8 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txex.tfm" 1572037354 1080 b674b4ba143004461509a754a0984b67 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm" 1572037354 688 f56006d6e56f46e63d9f63252958b828 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txi.tfm" 1572037354 2584 cf4a6a7c2a518d47468fe29ef0913ba0 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm" 1572037354 1944 f854e259cb2839e49d4aa2949544a6e1 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm" 1572037354 1180 72784d0ee5a983fba99a0986b31b0493 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txr.tfm" 1572037354 2408 aec793a3c45e495f7ad15b227c91f508 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txss.tfm" 1572037354 2812 58673a2de05c4f3a942b32b7ff5d1117 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm" 1572037354 1268 1d124f224979493f8fd017a7597ea1cd "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm" 1572037354 972 2c9ffac4bbd20f91c01aaef9bf3f8710 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm" 1572037354 988 098ca7e8cc5647b9ac21b82dbdce1f01 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm" 1572037354 1084 75e807e9e71f7a312e4e1187dce5e93b "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txtt.tfm" 1572037354 1200 1032be7d597a4dce33bcda3c08fc1be0 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy10.tfm" 1572037674 884 cb2a5aeb15d2c2fa75963576ff22778d "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy5.tfm" 1572037674 888 4cc43129a7cedbe8878dca9c1b7906f3 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy6.tfm" 1572037674 892 ce84734a3ce970a47ce7803be6d89b0f "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy7.tfm" 1572037674 888 5f102ebf31506247d60c56d7d473e774 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy8.tfm" 1572037674 884 df491db60492d6d4b55157a114e1a6bd "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xyatip10.tfm" 1572037875 608 50246cc71b0635b0ba0a5c10a0bf4257 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xybsql10.tfm" 1572037875 608 4db60f15ea23b4ec2d796c6d568a63fa "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xybtip10.tfm" 1572037875 608 50246cc71b0635b0ba0a5c10a0bf4257 "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xycirc10.tfm" 1572037875 844 3393210079fb4ed9347e214b3bfd7c1a "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xycmat10.tfm" 1572037875 608 f124f78ed50a1817738d2adb190cf2bd "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xycmbt10.tfm" 1572037875 608 f124f78ed50a1817738d2adb190cf2bd "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xydash10.tfm" 1572037875 984 5c01c46b93e3ba8369f3f8edc6e62aef "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xyluat10.tfm" 1572037875 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" + "c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xylubt10.tfm" 1572037875 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" + "c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xb.vf" 1572037354 2144 bab2875eda5b2344ea7b1db74ccc03a4 "" + "c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xi.vf" 1572037355 2120 35084608d79b6b13dd746dfcffe98243 "" + "c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf" 1572037355 2140 99e5b3a34695df6221a167ffa8b498d6 "" + "c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txmi.vf" 1572037355 960 cfcc9d587b40b769f64408b3ca115941 "" + "c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txr.vf" 1572037355 904 e582cae2d8ae3f48a0a520440ebcdb51 "" + "c:/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1572023574 71627 94eb9990bed73c364d7f53f960cc8c5b "" + "c:/texlive/2019/texmf-dist/tex/generic/babel-english/english.ldf" 1572020659 7008 9ff5fdcc865b01beca2b0fe4a46231d4 "" + "c:/texlive/2019/texmf-dist/tex/generic/babel-german/ngerman.ldf" 1572020666 2164 da22692bce498dcc4f70209c7185a346 "" + "c:/texlive/2019/texmf-dist/tex/generic/babel-german/ngermanb.ldf" 1572020666 7584 40e9a51a28a966f337267407ea4ab873 "" + "c:/texlive/2019/texmf-dist/tex/generic/babel/babel.def" 1572020641 81804 3bb5472a03aeb22f281905fcc1b735b2 "" + "c:/texlive/2019/texmf-dist/tex/generic/babel/babel.sty" 1572020641 19267 b3fa1edb8df025e71f6c509aae11febb "" + "c:/texlive/2019/texmf-dist/tex/generic/babel/switch.def" 1572020647 14543 c96dc306f16879b3fe9b42eccb82621a "" + "c:/texlive/2019/texmf-dist/tex/generic/babel/txtbabel.def" 1572020647 5178 5b21c28f495420030a8aa1a19d21f35f "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirc.defines.tex" 1572021160 84822 f9304f7960db1e049c1437278e051070 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircbipoles.tex" 1572021160 188580 f9942dd51e3a127b80d56eb8654ffc82 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirccurrent.tex" 1572021160 7608 20446c4d92baf533e0b4a4b08fa75f9b "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircflow.tex" 1572021160 7340 1de74e39d2bd67fa5c240598472fe065 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirclabel.tex" 1572021160 13583 5d73da3563231afaef41d7bcadf15344 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircmonopoles.tex" 1572021160 46073 70a8df563c8f29b090534d963745cce9 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircmultipoles.tex" 1572021160 47441 9dab08d51d358598296429966427fb78 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircpath.tex" 1572021160 57742 892bfd41486d2470ff21fd5a7cc40b01 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircquadpoles.tex" 1572021160 33854 814f1ea774b5034cc992a0e8c8ebc9d3 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircshapes.tex" 1572021160 26135 9e81301c79e7eb111ecf11ce0984ea40 "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirctripoles.tex" 1572021160 184990 f5266a7eef05c2bcf0a97b9d1b69c25d "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircutils.tex" 1572021160 1442 8643a3387b99ca03e3598ce273d346ec "" + "c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircvoltage.tex" 1572021160 22911 dd44590bd4f65305e95cbb8979bd012d "" + "c:/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty" 1572022591 1458 43ab4710dc82f3edeabecd0d099626b2 "" + "c:/texlive/2019/texmf-dist/tex/generic/oberdiek/gettitlestring.sty" 1572035815 8237 3b62ef1f7e2c23a328c814b3893bc11f "" + "c:/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty" 1572035815 185392 ed78c0cbc4fc8c3af82e7bffbdeeb1a9 "" + "c:/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty" 1572035815 70864 bcd5b216757bd619ae692a151d90085d "" + "c:/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty" 1572035815 1300 96620a7d94bc0ceb261d968770ce8315 "" + "c:/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty" 1572035815 6797 90b7f83b0ad46826bc16058b1e3d48df "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex" 1572035985 992 fb3cda354707a54fda62787a411c7c22 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex" 1572035985 43820 bc6cf5aa959817914ace33f5c6232161 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex" 1572035985 19324 c9a64402f22bd8d81821141a357af653 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex" 1572035985 6038 d639d02574be9a72f3c602c2a3510e02 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex" 1572035985 6948 284bbe3c9a7ca0a826c1c03895e69b9f "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex" 1572035985 4883 a6f3eb1f71d8c4affaf43a169828b043 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex" 1572035985 2544 3b1b198fd49f01e328adc9162a07b213 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex" 1572035985 44195 134d5eb267e64d2a6b6dc75008e7c5fd "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex" 1572035985 17311 3092579be20ef0f229c42ad3f09da85c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex" 1572035985 21302 d6c4b340248adbe650ebf6ca76bdccca "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex" 1572035985 9690 7585efa5a591822837f837bc5bc35621 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex" 1572035985 33356 19ca73d4aa24857120b230a5d06f6b4c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex" 1572035985 2965 502761b60f43ab2de5ecb2f4625163ae "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex" 1572035985 5196 f8c5c775d4d6e2cb050392127cabda72 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex" 1572035985 20817 1763e1bd1795e073004fa1b1d2d3a6ff "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex" 1572035985 35249 144a6b9c4df4644618bb3a0a40472608 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex" 1572035985 21989 266e83c51fe41eb8b8d5e6896dc71cc1 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex" 1572035985 8842 5cc856e132fac404805c6da091779283 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex" 1572035985 93709 233f19649f8c898adef02fa24663315b "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.code.tex" 1572035985 86563 b08e5287b936d25a56c508b76fc6ee77 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzexternalshared.code.tex" 1572035985 68832 d3fb188b0bd28ad6bf7cbf96d9d92059 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryangles.code.tex" 1572035985 3614 59f4355ade5fd6073a4e2be9b54c0b95 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex" 1572035985 319 8fc6edce901e074ba09de320a8fc686b "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybabel.code.tex" 1572035985 380 da9c51fa5041ab6902735fb3486588a8 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex" 1572035985 4572 980c82f01c0e3983edadbbc373d304cb "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybending.code.tex" 1572035985 345 6b38ae970b98b6801fe4ff50b7ef406b "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalc.code.tex" 1572035985 16976 905e5807909a67b2d43e9d0f29353b5f "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex" 1572035985 5493 6342997a7484f1ea9feacd1b25ead9ea "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex" 1572035985 321 61aafaff3134e44ce6305fdd6927cdc5 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathreplacing.code.tex" 1572035985 1319 b38e66120927828ef91b8bfec59e82f3 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex" 1572035985 3643 4a4bd51bd85886cc39d4073af8cf77a9 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfpu.code.tex" 1572035985 283 089230eb299a474ce2824678bcd1743a "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex" 1572035985 5056 925c1e52f24a98ec0bd8c6ee6a9d0cd3 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymath.code.tex" 1572035985 25517 40478218403d8186f231a45c46d0954b "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex" 1572035985 4202 e655aa2657da1088ec7745ece2876c4c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.code.tex" 1572035985 770 618a89f4ac550a393f10702d3046162f "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplotmarks.code.tex" 1572035985 325 dd99a5daacaad68231ba39fa31c3e277 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex" 1572035985 3937 20cd45386ca23052ce976464f0ada984 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryquotes.code.tex" 1572035985 3931 5fb0eaae891015bd03ff91a20998aec4 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.arrows.code.tex" 1572035985 410 0baf109afdeb5efd4e82375fc951e906 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.callouts.code.tex" 1572035985 1201 c97b39982196228cedd4fe1beaba358a "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.code.tex" 1572035985 494 6bd09f53d3585526ad2f70d59c84f151 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.geometric.code.tex" 1572035985 339 153f95b6d1982135aac9ba139d8a4870 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.misc.code.tex" 1572035985 329 b7a8d335163f5b4dbd019ac579f101d8 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex" 1572035985 919 da625675781832f2b61a7048a51ef656 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.symbols.code.tex" 1572035985 475 11d7e76bce6c5f2e43a1ca0426176e02 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarythrough.code.tex" 1572035985 1040 0a5dc9d58f9fa2ab1b79c0e76a2a8c9c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex" 1572035985 11541 e321ec3e21e160e06435fdfa0d0d8a91 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex" 1572035985 186348 e8665e6a32e2904287878bd61eb45f16 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathmorphing.code.tex" 1572035987 8843 8328b4068b5b11eaa173e0957cd0eac5 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathreplacing.code.tex" 1572035987 7474 acce7114514030373cc6cb938a73a92e "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex" 1572035987 31874 d843d507175f2bdfa3abf01f0349dac8 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex" 1572035987 58801 c503519b1e019b14dc7fb801de6de024 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibrarycurvilinear.code.tex" 1572035987 14117 7aa00d7855a2ab24d9dba045971a6e4c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex" 1572035987 83819 462261f65d4a9a752cd15bfdf76d688a "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryintersections.code.tex" 1572035987 44145 6117af84f1a02fc43cb1f8055867429e "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibrarypatterns.code.tex" 1572035987 7936 1d559f55663b722daf7ce26cef4c3906 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex" 1572035987 32995 a4d54c043ae5274ceaaddeb36ad43a6f "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryplotmarks.code.tex" 1572035987 14524 f7f259aa362ad7d5bf9235db788feef3 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.arrows.code.tex" 1572035987 91587 284e5410f9da89780999100af9508505 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.callouts.code.tex" 1572035987 33336 1455fcb963023436e4ae5922b22b67c5 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.code.tex" 1572035987 160992 a39094cdc3a2bf5a131b9fd00f9002aa "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.misc.code.tex" 1572035987 46241 d4ce0f60786a8555b975b7d1ddfb331c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex" 1572035987 62281 fd68e6d2c2dc178611c8f4d2d86e79ae "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.symbols.code.tex" 1572035987 90515 5bf95af0bc1f3f00a514d280bb1b458a "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfint.code.tex" 1572035987 3063 8c415c68a0f3394e45cfeca0b65f6ee6 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex" 1572035987 521 c70cf6ad609de83a27ee7929eb356332 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex" 1572035987 13391 933cab19c6d27039dbfc487330d1005a "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex" 1572035987 104938 15f2d8bdabd6bf9ca70f62cd8e3d4940 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex" 1572035987 10157 218d58ab074e5bd0d027de45ec64cc00 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex" 1572035987 28177 7c47c337a1d5dbef1983ad718b752780 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex" 1572035987 9054 388d21239a1b6df2cc8beaae31c976b0 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex" 1572035987 3865 cddf7ddc80f018587c55afdcc79fc333 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex" 1572035987 3177 27d85c44fbfe09ff3b2cf2879e3ea434 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex" 1572035987 10925 df50b8a6e5660a585e3a2bf55726dcc8 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex" 1572035987 7787 1750fc3f164703caf31fc8ea9218c67e "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex" 1572035987 3379 cbd0948a550bd7a495a160ca6beee9ed "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex" 1572035987 92405 bba89470858d7b0788a9c09331c39653 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex" 1572035987 36525 1a0afe71ab0664595ccf348e415006df "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex" 1572035987 7431 af3d75e118d051d25f998b340bda2432 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmodulebending.code.tex" 1572035987 10901 373b629dee187417370a2097c6a7ff18 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduledatavisualization.code.tex" 1572035987 95375 a8c89d05c52335982aa2c447fa9ee710 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduledecorations.code.tex" 1572035987 71722 1aa2adb2b5cb7aafc25e92426626ab63 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex" 1572035987 20905 32f5da2d6cf180962acc32cfde9fb2bc "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmodulenonlineartransformations.code.tex" 1572035987 12243 a19282a48187a1d7ddedd48a547f94f3 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduleoo.code.tex" 1572035987 27080 1bfeba23b1ab3083d5a8f0762ec1e3b0 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex" 1572035987 16121 9e240115374a8d489f2f786115df83a9 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex" 1572035987 43288 2af229b54b2b6653a0fe74a56326e98a "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/pgf.revision.tex" 1572035988 465 5de5005b4b42af76f0a1bf6846c2c46e "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg" 1572035988 926 70ff613fabeb70f5d1673dc0c93987bd "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def" 1572035988 5546 3586827e6032c95512b2a6682d2979a3 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-luatex.def" 1572035988 13214 dd7528d1b54531af922516f1e20068a2 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def" 1572035988 12603 c02869ea216d842c29d52fae8738264e "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex" 1572035988 60269 e86bc0081af83a4ad47e4500ee09a2e4 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex" 1572035988 1896 82c274ff520f9e450ccea4e3ef4edc12 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex" 1572035988 7778 a25a32a10ca820357491d4c7b3ac02ea "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex" 1572035988 23777 cb6c8f02f87d86d621f5cb92c44f4998 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex" 1572035988 36451 8396330cd99122375b9c7ec93aabe055 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex" 1572035988 37439 bd44d50aef702b03193f731207931834 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex" 1572035988 4494 7e5ace0ccf59408f2cf63219a5d36927 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex" 1572035988 7250 03b2b9fb5fa38e7ca5cc3c45860fb210 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex" 1572035988 27585 2311d713b44b84f56b9f0b06b703324e "" + "c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def" 1572035988 6286 1bd76fc45da9929ab2a64f51cba3ab6f "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/libs/pgflibrarypgfplots.surfshading.code.tex" 1572036010 22701 5fab7b8ebb90b053dc067d1bd37e43c2 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/libs/pgfplotslibrary.code.tex" 1572036010 3047 aa82404aec57311271f4991c44bd71dc "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsarray.code.tex" 1572036010 23537 54be8160344d894595f6d145b1311658 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsdeque.code.tex" 1572036010 4288 b8d6247899b21e3bb66bb11b24d30f2c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsliststructure.code.tex" 1572036010 13828 11d1b09335a4a8baa693dd1e6cac3edf "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsliststructureext.code.tex" 1572036010 24373 6544c1554e5da33118301011eb03058d "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsmatrix.code.tex" 1572036010 18861 7dc35832c8ccea3aa73cdcd75ec0a60b "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.code.tex" 1572036010 121113 9df0278e98c01331aae8902c7b0291b6 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.coltype.code.tex" 1572036010 2713 fd4cc0a81e533baadca64f656777ffd6 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstableshared.code.tex" 1572036010 79639 86777dd9ea988e5800e7d2826d481305 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_loader.code.tex" 1572036010 11930 011a1d7d82c7446501c720a1fa4637a3 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.code.tex" 1572036010 481695 ebf89fad86a29ee0f5494f7b8902726d "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.errorbars.code.tex" 1572036010 22428 72578a4c9324bc5dfafe23fe64f64024 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.markers.code.tex" 1572036010 12462 43d76eeeb8efa51f11a058cb813ba410 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.paths.code.tex" 1572036010 2419 026baafbf72a109e199ede6fbbfd9caa "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.revision.tex" 1572036010 516 984b5334f6dc5efb409e12ecc5d0fd99 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.scaling.code.tex" 1572036010 123680 d33fda4929d7200c3e6f0ec83c006aef "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotscoordprocessing.code.tex" 1572036010 364778 01f6e73e3b25a88c502f2fe8fbaf8fa6 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotscore.code.tex" 1572036010 19944 7957349fbe31c4e8dea9de4cd41cb086 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsmeshplothandler.code.tex" 1572036010 133871 7247b31742a2240343a6739cb76d6821 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsmeshplotimage.code.tex" 1572036010 24402 288fc3f6c7980728b8a519dfd1737d22 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsplothandlers.code.tex" 1572036010 117673 ba2a69982abb70115c5431acf313d1e6 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsstackedplots.code.tex" 1572036010 26190 c428334c805ae1d15110eb8670292947 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsticks.code.tex" 1572036010 91093 a67c3943f1672f56f56272bb501f7093 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/sys/pgflibrarypgfplots.surfshading.pgfsys-pdftex.def" 1572036011 5907 9dc460712c23e5b3338820499d47608c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/sys/pgfplotssysgeneric.code.tex" 1572036011 3095 c82d281b748902a65be2ccca97360b11 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsbinary.code.tex" 1572036011 23050 a369aa910ef860a3621fe0459faa335c "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsbinary.data.code.tex" 1572036011 26859 7a4ee9d206fb0a0daa0d3108445afb57 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotscolor.code.tex" 1572036011 23958 1b96260863091af1669c3a38b1c4c9af "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotscolormap.code.tex" 1572036011 88956 018b2512ef27998e97af72e8b1dcdbd5 "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsutil.code.tex" 1572036011 69300 d69422610b847918ed9c5f4455896b9f "" + "c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsutil.verb.code.tex" 1572036011 3286 c17079ba50483e1ac1721268ea016041 "" + "c:/texlive/2019/texmf-dist/tex/generic/tikz-cd/tikzlibrarycd.code.tex" 1572037151 23113 777d022ec96400121479223b4e174a8d "" + "c:/texlive/2019/texmf-dist/tex/generic/unicode-data/UnicodeData.txt" 1572037490 1797778 755f6af699f8c8d2d958da411f78f6c6 "" + "c:/texlive/2019/texmf-dist/tex/generic/xkeyval/xkeyval.tex" 1572037818 19231 26434a5656c684f5ffb1f26f98006baa "" + "c:/texlive/2019/texmf-dist/tex/generic/xkeyval/xkvutils.tex" 1572037818 7677 6f5ce7c1124cad7ec57d05b2562bd8fe "" + "c:/texlive/2019/texmf-dist/tex/generic/xstring/xstring.sty" 1572037860 123 a302f2c651a95033260db60e51527ae8 "" + "c:/texlive/2019/texmf-dist/tex/generic/xstring/xstring.tex" 1572037860 47762 87512aefe2c24c8c3ff58ba167aba4d9 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xy.sty" 1572037875 4692 1e1bcf75c622af1eefd9169948208302 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xy.tex" 1572037875 115380 413d5f789929a45aab7d12ce0d0aee7d "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xyall.tex" 1572037875 1449 24340b6befc66d28ee1ebb657efb5892 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xyarrow.tex" 1572037875 22657 990ce136a3cc15728ba417a2e78b25c8 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xycmtip.tex" 1572037875 1374 43fb8dc80dd748631d78096701166d76 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xycolor.tex" 1572037875 4586 edd672434f45626662368282c0322160 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xycurve.tex" 1572037875 109670 d412ee1ff259daefee5e927172e2f9a8 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xyframe.tex" 1572037875 24249 186931a828664624939ab0b347e3952c "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xygraph.tex" 1572037875 9619 b7e4d9a6936ba2ad6119a280abde9641 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xyidioms.tex" 1572037875 2907 1ee562fde0b53c9cd16f7a604f33fdf0 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xyline.tex" 1572037875 10928 c3a572983ccc9fc596b4e9ce454d5652 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xymatrix.tex" 1572037875 22583 25b1e7edeee41f181ee9733429da4a9c "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-co.tex" 1572037875 8442 90cb8a3b00c2081384c1ce988d2ba0a3 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-cu.tex" 1572037875 39762 25a964ebb390bcfcd35c040f477eef1d "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-fr.tex" 1572037875 16485 5686b19cc46d046c885428794ed9c114 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-li.tex" 1572037875 2619 1a12b316e2132654e44ba2cd21def637 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-ro.tex" 1572037875 5290 e16fc85c85f64d0a5c04708bf3312d00 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf.tex" 1572037875 18763 e61049d36bdfccb226f22e582d70d368 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xyrecat.tex" 1572037876 1391 c8763fc8e281cb6ecf697988b6608e4a "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xyrotate.tex" 1572037876 7008 cb768d8d63a12d35607cbb3c4e7ba163 "" + "c:/texlive/2019/texmf-dist/tex/generic/xypic/xytips.tex" 1572037876 3689 0d51788a4141bc66ab896f7ac63495fd "" + "c:/texlive/2019/texmf-dist/tex/latex/adjustbox/adjcalc.sty" 1572020417 5608 e823b3adfbc2ea70e453a21ea6e2ee12 "" + "c:/texlive/2019/texmf-dist/tex/latex/adjustbox/adjustbox.sty" 1572020417 55974 e90ddd9a6114a7008a6915da904f2847 "" + "c:/texlive/2019/texmf-dist/tex/latex/adjustbox/tc-pdftex.def" 1572020417 4061 aa67e478bd1a58a42e026c354f10b158 "" + "c:/texlive/2019/texmf-dist/tex/latex/adjustbox/trimclip.sty" 1572020417 7142 42aaa49a4afcdc52e9d95e3b19f439be "" + "c:/texlive/2019/texmf-dist/tex/latex/algorithmicx/algorithmicx.sty" 1572020477 26750 ce139c05a983e19ddca355b43e29c395 "" + "c:/texlive/2019/texmf-dist/tex/latex/algorithmicx/algpseudocode.sty" 1572020477 3457 d9077efe6b74c5a094199256af8d7d9a "" + "c:/texlive/2019/texmf-dist/tex/latex/algorithms/algorithm.sty" 1572020477 3249 15763257e50278eef5db1952ccde229c "" + "c:/texlive/2019/texmf-dist/tex/latex/amscls/amsthm.sty" 1572020496 12604 3dec726c041422879dc3268237f09026 "" + "c:/texlive/2019/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1572020503 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" + "c:/texlive/2019/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1572020503 13829 94730e64147574077f8ecfea9bb69af4 "" + "c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1572020507 2211 ca7ce284ab93c8eecdc6029dc5ccbd73 "" + "c:/texlive/2019/texmf-dist/tex/latex/amsmath/amscd.sty" 1572020507 5309 0c9ef5db85b924cdbb316f080dfd826e "" + "c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty" 1572020507 4161 7f6eb9092061a11f87d08ed13515b48d "" + "c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty" 1572020507 85514 eb45164c0234a1f8e9b74aa2f583bc21 "" + "c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty" 1572020507 4116 32e6abd27229755a83a8b7f18e583890 "" + "c:/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty" 1572020507 2432 8ff93b1137020e8f21930562a874ae66 "" + "c:/texlive/2019/texmf-dist/tex/latex/appendix/appendix.sty" 1572020533 8526 d0d9b5e2dd0c996c69c3bd05eb25b943 "" + "c:/texlive/2019/texmf-dist/tex/latex/base/bk10.clo" 1572022871 8245 8a337a6bb3da7b88a37a4c3136e6834d "" + "c:/texlive/2019/texmf-dist/tex/latex/base/book.cls" 1572022871 23055 a0c51513e424517b35c8e02a06953cfc "" + "c:/texlive/2019/texmf-dist/tex/latex/base/fontenc.sty" 1572022871 4571 68999fcec19eaab44a6e13159b4dca8a "" + "c:/texlive/2019/texmf-dist/tex/latex/base/ifthen.sty" 1572022871 5159 069c1682fef6225a1e2967ca0fe174f6 "" + "c:/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty" 1572022871 5050 aae684508bdbe288a555910330f17c1b "" + "c:/texlive/2019/texmf-dist/tex/latex/base/makeidx.sty" 1572022872 1940 56d7e65bf2f613c7fbe5d4befdc5fdf6 "" + "c:/texlive/2019/texmf-dist/tex/latex/base/t1enc.def" 1572022872 10687 a7567925dae1870ed1d4a2e413995d60 "" + "c:/texlive/2019/texmf-dist/tex/latex/base/textcomp.sty" 1572022872 16154 aa2e2ccb4112a609f28cbe297c11ef1d "" + "c:/texlive/2019/texmf-dist/tex/latex/base/ts1cmr.fd" 1572022872 2431 cc3b740992f1bf33ee159b31f0710d60 "" + "c:/texlive/2019/texmf-dist/tex/latex/base/ts1enc.def" 1572022872 7767 e781dcaece5057ee9243d19755558b5a "" + "c:/texlive/2019/texmf-dist/tex/latex/base/ts1enc.dfu" 1572022872 5059 63136e20674995b16bae7eab2e006347 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/bbx/numeric.bbx" 1572020808 1687 3a9153990dd5fa0af9f2af7749897393 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/bbx/standard.bbx" 1572020808 25703 d3ef9d5e51205b85b7c5803f5bc4945e "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.cfg" 1572020808 69 249fa6df04d948e51b6d5c67bea30c42 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.def" 1572020808 89841 f62b06d56749b219e24521443b5d62fa "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.sty" 1572020808 486351 35bd8b4d043ca2e145d6acbaf9bbccc3 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-bibtex.def" 1572020808 15868 e9bdfbf22934cf3cf970201ecfee5b82 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-compat.def" 1572020808 13136 44dd5518476508a5daf59afd6ef412e0 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-dm.def" 1572020808 31423 d09ac6e211af72fef55df039a2b3c3d6 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/cbx/numeric.cbx" 1572020808 4578 2d37f6a8c72f47aacef79870545a713d "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/english.lbx" 1572020808 38102 0107e531be1e2d63345edc3b268e7658 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/german.lbx" 1572020808 31969 85ee28750f096a5af49dc49511d7abd9 "" + "c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/ngerman.lbx" 1572020808 520 79db3ad588d8a32d9a5aa90a48bd8364 "" + "c:/texlive/2019/texmf-dist/tex/latex/cancel/cancel.sty" 1572021005 7592 dd751af313a16a0308545d5bfd7aaaa2 "" + "c:/texlive/2019/texmf-dist/tex/latex/caption/caption.sty" 1572021019 68688 0117141b30e5c5fec86154f541dec0d0 "" + "c:/texlive/2019/texmf-dist/tex/latex/caption/caption3.sty" 1572021019 68575 41af57b9d23e31041c5fb63021aa6d56 "" + "c:/texlive/2019/texmf-dist/tex/latex/circuitikz/circuitikz.sty" 1572021160 10465 78f9265b3932855b06abf20fe97dd2eb "" + "c:/texlive/2019/texmf-dist/tex/latex/collectbox/collectbox.sty" 1572021283 9116 495d44b5a3e7be0c46c5d1f053f457f0 "" + "c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.cfg" 1572021502 7068 06f8d141725d114847527a66439066b6 "" + "c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.def" 1572021502 19820 93221daf51aa801243ec22c065084f9c "" + "c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.sty" 1572021502 61418 900e3c73f3da1f59a4c66f0bbd6341e3 "" + "c:/texlive/2019/texmf-dist/tex/latex/currfile/currfile.sty" 1572021526 10656 96a2572aabaf4a47b8885127d7edcae1 "" + "c:/texlive/2019/texmf-dist/tex/latex/doublestroke/dsfont.sty" 1572021671 230 7bc61880b468bfd38aedc173be7c3486 "" + "c:/texlive/2019/texmf-dist/tex/latex/eepic/epic.sty" 1572021869 25873 0e813d2f6e266780f0cedef5eb5e2525 "" + "c:/texlive/2019/texmf-dist/tex/latex/environ/environ.sty" 1572021976 4378 f429f0da968c278653359293040a8f52 "" + "c:/texlive/2019/texmf-dist/tex/latex/etex-pkg/etex.sty" 1572022025 19013 c49da619eb7bd8093706fabc7ba9ceae "" + "c:/texlive/2019/texmf-dist/tex/latex/etoolbox/etoolbox.sty" 1572022032 45259 743c52a37a6e5ed83cfe0e128b2da10d "" + "c:/texlive/2019/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty" 1572022075 11128 a53805799bebfed6358fc1658a18e41f "" + "c:/texlive/2019/texmf-dist/tex/latex/filecontents/filecontents.sty" 1572022144 3408 71173360dc73c4a3f80bb0bc7b926ba0 "" + "c:/texlive/2019/texmf-dist/tex/latex/filehook/filehook.sty" 1572022147 13431 ea0e11ceec9d42295f42c12486dac890 "" + "c:/texlive/2019/texmf-dist/tex/latex/filemod/filemod-expmin.sty" 1572022149 2845 2b7393c472a738889b77cb266b9ef35d "" + "c:/texlive/2019/texmf-dist/tex/latex/float/float.sty" 1572022198 6749 16d2656a1984957e674b149555f1ea1d "" + "c:/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty" 1572022319 41645 0653033a985e06c69a2a9cea9a95e31a "" + "c:/texlive/2019/texmf-dist/tex/latex/gincltex/gincltex.sty" 1572022351 3594 7c105130ddd1211e8275b3c1288d84c8 "" + "c:/texlive/2019/texmf-dist/tex/latex/graphics-cfg/color.cfg" 1572022412 1213 620bba36b25224fa9b7e1ccb4ecb76fd "" + "c:/texlive/2019/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1572022412 1224 978390e9c2234eab29404bc21b268d1e "" + "c:/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def" 1572022413 17334 520b9b85ad8a2a48eda3f643e27a5179 "" + "c:/texlive/2019/texmf-dist/tex/latex/graphics/graphics.sty" 1572022410 16458 1bb0e1418e20f598314cbad8ab796f2f "" + "c:/texlive/2019/texmf-dist/tex/latex/graphics/graphicx.sty" 1572022410 9057 e434b0c2dbde71054f2dde205cf3bde4 "" + "c:/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty" 1572022410 2590 3aa06f747eb7e19c8d68947f1828fd06 "" + "c:/texlive/2019/texmf-dist/tex/latex/graphics/trig.sty" 1572022410 3976 f6c84526d8a14dceb492f9a764e82175 "" + "c:/texlive/2019/texmf-dist/tex/latex/hyperref/hpdftex.def" 1572022529 50230 309aa2909ff6290dbda5045c1337012c "" + "c:/texlive/2019/texmf-dist/tex/latex/hyperref/hyperref.sty" 1572022529 237978 e4178d76d356458ee5b5bd9824c0b5ad "" + "c:/texlive/2019/texmf-dist/tex/latex/hyperref/nameref.sty" 1572022529 13244 a88fa0a3a6ad5b15d16d610d96a714c3 "" + "c:/texlive/2019/texmf-dist/tex/latex/hyperref/pd1enc.def" 1572022529 14125 9a4c1cce42012c8e8ca01d29ccf79db0 "" + "c:/texlive/2019/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty" 1572022586 2148 0426cd8bb94163c1e23726d0c15e2c21 "" + "c:/texlive/2019/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def" 1572022844 25404 0825d673bb6474ecfa27715c709e4f08 "" + "c:/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3-code.tex" 1572022849 1018114 e3dfe1c1b943733676e2f9a37498ae07 "" + "c:/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3.sty" 1572022849 4381 0d422a3245e7ef6ef6d2a5419023d536 "" + "c:/texlive/2019/texmf-dist/tex/latex/l3kernel/l3deprecation.def" 1572022849 9892 1ec016acc4d32bf498c20738383470b5 "" + "c:/texlive/2019/texmf-dist/tex/latex/l3packages/l3keys2e/l3keys2e.sty" 1572022854 4520 1161269abe88ec94dddd509a3b3582fd "" + "c:/texlive/2019/texmf-dist/tex/latex/l3packages/xparse/xparse.sty" 1572022854 81717 03294ce0fabc3e7b7749bf6850c22be8 "" + "c:/texlive/2019/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1572022953 678 4792914a8f45be57bb98413425e4c7af "" + "c:/texlive/2019/texmf-dist/tex/latex/latexconfig/hyperref.cfg" 1572022953 235 6031e5765137be07eed51a510b2b8fb7 "" + "c:/texlive/2019/texmf-dist/tex/latex/listings/listings.cfg" 1572023106 1830 bbaba8afaf42cc048ec4d4ff73467521 "" + "c:/texlive/2019/texmf-dist/tex/latex/listings/listings.sty" 1572023106 80511 830f3f1d3ab7448dd84233e9c2f6462c "" + "c:/texlive/2019/texmf-dist/tex/latex/listings/lstmisc.sty" 1572023106 77022 32914f01b528131c47be2a1040d3856d "" + "c:/texlive/2019/texmf-dist/tex/latex/logreq/logreq.def" 1572023149 1620 fb1c32b818f2058eca187e5c41dfae77 "" + "c:/texlive/2019/texmf-dist/tex/latex/logreq/logreq.sty" 1572023149 6187 b27afc771af565d3a9ff1ca7d16d0d46 "" + "c:/texlive/2019/texmf-dist/tex/latex/mathtools/mathtools.sty" 1572023363 55028 f5cc7f943da0d539d33e527fd34088c8 "" + "c:/texlive/2019/texmf-dist/tex/latex/mathtools/mhsetup.sty" 1572023363 5317 cf75154a8a7e6436f05a5be497f0b05e "" + "c:/texlive/2019/texmf-dist/tex/latex/ms/everyshi.sty" 1572023576 3878 6aa7c08ff2621006e0603349e40a30a8 "" + "c:/texlive/2019/texmf-dist/tex/latex/multirow/multirow.sty" 1572023602 5486 a1d954b09782ba0acd8a8abfd98e1028 "" + "c:/texlive/2019/texmf-dist/tex/latex/oberdiek/atveryend.sty" 1572035815 19205 dcac4af7cbae59b1f2163f96c36a1de6 "" + "c:/texlive/2019/texmf-dist/tex/latex/oberdiek/auxhook.sty" 1572035815 3834 4363110eb0ef1eb2b71c8fcbcdb6c357 "" + "c:/texlive/2019/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty" 1572035815 12095 5337833c991d80788a43d3ce26bd1c46 "" + "c:/texlive/2019/texmf-dist/tex/latex/oberdiek/grfext.sty" 1572035815 7075 2fe3d848bba95f139de11ded085e74aa "" + "c:/texlive/2019/texmf-dist/tex/latex/oberdiek/kvoptions.sty" 1572035815 22417 1d9df1eb66848aa31b18a593099cf45c "" + "c:/texlive/2019/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty" 1572035816 9581 023642318cef9f4677efe364de1e2a27 "" + "c:/texlive/2019/texmf-dist/tex/latex/paralist/paralist.sty" 1572035907 14857 82c76ebe8f06becf69ab309565b2a0cb "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty" 1572035988 1090 d20f587ea9464d1841bd0d13d3ff9856 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty" 1572035988 410 5bf12ea7330e5f12c445332a4fe9a263 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty" 1572035988 21013 e98e1aaaf40d31632787c2bd25d24b57 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty" 1572035988 989 2cf3da8e8ec55131c49389428d565e37 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/frontendlayer/libraries/tikzlibraryexternal.code.tex" 1572035988 4032 5195761335c7fffcd19348b024d9d881 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty" 1572035988 339 592cf35cba3d400082b8a9a5d0199d70 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/math/pgfmath.sty" 1572035988 306 0796eafca5e159e6ec2167a6d22d81b1 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty" 1572035988 443 0b2e781830192df35c0fd357cf13e26e "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgffor.sty" 1572035988 348 8927fde343487e003b01a4c2ca34073b "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty" 1572035988 274 4cad6e665cc93ac2ac979039a94fa1e1 "" + "c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty" 1572035988 325 2bcd023400636339210573e2b3ee298b "" + "c:/texlive/2019/texmf-dist/tex/latex/pgfplots/pgfplots.sty" 1572036011 4904 ee78b44e85d6fccf08cd99370557481e "" + "c:/texlive/2019/texmf-dist/tex/latex/pgfplots/pgfplotstable.sty" 1572036011 1440 4c1495abf57fc4dd215ebbf2a95b1cf8 "" + "c:/texlive/2019/texmf-dist/tex/latex/placeins/placeins.sty" 1572036059 4087 636308456f60d2b31cbf97867db5708d "" + "c:/texlive/2019/texmf-dist/tex/latex/psnfss/times.sty" 1572036179 857 6c716f26c5eadfb81029fcd6ce2d45e6 "" + "c:/texlive/2019/texmf-dist/tex/latex/siunitx/siunitx-abbreviations.cfg" 1572036709 4745 5e578e91b3a2e2e7f888f49fe4d3df59 "" + "c:/texlive/2019/texmf-dist/tex/latex/siunitx/siunitx.sty" 1572036709 277239 5fe87c621fe5497b7e396a7f0945e099 "" + "c:/texlive/2019/texmf-dist/tex/latex/standalone/standalone.sty" 1572036799 34858 3be45da0358383f6555e8118e77e3503 "" + "c:/texlive/2019/texmf-dist/tex/latex/subfigure/subfigure.cfg" 1572036857 2062 a0e7d66e09e508f51289a656aec06ed2 "" + "c:/texlive/2019/texmf-dist/tex/latex/subfigure/subfigure.sty" 1572036857 15188 91281c7ddbccfa54a8e0c3b56ab5aa72 "" + "c:/texlive/2019/texmf-dist/tex/latex/svn-prov/svn-prov.sty" 1572036879 6852 44ea8d7e58290cde708a34ebf3953571 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbbreakable.code.tex" 1572036936 33368 cf5f26c55f852c142397a04d5c9e470d "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbfitting.code.tex" 1572036936 14602 8f73a0800c020938707490a8ff5df4d7 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbhooks.code.tex" 1572036936 8118 d4655df69bb24afb189d64d5bc575323 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbraster.code.tex" 1572036936 8920 15abf43e83bfc135f9bb2dd5c4a05f10 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbskins.code.tex" 1572036936 84989 d55beee9ec85a3d2ed47ec5132151162 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbskinsjigsaw.code.tex" 1572036936 9020 b40daceb0dcd600a86088bcf8f43e923 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbtheorems.code.tex" 1572036936 8512 ef44b802a30469a787fb98a74a98d3b5 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbxparse.code.tex" 1572036936 9618 8f4fa7f9c519c6559d0070a02f8a26b3 "" + "c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcolorbox.sty" 1572036936 84932 34a574abc5eb4d79443911aa40d43d61 "" + "c:/texlive/2019/texmf-dist/tex/latex/tikz-cd/tikz-cd.sty" 1572037151 858 fe1b4d077c61915fa7d05919d4f7282f "" + "c:/texlive/2019/texmf-dist/tex/latex/tools/array.sty" 1572037272 12560 4a5687b6718c08af61b1ad834ba27b87 "" + "c:/texlive/2019/texmf-dist/tex/latex/tools/bm.sty" 1572037272 12671 adbf10c406b6bea2e2563bf450a7ef2c "" + "c:/texlive/2019/texmf-dist/tex/latex/tools/calc.sty" 1572037272 10216 54c740cb9d999378b16df7e5c92c17a0 "" + "c:/texlive/2019/texmf-dist/tex/latex/tools/shellesc.sty" 1572037273 3347 7063a0c865ee389271de2b0ea22b3afe "" + "c:/texlive/2019/texmf-dist/tex/latex/tools/tabularx.sty" 1572037273 7149 0761e0046ae54b8c3b512ab8e07fef1c "" + "c:/texlive/2019/texmf-dist/tex/latex/tools/verbatim.sty" 1572037273 7266 b86aedea6878967562d57e7fa72d2976 "" + "c:/texlive/2019/texmf-dist/tex/latex/translator/translator-basic-dictionary-English.dict" 1572037312 3435 0a4d096dde3f8fe682c2aedd33b8137d "" + "c:/texlive/2019/texmf-dist/tex/latex/translator/translator.sty" 1572037312 8691 e154b4b39c7cd1cfa9301a391c44afdd "" + "c:/texlive/2019/texmf-dist/tex/latex/trimspaces/trimspaces.sty" 1572037317 1380 971a51b00a14503ddf754cab24c3f209 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/omltxmi.fd" 1572037355 492 e7f8afe4428797548d4301de03a1b15f "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/omstxsy.fd" 1572037355 329 6ac7e19535b9f1d64e4d8e3f77dc30a3 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/omxtxex.fd" 1572037355 312 11fe1916b0a13a81a05234a6fc7f8738 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txr.fd" 1572037355 1271 4e3afbd8e832f2f9c7f064894e6e68e4 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txss.fd" 1572037355 1375 b9d8628471eb35e3cf16d9665f977016 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txtt.fd" 1572037355 1318 4f519eea77a36de881f47283e1201390 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/t1txr.fd" 1572037355 1242 cbf8a0d4f750f9833a0bfb05fb39f1cb "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/t1txtt.fd" 1572037355 1324 7b6c95370a64cd8c7620cbefefb53dba "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/ts1txr.fd" 1572037355 1278 7b91d84c3d8b7d0dd9e34d557ca00ff0 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/txfonts.sty" 1572037355 50381 d367461010070c7a491b1f6979ab2062 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxexa.fd" 1572037355 310 1b00b0b05685b816e4c6caccce437e0d "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxmia.fd" 1572037355 334 87436a82076ca2e35cd305f852507afc "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsya.fd" 1572037355 310 cee07e4964749ccbc77d84fc49726a79 "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsyb.fd" 1572037355 310 8c5467c8932c259af51b0f116c9734bd "" + "c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsyc.fd" 1572037355 310 4b5d6fe830337242ef847b3bff48ba21 "" + "c:/texlive/2019/texmf-dist/tex/latex/url/url.sty" 1572037547 12796 8edb7d69a20b857904dd0ea757c14ec9 "" + "c:/texlive/2019/texmf-dist/tex/latex/varwidth/varwidth.sty" 1572037576 10894 d359a13923460b2a73d4312d613554c8 "" + "c:/texlive/2019/texmf-dist/tex/latex/was/gensymb.sty" 1572037672 4612 29d19942d7123701aa6a3876b9ba11b1 "" + "c:/texlive/2019/texmf-dist/tex/latex/wasysym/uwasy.fd" 1572037676 2127 de456b4fb7b20e6651c727c9fdc94803 "" + "c:/texlive/2019/texmf-dist/tex/latex/wasysym/wasysym.sty" 1572037676 10611 eca9e56dd071530be0c56f0b968bbdb6 "" + "c:/texlive/2019/texmf-dist/tex/latex/xcolor/xcolor.sty" 1572037739 55589 34128738f682d033422ca125f82e5d62 "" + "c:/texlive/2019/texmf-dist/tex/latex/xkeyval/xkeyval.sty" 1572037818 4962 9c1069474ff71dbc47d5006555e352d3 "" + "c:/texlive/2019/texmf-dist/web2c/texmf.cnf" 1572022811 39452 758acee3f2beaeeedff570c5f5d76d98 "" + "c:/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1572038008 4743761 46ebadd265dfe07977acec471a78b166 "" + "c:/texlive/2019/texmf-var/web2c/pdftex/pdflatex.fmt" 1572038228 4289527 1002f58e38ec16c649e0243e3ceb98aa "" + "c:/texlive/2019/texmf.cnf" 1572037975 673 4ae7b2f49cee444c5343a45b5d0f169c "" + "chapters/00-einleitung/chapter.tex" 1617288090 8444 f770a9f593a113ceed222ac43ec5cf4e "" + "chapters/05-zahlen/chapter.tex" 1617288090 1284 11415bc971a305038c01d3020037ff1f "" + "chapters/05-zahlen/ganz.tex" 1617288090 4365 3979cd642db7db23efa16dfbff0b6034 "" + "chapters/05-zahlen/images/komplex.pdf" 1617288090 18852 2b3701b4352852f11018e98f5f98f75a "" + "chapters/05-zahlen/komplex.tex" 1617288090 12608 bbf4fd4ff4234cae28539478b26516c2 "" + "chapters/05-zahlen/natuerlich.tex" 1617288090 8961 27e3ab1c5fd2932062361a1225af3b21 "" + "chapters/05-zahlen/rational.tex" 1617288090 5177 2f78313f8c61f5d4b8ad9ee4d58e2ed4 "" + "chapters/05-zahlen/reell.tex" 1617288090 3165 57276583fc9f0a3775513fa8fcc2266a "" + "chapters/10-vektorenmatrizen/algebren.tex" 1617288090 3710 58918311c4270b6477237c958d9d0368 "" + "chapters/10-vektorenmatrizen/chapter.tex" 1617288090 665 1683f15861d6831e5ab082160d7f63eb "" + "chapters/10-vektorenmatrizen/gruppen.tex" 1624097835 10392 9e6a090448329022491cb8888fc57483 "" + "chapters/10-vektorenmatrizen/hadamard.tex" 1617288090 7982 03b4bce1f1a4f6ab69471248e8e77d85 "" + "chapters/10-vektorenmatrizen/images/gausszahlen.pdf" 1617288091 19127 42de8a9bfe1f0ac6ae654591cf06a884 "" + "chapters/10-vektorenmatrizen/images/ideale.pdf" 1617288091 73185 12e5dff7a1f2bb8451c5848f612fba46 "" + "chapters/10-vektorenmatrizen/images/rref.pdf" 1617288091 15112 1438dc421f36390ab54f539f7d16e0f7 "" + "chapters/10-vektorenmatrizen/images/strukturen.pdf" 1617288091 45339 4d122d63733ceb13cd2899d58f5aac54 "" + "chapters/10-vektorenmatrizen/koerper.tex" 1617288091 459 28a334abca5e215fda3beaeded98d381 "" + "chapters/10-vektorenmatrizen/linear.tex" 1624966622 41347 3184e116caa4b57b6fe251d6297052be "" + "chapters/10-vektorenmatrizen/ringe.tex" 1617288091 11200 d47bdbddfbe531964be600f0c16a1eb1 "" + "chapters/10-vektorenmatrizen/skalarprodukt.tex" 1617288091 22915 7eb5459ce86dbf02f7cca5512cfb146d "" + "chapters/10-vektorenmatrizen/strukturen.tex" 1617288091 1459 1c97a44c84ac56d8bfdc6a3faabf7c58 "" + "chapters/10-vektorenmatrizen/uebungsaufgaben//1001.tex" 1617288091 3378 3204d8b5d1d01f9a95e2b4779e6671ea "" + "chapters/10-vektorenmatrizen/uebungsaufgaben//1002.tex" 1617288091 1822 c4b7c4c73a27ebd75737b4e01b92ab55 "" + "chapters/20-polynome/chapter.tex" 1617288091 4805 d11f446202abde195985668de79be333 "" + "chapters/20-polynome/definitionen.tex" 1617288091 20105 f4f65922ce864cbdfcffe3aead5ec9dd "" + "chapters/20-polynome/matrizen.tex" 1617288092 239 4572c1ccf7a7dfc805c70535c37c7eeb "" + "chapters/20-polynome/minimalpolynom.tex" 1617288092 188 55c767e6bd65c5814c8223e42046683d "" + "chapters/20-polynome/vektoren.tex" 1617288092 3714 b8df5257256295a72743b27a52c08fc3 "" + "chapters/30-endlichekoerper/chapter.tex" 1617288092 1962 517078637eb632bbae37a73a45089ae1 "" + "chapters/30-endlichekoerper/euklid.tex" 1621604297 29296 f99dd0b5a9d8ca38a5e13fedfdfab7dd "" + "chapters/30-endlichekoerper/galois.tex" 1624966622 20609 54ce2428fe83515f4cacae87bc5fa6d1 "" + "chapters/30-endlichekoerper/images/binomial2.pdf" 1619271503 19417 50b461013a7ac6ccd7297ac97e1aaee5 "" + "chapters/30-endlichekoerper/images/binomial5.pdf" 1619271503 27894 0f0dd956bbc53f0f8e4063c6bef99708 "" + "chapters/30-endlichekoerper/images/farben.tex" 1617288092 134 940b24ec68979815005073dcc4cff37d "" + "chapters/30-endlichekoerper/uebungsaufgaben//3001.tex" 1617288092 1688 db47284348820f55a262edfdef23fd5e "" + "chapters/30-endlichekoerper/uebungsaufgaben//3002.tex" 1617288093 337 9152e8c2293eb8bcc87c4481949e8d00 "" + "chapters/30-endlichekoerper/uebungsaufgaben//3003.tex" 1617288093 2175 64a3ca2464ec5cac8cab891e26f1fc21 "" + "chapters/30-endlichekoerper/uebungsaufgaben//3004.tex" 1617288093 5745 be722ac378b368c5acda3a8398eaf5c8 "" + "chapters/30-endlichekoerper/uebungsaufgaben//3005.tex" 1617288093 4954 90bdfe38b57ed2d2ac1ef9dfc5774eb9 "" + "chapters/30-endlichekoerper/wurzeln.tex" 1621604298 27602 933ec64e167a05d6b7f361175ce6ce3b "" + "chapters/40-eigenwerte/chapter.tex" 1624097835 2059 e0c70d85713b24ea512dc2e4fa742c87 "" + "chapters/40-eigenwerte/grundlagen.tex" 1617288093 36785 f0e06f0d4bb8ce75ea744a58fe441988 "" + "chapters/40-eigenwerte/images/dimjk.pdf" 1617288093 23762 eb4bfc6190ead79640e141342a3cd665 "" + "chapters/40-eigenwerte/images/jknilp.pdf" 1617288094 23241 7c0d0ce4e46dff22b512a9a11962b6bd "" + "chapters/40-eigenwerte/images/kernbild.pdf" 1617288094 189482 4b4467fe28b22848393cc70af74cdcac "" + "chapters/40-eigenwerte/images/kombiniert.pdf" 1617288094 131131 a494a73ee5bfaec29aebd1a56f2f9676 "" + "chapters/40-eigenwerte/images/minmax.pdf" 1619271503 53375 7b0eeeca80557c6392d6a700f609ab7f "" + "chapters/40-eigenwerte/images/nilpotent.pdf" 1617288094 14254 2ce05c168ddbce1ca8af970424569573 "" + "chapters/40-eigenwerte/images/normalform.pdf" 1617288094 18132 5c8be1369fb99763eadf56ceb839ca37 "" + "chapters/40-eigenwerte/images/wurzel.pdf" 1617288095 19221 7c72a78f2e56cdaa3b8be9aa6fdad5e5 "" + "chapters/40-eigenwerte/images/wurzelapprox.pdf" 1619271503 33171 b3375e0345d3a4e759d3d22e65913bf2 "" + "chapters/40-eigenwerte/normalformen.tex" 1624097835 18288 b12beab0e2712913d2de2ab2f54ee3b6 "" + "chapters/40-eigenwerte/spektralradius.tex" 1617288095 22120 852e9ab37b28c4ec4afa96c2b295fbc0 "" + "chapters/40-eigenwerte/spektraltheorie.tex" 1624097835 30458 bd56a08a724b8ebceddb2126d1f81a89 "" + "chapters/40-eigenwerte/uebungsaufgaben//4001.tex" 1617288095 1379 2b546179f3b3252ae89437d8f8616c2e "" + "chapters/40-eigenwerte/uebungsaufgaben//4002.tex" 1617288095 598 f53350a2fb362a77c4d4559f50294f55 "" + "chapters/40-eigenwerte/uebungsaufgaben//4003.tex" 1617288095 4735 6c2f272c3fcda6a7d7ce6c33bc8c3cff "" + "chapters/40-eigenwerte/uebungsaufgaben//4004.tex" 1617288095 1532 067b701faa189dc417f47db3e28d7a41 "" + "chapters/40-eigenwerte/uebungsaufgaben//4005.tex" 1617288095 2937 d18a4bc3c86b2d127b64a798fd4466c2 "" + "chapters/40-eigenwerte/uebungsaufgaben//4006.tex" 1624097835 1760 b5c809228d5e2f61e011eaed9564b9fa "" + "chapters/50-permutationen/chapter.tex" 1617288095 1055 30380f54c19daad6678c528b030e76d4 "" + "chapters/50-permutationen/determinante.tex" 1617288095 246 eb0e2414b38e572e53db3de363ca0a49 "" + "chapters/50-permutationen/endlich.tex" 1617288095 6368 bf9d3d7d10f9c9bd97e3aff4d3473b1e "" + "chapters/50-permutationen/images/komposition.pdf" 1617288096 13951 17e45a3e2ab30caf216931c7bab5df30 "" + "chapters/50-permutationen/images/permutation.pdf" 1617288096 13814 d9656afa12d603cc538319e3995ba420 "" + "chapters/50-permutationen/images/transpositionen.pdf" 1617288096 22548 b2aabfcb9eb7f09731572cc5aa42aef5 "" + "chapters/50-permutationen/images/zyklenzerlegung.pdf" 1617288096 14937 0b400a0cc00141e669d66d4760bf5c70 "" + "chapters/50-permutationen/matrizen.tex" 1617288096 4589 a3ecf1515579db509a7e2b882bd0af24 "" + "chapters/50-permutationen/transpositionen.tex" 1624097835 4633 6511d3b6e27ab127cb88b8107f8806bd "" + "chapters/50-permutationen/uebungsaufgaben//5001.tex" 1617288096 3139 0c5f655115cfa87eedfc124bdd27b2c7 "" + "chapters/60-gruppen/chapter.tex" 1624097835 1914 dbf23e732520fcf75fb090af6bf143da "" + "chapters/60-gruppen/images/castle.jpeg" 1617288096 148054 e47e2dc81c480dbb2d01ee4d0722cc14 "" + "chapters/60-gruppen/images/karten.pdf" 1619271503 487946 3dad8ebf83e5428683ed5d3fe67d7b46 "" + "chapters/60-gruppen/images/kartenkreis.pdf" 1619271503 26755 f1fea1330f3552a5410c82b659e977c1 "" + "chapters/60-gruppen/images/phasenraum.pdf" 1619271503 72789 3c2ea5d0b86314ed140b739cb6ecd889 "" + "chapters/60-gruppen/images/scherungen.pdf" 1619271503 24544 39f73790b326fa6d9ea97103cafadfba "" + "chapters/60-gruppen/images/sl2.pdf" 1619271503 27116 723e7416b02d748e4f8f59d7cf2c6db9 "" + "chapters/60-gruppen/lie-gruppen.tex" 1624097835 25431 eeeb669f1621f427799a54aca130ef02 "" + "chapters/60-gruppen/symmetrien.tex" 1624097835 26460 1c62a55815845c195ea3796dd1b76461 "" + "chapters/part1.tex" 1617288100 874 5dd0465d3dd8b46afc3a4b9e2ec46579 "" + "chapters/vorwort.tex" 1617288100 1207 63950796d341049918f1e505b5603ffe "" + "common/lststyles.tex" 1626109319 4112 9e411049231302314eecdb24ab27b07a "" + "common/macros.tex" 1617288101 2950 006cdaa0b42c9b3fc81458d9e1f28fbc "" + "common/packages.tex" 1617288101 2086 f5a6a26e1bc1eac0456d7c6fc90a82ce "" + "common/teilnehmer.tex" 1617288101 795 512a21d2f0fc45fcb15547d79b527ba7 "" + "common/titlepage.tex" 1617288101 555 14512c8d698cbe55b220f3a956c2e9bf "" + "nul" 0 0 d41d8cd98f00b204e9800998ecf8427e "" + "papers/clifford/packages.tex" 1626345216 292 2b357b2b1784de1a2c04bc539fc37dcc "" + "papers/common/addbibresources.tex" 1617288101 558 d55643069b0d27a40573bcd4a0192557 "" + "papers/common/addpackages.tex" 1624980588 498 bea0ec50550c94420c64f507f326b631 "" + "papers/erdbeben/packages.tex" 1617288102 241 952ad7202bd42a8650920280e5575d34 "" + "papers/ifs/packages.tex" 1617288102 236 c9eafc894fd39ad1a6eb6af798907cd3 "" + "papers/mceliece/packages.tex" 1617288102 241 390a370595b554982994eeed032349d7 "" + "papers/multiplikation/packages.tex" 1617288103 247 647fcd190bbe1c6bb6cb97ca9b1bf5e0 "" + "papers/munkres/packages.tex" 1617288103 240 63c4b80a737a5717be4264d871898277 "" + "papers/punktgruppen/packages.tex" 1624097835 154 d2ff2f93837094752b9e01b860a5a52d "" + "papers/reedsolomon/packages.tex" 1626876699 304 a4540dcb2d44e1102579ed1b71496a54 "" + "papers/spannung/packages.tex" 1617288104 241 c47878756bc3ea073ec5c928a1ff40e9 "" + "papers/verkehr/packages.tex" 1617288104 240 ced2fad36cbca5cb3f2ae419ede381ce "" + (generated) + "buch.aux" + "buch.out" + "buch-blx.bib" + "buch.log" + "c:/JB/LaTex/SeminarMatrizen/buch/buch.log" + "buch.toc" + "buch.idx" + "buch1-blx.aux" + "c:/JB/LaTex/SeminarMatrizen/buch/buch.pdf" diff --git a/buch/buch.fls b/buch/buch.fls new file mode 100644 index 0000000..a1e07a1 --- /dev/null +++ b/buch/buch.fls @@ -0,0 +1,1033 @@ +PWD c:/JB/LaTex/SeminarMatrizen/buch +INPUT c:/texlive/2019/texmf.cnf +INPUT c:/texlive/2019/texmf-dist/web2c/texmf.cnf +INPUT c:/texlive/2019/texmf-var/web2c/pdftex/pdflatex.fmt +INPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.tex +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.log +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/book.cls +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/book.cls +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/bk10.clo +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/bk10.clo +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/packages.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/etex-pkg/etex.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/etex-pkg/etex.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel/babel.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel/babel.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel/switch.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel-english/english.ldf +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel-english/english.ldf +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel/babel.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel/txtbabel.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel-german/ngerman.ldf +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel-german/ngerman.ldf +INPUT c:/texlive/2019/texmf-dist/tex/generic/babel-german/ngermanb.ldf +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/fontenc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/fontenc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/t1enc.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/t1enc.def +INPUT c:/texlive/2019/texmf-dist/fonts/map/fontname/texfonts.map +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/jknappen/ec/ecrm1000.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/cancel/cancel.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/cancel/cancel.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/psnfss/times.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/psnfss/times.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amscd.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsmath/amscd.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/graphicx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/graphicx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/graphics.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/graphics.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/trig.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics/trig.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/textcomp.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/textcomp.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ts1enc.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ts1enc.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ts1enc.dfu +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ts1enc.dfu +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/txfonts.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/txfonts.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/bm.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/bm.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/eepic/epic.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/eepic/epic.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/verbatim.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/verbatim.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/paralist/paralist.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/paralist/paralist.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/makeidx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/makeidx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/array.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/array.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/multirow/multirow.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/multirow/multirow.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/hyperref.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/hyperref.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/auxhook.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/auxhook.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/kvoptions.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/kvoptions.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/pd1enc.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/pd1enc.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/latexconfig/hyperref.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/latexconfig/hyperref.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/url/url.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/url/url.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/hpdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/hpdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/subfigure/subfigure.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/subfigure/subfigure.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/subfigure/subfigure.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/subfigure/subfigure.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/ms/everyshi.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/ms/everyshi.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/pgf.revision.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/pgf.revision.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/xcolor/xcolor.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/xcolor/xcolor.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics-cfg/color.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/graphics-cfg/color.cfg +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfint.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgffor.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgffor.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/math/pgfmath.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/math/pgfmath.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tikz-cd/tikz-cd.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tikz-cd/tikz-cd.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/tikz-cd/tikzlibrarycd.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/tikz-cd/tikzlibrarycd.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryquotes.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryquotes.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgfplots/pgfplots.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgfplots/pgfplots.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.revision.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.revision.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-luatex.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotscore.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/sys/pgfplotssysgeneric.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/libs/pgfplotslibrary.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_loader.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsutil.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsliststructure.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsliststructureext.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsarray.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsmatrix.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstableshared.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/liststructure/pgfplotsdeque.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsbinary.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsbinary.data.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotsutil.verb.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/libs/pgflibrarypgfplots.surfshading.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/sys/pgflibrarypgfplots.surfshading.pgfsys-pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/sys/pgflibrarypgfplots.surfshading.pgfsys-pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotscolormap.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/util/pgfplotscolor.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsstackedplots.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsplothandlers.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsmeshplothandler.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsmeshplotimage.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.scaling.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotscoordprocessing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.errorbars.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.markers.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplotsticks.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.paths.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduledecorations.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathmorphing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathmorphing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathreplacing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathreplacing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathreplacing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathreplacing.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplotmarks.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplotmarks.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryplotmarks.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryplotmarks.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgfplots/pgfplotstable.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgfplots/pgfplotstable.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.revision.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/pgfplots.revision.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgfplots/numtable/pgfplotstable.coltype.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/etoolbox/etoolbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/etoolbox/etoolbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/csquotes/csquotes.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/wasysym/wasysym.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/wasysym/wasysym.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/environ/environ.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/environ/environ.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/trimspaces/trimspaces.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/trimspaces/trimspaces.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/appendix/appendix.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/appendix/appendix.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/placeins/placeins.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/placeins/placeins.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xy.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xy.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xy.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyrecat.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyidioms.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xydash10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xyatip10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xybtip10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xybsql10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xycirc10.tfm +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyall.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyall.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xycurve.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xycurve.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyframe.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyframe.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xycmtip.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xycmtip.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xytips.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xytips.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xycmat10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xycmbt10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xyluat10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/xypic/xylubt10.tfm +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyline.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyline.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyrotate.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyrotate.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xycolor.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xycolor.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xymatrix.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xymatrix.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyarrow.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xyarrow.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xygraph.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xygraph.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-co.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-cu.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-fr.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-li.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xypic/xypdf-ro.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryintersections.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryintersections.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarythrough.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarythrough.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.geometric.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.geometric.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.misc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.misc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.misc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.misc.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.symbols.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.symbols.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.symbols.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.symbols.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.arrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.arrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.arrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.arrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.callouts.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.callouts.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.callouts.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.callouts.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymath.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfpu.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfpu.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibrarypatterns.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibrarypatterns.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/frontendlayer/libraries/tikzlibraryexternal.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/pgf/frontendlayer/libraries/tikzlibraryexternal.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/atveryend.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzexternalshared.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduledatavisualization.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmoduleoo.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/circuitikz/circuitikz.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/circuitikz/circuitikz.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybending.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybending.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmodulebending.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmodulenonlineartransformations.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibrarycurvilinear.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibrarycurvilinear.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirc.defines.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircutils.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircshapes.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircmonopoles.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircbipoles.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirctripoles.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircquadpoles.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircmultipoles.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirclabel.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircvoltage.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcirccurrent.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircflow.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/circuitikz/pgfcircpath.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xstring/xstring.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/xstring/xstring.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/xstring/xstring.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/siunitx/siunitx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/siunitx/siunitx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3-code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3-code.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/nul +INPUT c:/JB/LaTex/SeminarMatrizen/buch/nul +INPUT c:/JB/LaTex/SeminarMatrizen/buch/nul +INPUT c:/JB/LaTex/SeminarMatrizen/buch/nul +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr10.tfm +INPUT c:/texlive/2019/texmf-dist/tex/generic/unicode-data/UnicodeData.txt +INPUT c:/texlive/2019/texmf-dist/tex/generic/unicode-data/UnicodeData.txt +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3kernel/l3deprecation.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3kernel/l3deprecation.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3packages/xparse/xparse.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3packages/xparse/xparse.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3packages/l3keys2e/l3keys2e.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/l3packages/l3keys2e/l3keys2e.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/translator/translator.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/translator/translator.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/translator/translator.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/tabularx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/tabularx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/algorithmicx/algpseudocode.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/algorithmicx/algpseudocode.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ifthen.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ifthen.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/algorithmicx/algorithmicx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/algorithmicx/algorithmicx.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/algorithms/algorithm.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/algorithms/algorithm.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/float/float.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/float/float.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/was/gensymb.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/was/gensymb.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/mathtools/mathtools.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/mathtools/mathtools.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/calc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/calc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/mathtools/mhsetup.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/mathtools/mhsetup.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcolorbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcolorbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbraster.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbskins.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbskinsjigsaw.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbbreakable.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbhooks.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbtheorems.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbfitting.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/tcolorbox/tcbxparse.code.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/lststyles.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/lststyles.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/listings/listings.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/listings/listings.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/listings/lstmisc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/listings/lstmisc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/listings/listings.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/listings/listings.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/caption/caption.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/caption/caption.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/caption/caption3.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/caption/caption3.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/standalone/standalone.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/standalone/standalone.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/shellesc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/shellesc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/tools/shellesc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/xkeyval/xkeyval.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/xkeyval/xkeyval.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/xkeyval/xkeyval.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/xkeyval/xkvutils.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/currfile/currfile.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/currfile/currfile.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/filehook/filehook.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/filehook/filehook.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/gincltex/gincltex.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/gincltex/gincltex.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/gincltex/gincltex.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/svn-prov/svn-prov.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/svn-prov/svn-prov.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/adjustbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/adjustbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/adjcalc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/adjcalc.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/trimclip.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/trimclip.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/collectbox/collectbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/collectbox/collectbox.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/tc-pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/adjustbox/tc-pdftex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/varwidth/varwidth.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/varwidth/varwidth.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/varwidth/varwidth.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/filemod/filemod-expmin.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/filemod/filemod-expmin.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/logreq/logreq.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/logreq/logreq.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/logreq/logreq.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/logreq/logreq.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-dm.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-dm.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-compat.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-compat.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-bibtex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/blx-bibtex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.def +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/bbx/numeric.bbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/bbx/numeric.bbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/bbx/standard.bbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/bbx/standard.bbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/cbx/numeric.cbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/cbx/numeric.cbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/biblatex.cfg +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/common/addpackages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/common/addpackages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/verkehr/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/verkehr/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/multiplikation/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/multiplikation/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/punktgruppen/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/punktgruppen/packages.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/doublestroke/dsfont.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/doublestroke/dsfont.sty +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/reedsolomon/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/reedsolomon/packages.tex +INPUT c:/texlive/2019/texmf-dist/tex/latex/filecontents/filecontents.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/filecontents/filecontents.sty +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/ifs/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/ifs/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/mceliece/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/mceliece/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/clifford/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/clifford/packages.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryangles.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryangles.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybabel.code.tex +INPUT c:/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybabel.code.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/spannung/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/spannung/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/erdbeben/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/erdbeben/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/munkres/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/munkres/packages.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/common/addbibresources.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/papers/common/addbibresources.tex +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.idx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/ngerman.lbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/ngerman.lbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/german.lbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/german.lbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/german.lbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/german.lbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/english.lbx +INPUT c:/texlive/2019/texmf-dist/tex/latex/biblatex/lbx/english.lbx +INPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.aux +INPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.aux +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.aux +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/omltxmi.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/omltxmi.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/omstxsy.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/omstxsy.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/omxtxex.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/omxtxex.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxexa.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxexa.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ts1cmr.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/base/ts1cmr.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/t1txr.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/t1txr.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii +INPUT c:/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/grfext.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/oberdiek/grfext.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/nameref.sty +INPUT c:/texlive/2019/texmf-dist/tex/latex/hyperref/nameref.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/gettitlestring.sty +INPUT c:/texlive/2019/texmf-dist/tex/generic/oberdiek/gettitlestring.sty +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.out +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.pdf +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txr.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txr.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsya.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsya.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsyb.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsyb.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxmia.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxmia.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsyc.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/utxsyc.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/wasysym/uwasy.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/wasysym/uwasy.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy7.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy5.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/translator/translator-basic-dictionary-English.dict +INPUT c:/texlive/2019/texmf-dist/tex/latex/translator/translator-basic-dictionary-English.dict +INPUT c:/texlive/2019/texmf-dist/tex/latex/siunitx/siunitx-abbreviations.cfg +INPUT c:/texlive/2019/texmf-dist/tex/latex/siunitx/siunitx-abbreviations.cfg +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch-blx.bib +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txss.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txss.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txss.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txss.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txss.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txtt.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ot1txtt.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txtt.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txtt.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txtt.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/titlepage.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/titlepage.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/teilnehmer.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/teilnehmer.tex +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/macros.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/common/macros.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch.toc +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xb.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/part1.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/part1.tex +OUTPUT c:/JB/LaTex/SeminarMatrizen/buch/buch1-blx.aux +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/vorwort.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/vorwort.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txss.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txss.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txtt.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txtt.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy8.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy6.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ts1txr.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/ts1txr.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/tcxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/tcxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/tcxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/t1txtt.fd +INPUT c:/texlive/2019/texmf-dist/tex/latex/txfonts/t1txtt.fd +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xtt.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xb.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xb.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/00-einleitung/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/00-einleitung/chapter.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/tcxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/tcxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xi.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/natuerlich.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/natuerlich.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xb.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/ganz.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/ganz.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/rational.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/rational.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/reell.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/reell.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/komplex.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/komplex.tex +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/images/komplex.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/images/komplex.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/05-zahlen/images/komplex.pdf +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xb.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/linear.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/linear.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xb.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xi.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/rref.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/rref.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/rref.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/skalarprodukt.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/skalarprodukt.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/t1xi.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxi.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/strukturen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/strukturen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/strukturen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/gruppen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/gruppen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/ringe.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/ringe.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/gausszahlen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/gausszahlen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/gausszahlen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/ideale.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/ideale.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/images/ideale.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/algebren.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/algebren.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/koerper.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/koerper.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/hadamard.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/hadamard.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/uebungsaufgaben//1001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/uebungsaufgaben//1001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/uebungsaufgaben//1002.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/10-vektorenmatrizen/uebungsaufgaben//1002.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/definitionen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/definitionen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/vektoren.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/vektoren.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/matrizen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/matrizen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/minimalpolynom.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/20-polynome/minimalpolynom.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/euklid.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/euklid.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/t1xtt.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/galois.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/galois.tex +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txss.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txtt.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/wasy/wasy10.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/tcxr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/binomial2.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/binomial2.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/binomial2.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/farben.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/farben.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/binomial5.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/binomial5.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/images/binomial5.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/wurzeln.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/wurzeln.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3004.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3004.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3003.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3003.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3002.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3002.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3005.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/30-endlichekoerper/uebungsaufgaben//3005.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/grundlagen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/grundlagen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/kernbild.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/kernbild.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/kernbild.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/kombiniert.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/kombiniert.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/kombiniert.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/dimjk.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/dimjk.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/dimjk.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/nilpotent.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/nilpotent.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/nilpotent.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/jknilp.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/jknilp.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/jknilp.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/normalform.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/normalform.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/normalform.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/normalformen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/normalformen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/spektralradius.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/spektralradius.tex +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/spektraltheorie.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/spektraltheorie.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/wurzel.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/wurzel.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/wurzel.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/wurzelapprox.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/wurzelapprox.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/wurzelapprox.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/minmax.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/minmax.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/images/minmax.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4002.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4002.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4003.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4003.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4004.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4004.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4005.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4005.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4006.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/40-eigenwerte/uebungsaufgaben//4006.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/endlich.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/endlich.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/permutation.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/permutation.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/permutation.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/komposition.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/komposition.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/komposition.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/zyklenzerlegung.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/zyklenzerlegung.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/zyklenzerlegung.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/transpositionen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/transpositionen.tex +INPUT c:/texlive/2019/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT c:/texlive/2019/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/transpositionen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/transpositionen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/images/transpositionen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/matrizen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/matrizen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/determinante.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/determinante.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/uebungsaufgaben//5001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/50-permutationen/uebungsaufgaben//5001.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/chapter.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/symmetrien.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/symmetrien.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/castle.jpeg +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/castle.jpeg +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/castle.jpeg +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/phasenraum.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/phasenraum.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/phasenraum.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/karten.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/karten.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/karten.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/kartenkreis.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/kartenkreis.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/kartenkreis.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/lie-gruppen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/lie-gruppen.tex +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/sl2.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/sl2.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/sl2.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/scherungen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/scherungen.pdf +INPUT c:/JB/LaTex/SeminarMatrizen/buch/chapters/60-gruppen/images/scherungen.pdf diff --git a/buch/chapters/10-vektorenmatrizen/linear.tex b/buch/chapters/10-vektorenmatrizen/linear.tex index e368364..3ad51f1 100644..100755 --- a/buch/chapters/10-vektorenmatrizen/linear.tex +++ b/buch/chapters/10-vektorenmatrizen/linear.tex @@ -33,7 +33,7 @@ aber mit Punkten kann man trotzdem noch nicht rechnen. Ein Vektor fasst die Koordinaten eines Punktes in einem Objekt zusammen, mit dem man auch rechnen und zum Beispiel Parallelverschiebungen algebraisieren kann. -Um auch Streckungen ausdrücken zu können, wird auch eine Menge von +Um auch Streckungen ausdrücken zu können, wird auch eine Menge von Streckungsfaktoren benötigt, mit denen alle Komponenten eines Vektors multipliziert werden können. Sie heissen auch {\em Skalare} und liegen in $\Bbbk$. @@ -73,7 +73,7 @@ a+b = \begin{pmatrix}\lambda a_1\\\vdots\\\lambda a_n\end{pmatrix}. \] -Die üblichen Rechenregeln sind erfüllt, nämlich +Die üblichen Rechenregeln sind erfüllt, nämlich \begin{equation} \begin{aligned} &\text{Kommutativität:} @@ -149,7 +149,7 @@ kann als (abstrakter) Vektor betrachtet werden. \begin{definition} Eine Menge $V$ von Objekten, auf der zwei Operationen definiert, nämlich die Addition, geschrieben $a+b$ für $a,b\in V$ und die -Multiplikation mit Skalaren, geschrieben $\lambda a$ für $a\in V$ und +Multiplikation mit Skalaren, geschrieben $\lambda a$ für $a\in V$ und $\lambda\in \Bbbk$, heisst ein {\em $\Bbbk$-Vektorraum} oder {\em Vektorraum über $\Bbbk$} (oder einfach nur {\em Vektorraum}, wenn $\Bbbk$ aus dem Kontext klar sind), @@ -172,7 +172,7 @@ $\mathbb{C}$ ein Vektorraum über $\mathbb{R}$. \end{beispiel} \begin{beispiel} -Die Menge $C([a,b])$ der stetigen Funktionen $[a,b]\to\mathbb{Re}$ +Die Menge $C([a,b])$ der stetigen Funktionen $[a,b]\to\mathbb{Re}$ bildet ein Vektorraum. Funktionen können addiert und mit reellen Zahlen multipliziert werden: \[ @@ -188,7 +188,7 @@ Die Vektorraum-Rechenregeln \end{beispiel} Die Beispiele zeigen, dass der Begriff des Vektorraums die algebraischen -Eigenschaften eine grosse Zahl sehr verschiedenartiger mathematischer +Eigenschaften eine grosse Zahl sehr verschiedenartiger mathematischer Objekte beschreiben kann. Alle Erkenntnisse, die man ausschliesslich aus Vekotorraumeigenschaften gewonnen hat, sind auf alle diese Objekte übertragbar. @@ -300,7 +300,7 @@ folgt, dass alle $\lambda_1,\dots,\lambda_n=0$ sind. Lineare Abhängigkeit der Vektoren $a_1,\dots,a_n$ bedeutet auch, dass man einzelne der Vektoren durch andere ausdrücken kann. Hat man nämlich eine -Linearkombination~\eqref{buch:vektoren-und-matrizen:eqn:linabhdef} und +Linearkombination~\eqref{buch:vektoren-und-matrizen:eqn:linabhdef} und ist der Koeffizient $\lambda_k\ne 0$, dann kann man nach $a_k$ auflösen: \[ a_k = -\frac{1}{\lambda_k}(\lambda_1a_1+\dots+\widehat{\lambda_ka_k}+\dots+\lambda_na_n). @@ -323,7 +323,7 @@ offenbar eine besondere Bedeutung. Eine linear unabhängig Menge von Vektoren $\mathcal{B}=\{a_1,\dots,a_n\}\subset V$ heisst {\em Basis} von $V$. -Die maximale Anzahl linear unabhängiger Vektoren in $V$ heisst +Die maximale Anzahl linear unabhängiger Vektoren in $V$ heisst {\em Dimension} von $V$. \end{definition} @@ -331,7 +331,7 @@ Die Standardbasisvektoren bilden eine Basis von $V=\Bbbk^n$. \subsubsection{Unterräume} Die Mengen $\langle a_1,\dots,a_n\rangle$ sind Teilmengen -von $V$, in denen die Addition von Vektoren und die Multiplikation mit +von $V$, in denen die Addition von Vektoren und die Multiplikation mit Skalaren immer noch möglich ist. \begin{definition} @@ -352,7 +352,7 @@ gilt. % \subsection{Matrizen \label{buch:grundlagen:subsection:matrizen}} -Die Koeffizienten eines linearen Gleichungssystems finden in einem +Die Koeffizienten eines linearen Gleichungssystems finden in einem Zeilen- oder Spaltenvektor nicht Platz. Wir erweitern das Konzept daher in einer Art, dass Zeilen- und Spaltenvektoren Spezialfälle sind. @@ -378,14 +378,14 @@ M_{m\times n}(\Bbbk) = \{ A\;|\; \text{$A$ ist eine $m\times n$-Matrix}\}. \] Falls $m=n$ gilt, heisst die Matrix $A$ auch {\em quadratisch} \index{quadratische Matrix}% -Man kürzt die Menge der quadratischen Matrizen als +Man kürzt die Menge der quadratischen Matrizen als $M_n(\Bbbk) = M_{n\times n}(\Bbbk)$ ab. \end{definition} -Die $m$-dimensionalen Spaltenvektoren $v\in \Bbbk^m$ sind $m\times 1$-Matrizen +Die $m$-dimensionalen Spaltenvektoren $v\in \Bbbk^m$ sind $m\times 1$-Matrizen $v\in M_{n\times 1}(\Bbbk)$, die $n$-dimensionalen Zeilenvetoren $u\in\Bbbk^n$ sind $1\times n$-Matrizen $v\in M_{1\times n}(\Bbbk)$. -Eine $m\times n$-Matrix $A$ mit den Koeffizienten $a_{ij}$ besteht aus +Eine $m\times n$-Matrix $A$ mit den Koeffizienten $a_{ij}$ besteht aus den $n$ Spaltenvektoren \[ a_1 = \begin{pmatrix} a_{11} \\ a_{21} \\ \vdots \\ a_{m1} \end{pmatrix},\quad @@ -435,7 +435,7 @@ werden kann. \begin{definition} Eine $m\times n$-Matrix $A\in M_{m\times n}(\Bbbk)$ und eine $n\times l$-Matrix $B\in M_{n\times l}(\Bbbk)$ haben als Produkt -eine $n\times l$-Matrix $C=AB\in M_{n\times l}(\Bbbk)$ mit den +eine $m\times l$-Matrix $C=AB\in M_{m\times l}(\Bbbk)$ mit den Koeffizienten \begin{equation} c_{ij} = \sum_{k=1}^n a_{ik} b_{kj}. @@ -483,7 +483,7 @@ I 1 &0 &\dots &0 \\ 0 &1 &\dots &0 \\[-2pt] \vdots&\vdots&\ddots&\vdots\\ -0 &0 &\dots &1 +0 &0 &\dots &1 \end{pmatrix}. \] @@ -521,10 +521,10 @@ Ein Gleichungssystem mit $0$ auf der rechten Seite ist also bereits ausreichend um zu entscheiden, ob die Lösung eindeutig ist. Ein Gleichungssystem mit rechter Seite $0$ heisst {\em homogen}. \index{homogenes Gleichungssystem}% -Zu jedem {\em inhomogenen} Gleichungssystem $Ax=b$ mit $b\ne 0$ +Zu jedem {\em inhomogenen} Gleichungssystem $Ax=b$ mit $b\ne 0$ ist $Ax=0$ das zugehörige homogene Gleichungssystem. -Ein homogenes Gleichungssytem $Ax=0$ hat immer mindestens die +Ein homogenes Gleichungssytem $Ax=0$ hat immer mindestens die Lösung $x=0$, man nennt sie auch die {\em triviale} Lösung. Eine Lösung $x\ne 0$ heisst auch eine nichttriviale Lösung. Die Lösungen eines inhomgenen Gleichungssystem $Ax=b$ ist also nur dann @@ -535,7 +535,7 @@ Lösung hat. Der Gauss-Algorithmus oder genauer Gausssche Eliminations-Algorithmus löst ein lineare Gleichungssystem der Form~\eqref{buch:vektoren-und-matrizen:eqn:vektorform}. -Die Koeffizienten werden dazu in das Tableau +Die Koeffizienten werden dazu in das Tableau \[ \begin{tabular}{|>{$}c<{$}>{$}c<{$}>{$}c<{$}|>{$}c<{$}|} \hline @@ -552,7 +552,7 @@ Der Algorithmus is so gestaltet, dass er nicht mehr Speicher als das Tableau benötigt, alle Schritte operieren direkt auf den Daten des Tableaus. -In jedem Schritt des Algorithmus wird zunächst eine Zeile $i$ und +In jedem Schritt des Algorithmus wird zunächst eine Zeile $i$ und Spalte $j$ ausgewählt, das Elemente $a_{ij}$ heisst das Pivotelement. \index{Pivotelement}% Die {\em Pivotdivision} @@ -646,7 +646,7 @@ In der Phase der {\em Vorwärtsreduktion} werden Pivotelemente von links nach rechts möglichst auf der Diagonale gewählt und mit Zeilensubtraktionen die darunterliegenden Spalten freigeräumt. \index{Vorwärtsreduktion}% -Während des Rückwärtseinsetzens werden die gleichen Pivotelemente von +Während des Rückwärtseinsetzens werden die gleichen Pivotelemente von rechts nach links genutzt, um mit Zeilensubtraktionen auch die Spalten über den Pivotelemnten frei zu räumen. \index{Rückwärtseinsetzen}% @@ -800,7 +800,7 @@ $x = b_1c_1+b_2c_2+\dots+b_nc_n$ konstruieren. Tatsächlich gilt \begin{align*} Ax -&= +&= A( b_1c_1+b_2c_2+\dots+b_nc_n) \\ &= @@ -851,10 +851,10 @@ für eine Gleichungssystem mit quadratischer Koeffizientenmatrix $A$ heisst die Determinante $\det(A)$ der Matrix $A$. \end{definition} -Aus den Regeln für die Durchführung des Gauss-Algorithmus kann man die +Aus den Regeln für die Durchführung des Gauss-Algorithmus kann man die folgenden Regeln für die Determinante ableiten. Wir stellen die Eigenschaften hier nur zusammen, detaillierte Herleitungen -kann man in jedem Kurs zur linearen Algebra finden, zum Beispiel im +kann man in jedem Kurs zur linearen Algebra finden, zum Beispiel im Kapitel~2 des Skripts \cite{buch:linalg}. \begin{enumerate} \item @@ -877,11 +877,11 @@ wird auch der Wert der Determinanten mit $\lambda$ multipliziert. \item \label{buch:linear:determinante:asymetrisch} Die Determinante ist eine lineare Funktion der Zeilen von $A$. -Zusammen mit der Eigeschaft~\ref{buch:linear:determinante:vorzeichen} +Zusammen mit der Eigeschaft~\ref{buch:linear:determinante:vorzeichen} folgt, dass die Determinante eine antisymmetrische lineare Funktion der Zeilen ist. \item -Die Determinante ist durch die Eigenschaften +Die Determinante ist durch die Eigenschaften \ref{buch:linear:determinante:einheitsmatrix} und \ref{buch:linear:determinante:asymetrisch} @@ -895,7 +895,7 @@ Die Determinante der $n\times n$-Matrix $A$ kann mit der Formel = \sum_{i=1}^n (-1)^{i+j} a_{ij} \cdot \det(A_{ij}) \end{equation} -wobei die $(n-1)\times(n-1)$-Matrix $A_{ij}$ die Matrix $A$ ist, aus der +wobei die $(n-1)\times(n-1)$-Matrix $A_{ij}$ die Matrix $A$ ist, aus der man Zeile $i$ und Spalte $j$ entfernt hat. $A_{ij}$ heisst ein {\em Minor} der Matrix $A$. \index{Minor einer Matrix}% @@ -949,7 +949,7 @@ der rechten Seiten ersetzt worden ist. \end{satz} Die Cramersche Formel ist besonders nützlich, wenn die Abhängigkeit -einer Lösungsvariablen von den Einträgen der Koeffizientenmatrix +einer Lösungsvariablen von den Einträgen der Koeffizientenmatrix untersucht werden soll. Für die Details der Herleitung sei wieder auf \cite{buch:linalg} verwiesen. @@ -993,7 +993,7 @@ heisst die {\em Adjunkte} $\operatorname{adj}A$ von $A$. \end{satz} Der Satz~\ref{buch:linalg:inverse:adjoint} liefert eine algebraische -Formel für die Elemente der inversen Matrix. +Formel für die Elemente der inversen Matrix. Für kleine Matrizen wie im nachfolgenden Beispiel ist die Formel~\eqref{buch:linalg:inverse:formel} oft einfachter anzuwenden. Besonders einfach wird die Formel für eine $2\times 2$-Matrix, @@ -1035,7 +1035,7 @@ Die Adjunkte ist \begin{pmatrix*}[r] \det A_{11} & -\det A_{21} & \det A_{31} \\ -\det A_{12} & \det A_{22} & -\det A_{32} \\ - \det A_{13} & -\det A_{23} & \det A_{33} + \det A_{13} & -\det A_{23} & \det A_{33} \end{pmatrix*} \intertext{und damit ist die inverse Matrix} A^{-1} @@ -1084,7 +1084,7 @@ A^{-1} \end{pmatrix}. \label{buch:vektoren-und-matrizen:abeispiel:eqn2} \end{equation} -für die Inverse einer Matrix der Form +für die Inverse einer Matrix der Form \eqref{buch:vektoren-und-matrizen:abeispiel:eqn1}. \end{beispiel} @@ -1118,7 +1118,7 @@ Eine Abbildung $f\colon V\to U$ zwischen Vektorräumen $V$ und $U$ heisst linear, wenn \[ \begin{aligned} -f(v+w) &= f(v) + f(w)&&\forall v,w\in V +f(v+w) &= f(v) + f(w)&&\forall v,w\in V \\ f(\lambda v) &= \lambda f(v) &&\forall v\in V,\lambda \in \Bbbk \end{aligned} @@ -1129,16 +1129,16 @@ gilt. Lineare Abbildungen sind in der Mathematik sehr verbreitet. \begin{beispiel} -Sie $V=C^1([a,b])$ die Menge der stetig differenzierbaren Funktionen +Sie $V=C^1([a,b])$ die Menge der stetig differenzierbaren Funktionen auf dem Intervall $[a,b]$ und $U=C([a,b])$ die Menge der -stetigen Funktion aif $[a,b]$. +stetigen Funktion aif $[a,b]$. Die Ableitung $\frac{d}{dx}$ macht aus einer Funktion $f(x)$ die Ableitung $f'(x)$. -Die Rechenregeln für die Ableitung stellen sicher, dass +Die Rechenregeln für die Ableitung stellen sicher, dass \[ \frac{d}{dx} \colon -C^1([a,b]) \to C([a,b]) +C^1([a,b]) \to C([a,b]) : f \mapsto f' \] @@ -1157,7 +1157,7 @@ eine lineare Abbildung. \end{beispiel} \subsubsection{Matrix} -Um mit linearen Abbildungen rechnen zu können, ist eine Darstellung +Um mit linearen Abbildungen rechnen zu können, ist eine Darstellung mit Hilfe von Matrizen nötig. Sei also $\mathcal{B}=\{b_1,\dots,b_n\}$ eine Basis von $V$ und $\mathcal{C} = \{ c_1,\dots,c_m\}$ eine Basis von $U$. @@ -1165,12 +1165,12 @@ Das Bild des Basisvektors $b_i$ kann als Linearkombination der Vektoren $c_1,\dots,c_m$ dargestellt werden. Wir verwenden die Bezeichnung \[ -f(b_i) +f(b_i) = a_{1i} c_1 + \dots + a_{mi} c_m. \] Die lineare Abbildung $f$ bildet den Vektor $x$ mit Koordinaten -$x_1,\dots,x_n$ ab auf +$x_1,\dots,x_n$ ab auf \begin{align*} f(x) &= @@ -1193,7 +1193,7 @@ x_n(a_{1n} c_1 + \dots + a_{mn} c_m) + ( a_{m1} x_1 + \dots + a_{mn} x_n ) c_m \end{align*} -Die Koordinaten von $f(x)$ in der Basis $\mathcal{C}$ in $U$ sind +Die Koordinaten von $f(x)$ in der Basis $\mathcal{C}$ in $U$ sind also gegeben durch das Matrizenprodukt $Ax$, wenn $x$ der Spaltenvektor aus den Koordinaten in der Basis $\mathcal{B}$ in $V$ ist. @@ -1231,7 +1231,7 @@ b_{m1}x_1&+& \dots &+&b_{mn}x_n&=&b_{m1}'x_1'&+& \dots &+&b_{mn}'x_n' \end{linsys} \] Dieses Gleichungssystem kann man mit Hilfe eines Gauss-Tableaus lösen. -Wir schreiben die zugehörigen Variablen +Wir schreiben die zugehörigen Variablen \[ \renewcommand{\arraystretch}{1.1} \begin{tabular}{|>{$}c<{$} >{$}c<{$} >{$}c<{$}|>{$}c<{$}>{$}c<{$}>{$}c<{$}|} @@ -1277,7 +1277,7 @@ Für zwei Vektoren $u$ und $w$ in $U$ gibt es daher Vektoren $a=g(u)$ und $b=g(w)$ in $V$ derart, dass $f(a)=u$ und $f(b)=w$. Weil $f$ linear ist, folgt daraus $f(a+b)=u+w$ und $f(\lambda a)=\lambda a$ für jedes $\lambda\in\Bbbk$. -Damit kann man jetzt +Damit kann man jetzt \begin{align*} g(u+w)&=g(f(a)+f(b)) = g(f(a+b)) = a+b = g(u)+g(w) \\ @@ -1315,7 +1315,7 @@ Der Kern oder Nullraum der Matrix $A$ ist die Menge \] \end{definition} -Der Kern ist ein Unterraum, denn für zwei Vektoren $u,w\in \ker f$ +Der Kern ist ein Unterraum, denn für zwei Vektoren $u,w\in \ker f$ \[ \begin{aligned} f(u+v)&=f(u) + f(v) = 0+0 = 0 &&\Rightarrow& u+v&\in\ker f\\ @@ -1331,7 +1331,7 @@ Wir definieren daher das Bild einer linearen Abbildung oder Matrix. \begin{definition} Ist $f\colon V\to U$ eine lineare Abbildung dann ist das Bild von $f$ -der Unterraum +der Unterraum \[ \operatorname{im}f = \{ f(v)\;|\;v\in V\} \subset U \] @@ -1375,7 +1375,7 @@ $\operatorname{def}A=\dim\ker A$. \end{definition} Da der Kern mit Hilfe des Gauss-Algorithmus bestimmt werden kann, -können Rang und Defekt aus dem Schlusstableau +können Rang und Defekt aus dem Schlusstableau eines homogenen Gleichungssystems mit $A$ als Koeffizientenmatrix abgelesen werden. @@ -1391,8 +1391,3 @@ n-\operatorname{def}A. \subsubsection{Quotient} TODO: $\operatorname{im} A \simeq \Bbbk^m/\ker A$ - - - - - diff --git a/buch/chapters/95-homologie/Makefile.inc b/buch/chapters/95-homologie/Makefile.inc index 7e6f1e7..41b1569 100644 --- a/buch/chapters/95-homologie/Makefile.inc +++ b/buch/chapters/95-homologie/Makefile.inc @@ -8,7 +8,6 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/95-homologie/simplex.tex \ chapters/95-homologie/komplex.tex \ chapters/95-homologie/homologie.tex \ - chapters/95-homologie/mayervietoris.tex \ chapters/95-homologie/fixpunkte.tex \ chapters/95-homologie/chapter.tex diff --git a/buch/chapters/95-homologie/chapter.tex b/buch/chapters/95-homologie/chapter.tex index eaa56c4..994c400 100644 --- a/buch/chapters/95-homologie/chapter.tex +++ b/buch/chapters/95-homologie/chapter.tex @@ -38,7 +38,7 @@ Damit wird es möglich, das Dreieck vom Rand des Dreiecks zu unterschieden. \input{chapters/95-homologie/simplex.tex} \input{chapters/95-homologie/komplex.tex} \input{chapters/95-homologie/homologie.tex} -\input{chapters/95-homologie/mayervietoris.tex} +%\input{chapters/95-homologie/mayervietoris.tex} \input{chapters/95-homologie/fixpunkte.tex} diff --git a/buch/chapters/95-homologie/homologie.tex b/buch/chapters/95-homologie/homologie.tex index 2b80a17..905ecc3 100644 --- a/buch/chapters/95-homologie/homologie.tex +++ b/buch/chapters/95-homologie/homologie.tex @@ -6,13 +6,349 @@ \section{Homologie \label{buch:section:homologie}} \rhead{Homologie} +Die Idee der Trangulation ermöglicht, komplizierte geometrische +Objekte mit einem einfachen ``Gerüst'' auszustatten und so zu +analysieren. +Projiziert man ein mit einer Kugel konzentrisches Tetraeder auf die +Kugel, entsteht eine Triangulation der Kugeloberfläche. +Statt eine Kugel zu studieren, kann man also auch ein Tetraeder untersuchen. + +Das Gerüst kann natürlich nicht mehr alle Eigenschaften des ursprünglichen +Objektes wiedergeben. +Im Beispiel der Kugel geht die Information darüber, dass es sich um eine +glatte Mannigfaltigkeit handelt, verloren. +Was aber bleibt, sind Eigenschaften des Zusammenhangs. +Wenn sich zwei Punkte mit Wegen verbinden lassen, dann gibt es auch eine +Triangulation mit eindimensionalen Simplices, die diese Punkte als Ecken +enthalten, die sich in der Triangulation mit einer Folge von Kanten +verbinden lassen. +Algebraisch bedeutet dies, dass die beiden Punkte der Rand eines +Weges sind. +Fragen der Verbindbarkeit von Punkten mit Wegen lassen sich also +dadurch studieren, dass man das geometrische Objekt auf einen Graphen +reduziert. + +In diesem Abschnitt soll gezeigt werden, wie diese Idee auf höhere +Dimensionen ausgedehnt werden. +Es soll möglich werden, kompliziertere Fragen des Zusammenhangs, zum +Beispiel das Vorhandensein von Löchern mit algebraischen Mitteln +zu analysieren. \subsection{Homologie eines Kettenkomplexes \label{buch:subsection:homologie-eines-kettenkomplexes}} +Wegzusammenhang lässt sich untersuchen, indem man in der Triangulation +nach Linearkombinationen von Kanten sucht, die als Rand die beiden Punkte +haben. +Zwei Punkte sind also nicht verbindbar und liegen damit in verschiedenen +Komponenten, wenn die beiden Punkte nicht Rand irgend einer +Linearkombination von Kanten sind. +Komponenten können also identifiziert werden, indem man unter allen +Linearkombinationen von Punkten, also $C_0$ all diejenigen ignoriert, +die Rand einer Linearkombinationv on Kanten sind, also $\partial_1C_1$. +Der Quotientenraum $H_0=C_0/\partial_1C_1$ enthält also für jede Komponente +eine Dimension. + +Eine Dimension höher könnten wir danach fragen, ob sich ein geschlossener +Weg zusammenziehen lässt. +In der Triangulation zeichnet sich ein geschlossener Weg dadurch aus, +dass jedes Ende einer Kante auch Anfang einer Folgekante ist, dass also +der Rand der Linearkombination von Kanten 0 ist. +Algebraisch bedeutet dies, dass wir uns für diejenigen Linearkombinationen +$z\in C_1$ interessieren, die keinen Rand haben, für die also $\partial_1z=0$ +gilt. + +\begin{definition} +Die Elemente von +\[ +Z_k += +Z_k^C += +\{z\in C_k\;|\; \partial_k z = 0\} += +\ker \partial_k +\] +heissen die {\em ($k$-dimensionalen) Zyklen} von $C_*$. +\end{definition} + +In einem Dreieck ist der Rand ein geschlossener Weg, der sich zusammenziehen +lässt, indem man ihn durch die Dreiecksfläche deformiert. +Entfernt man aber die Dreiecksfläche, ist diese Deformation nicht mehr +möglich. +Einen zusammenziehbaren Weg kann man sich also als den Rand eines Dreiecks +einer vorstellen. +``Löcher'' sind durch geschlossene Wege erkennbar, die nicht Rand eines +Dreiecks sein können. +Wir müssen also ``Ränder'' ignorieren. + +\begin{definition} +Die Elemente von +\[ +B_k += +B_k^C += +\{\partial_{k+1}z\;|\; C_{k+1}\} += +\operatorname{im} \partial_{k+1} +\] +heissen die {\em ($k$-dimensionalen) Ränder} von $C_*$. +\end{definition} + +Algebraisch ausgedrückt interessieren uns also nur Zyklen, die selbst +keine Ränder sind. +Der Quotientenraum $Z_1/B_1$ ignoriert unter den Zyklen diejenigen, die +Ränder sind, drückt also algebraisch die Idee des eindimensionalen +Zusammenhangs aus. +Wir definieren daher + +\begin{definition} +Die $k$-dimensionale Homologiegruppe des Kettenkomplexes $C_*$ ist +\[ +H_k(C) = Z_k/B_k = \ker \partial_k / \operatorname{im} \partial_{k+1}. +\] +Wenn nur von einem Kettenkomplex die Rede ist, kann auch $H_k(C)=H_k$ +abgekürzt werden. +\end{definition} + +Die folgenden zwei ausführlichen Beispiele sollen zeigen, wie die +Homologiegruppe $H_2$ die Anwesenheit eines Hohlraumes detektieren kann, +der entsteht, wenn man aus einem Tetraeder das innere entfernt. + +\begin{beispiel} +\begin{figure} +\centering +XXX Bild eines Tetraeders mit Bezeichnung der Ecken und Kanten +\caption{Triangulation eines Tetraeders, die Orientierung von Kanten +und Seitenflächen ist immer so gewählt, dass die Nummern der Ecken +aufsteigend sind. +\label{buch:homologie:tetraeder:fig}} +\end{figure} +Ein Tetraeder ist ein zweidmensionales Simplex, wir untersuchen seinen +Kettenkomplex und bestimmen die zugehörigen Homologiegruppen. +Zunächst müssen wir die einzelnen Mengen $C_k$ beschreiben und verwenden +dazu die Bezeichnungen gemäss Abbildung~\ref{buch:homologie:tetraeder:fig}. +$C_0$ ist der vierdimensionale Raum aufgespannt von den vier Ecken +$0$, $1$, $2$ und $3$ des Tetraeders. +$C_1$ ist der sechsdimensionale Vektorraum der Kanten +\[ +k_0 = [0,1],\quad +k_1 = [0,2],\quad +k_2 = [0,3],\quad +k_3 = [1,2],\quad +k_4 = [1,3],\quad +k_5 = [2,3] +\] +Der Randoperator $\partial_1$ hat die Matrix +\[ +\partial_1 += +\begin{pmatrix*}[r] +-1&-1&-1& 0& 0& 0\\ + 1& 0& 0&-1&-1& 0\\ + 0& 1& 0& 1& 0&-1\\ + 0& 0& 1& 0& 1& 1 +\end{pmatrix*}. +\] + +Wir erwarten natürlich, dass sich zwei beliebige Ecken verbinden lassen, +dass es also nur eine Komponente gibt und dass damit $H_1=\Bbbk$ ist. +Dazu beachten wir, dass das Bild von $\partial_1$ genau aus den Vektoren +besteht, deren Komponentensumme $0$ ist. +Das Bild $B_0$ von $\partial_1$ ist daher die Lösungsmenge der einen +Gleichung +\( +x_0+x_1+x_2+x_3=0. +\) +Der Quotientenraum $H_0=Z_0/B_0 = C_0/\operatorname{im}\partial_1$ +ist daher wie erwartet eindimensional. + +Wir bestimmen jetzt die Homologiegruppe $H_1$. +Da sich im Tetraeder jeder geschlossene Weg zusammenziehen lässt, +erwarten wir $H_1=0$. + +Die Menge der Zyklen $Z_1$ wird bestimmt, indem man die Lösungsmenge +des Gleichungssystems $\partial_1z=0$ bestimmt. +Der Gauss-Algorithmus für die Matrix $\partial_1$ liefert das +Schlusstableau +\[ +\begin{tabular}{|>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}|} +\hline +k_0&k_1&k_2&k_3&k_4&k_5\\ +\hline + 1& 0& 0& -1& -1& 0\\ + 0& 1& 0& 1& 0& -1\\ + 0& 0& 1& 0& 1& 1\\ + 0& 0& 0& 0& 0& 0\\ +\hline +\end{tabular} +\] +Daraus lassen sich drei linear unabhängig eindimensionale Zyklen ablesen, +die zu den Lösungsvektoren +\[ +z_1 += +\begin{pmatrix*}[r] +1\\ +-1\\ +0\\ +1\\ +0\\ +0 +\end{pmatrix*}, +\qquad +z_2 += +\begin{pmatrix*}[r] +1\\ +0\\ +-1\\ +0\\ +1\\ +0 +\end{pmatrix*}, +\qquad +z_3 += +\begin{pmatrix*}[r] +0\\ +1\\ +-1\\ +0\\ +0\\ +1 +\end{pmatrix*} +\] +gehören. + +$C_2$ hat die vier Seitenflächen +\[ +f_0=[0,1,2],\quad +f_1=[0,1,3],\quad +f_2=[0,2,3],\quad +f_3=[1,2,3] +\] +als Basis. +Der zweidimensionale Randoperator ist die $6\times 4$-Matrix +\[ +\partial_2 += +\begin{pmatrix*}[r] + 1& 1& 0& 0\\ +-1& 0& 1& 0\\ + 0&-1&-1& 0\\ + 1& 0& 0& 1\\ + 0& 1& 0&-1\\ + 0& 0& 1& 1 +\end{pmatrix*}. +\] +Man kann leicht nachrechnen, dass $\partial_1\partial_2=0$ ist, wie es +für einen Kettenkomplex sein muss. + +Um nachzurechnen, dass die Homologiegruppe $H_1=0$ ist, müssen wir jetzt +nachprüfen, ob jeder Zyklus in $Z_1$ auch Bild der Randabbildung $\partial_2$ +ist. +Die ersten drei Spalten von $\partial_2$ sind genau die drei Zyklen +$z_1$, $z_2$ und $z_3$. +Insbesondere lassen sich alle Zyklen als Ränder darstellen, die +Homologiegruppe $H_1=0$ verschwindet. + +Die Zyklen in $C_2$ sind die Lösungen von $\partial_2z=0$. +Der Gauss-Algorithmus für $\partial_2$ liefert das -Tableau +\[ +\begin{tabular}{|>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}|} +\hline +f_0&f_1&f_2&f_3\\ +\hline +1&0&0& 1\\ +0&1&0&-1\\ +0&0&1& 1\\ +0&0&0& 0\\ +0&0&0& 0\\ +0&0&0& 0\\ +\hline +\end{tabular} +\] +Daraus liest man ab, dass es genau einen Zyklus nämlich +\[ +z += +\begin{pmatrix} +-1\\1\\-1\\1 +\end{pmatrix} +\] +$Z_2$ besteht also aus Vielfachen des Vektors $z$. + +Da es nur ein zweidimensionales Simplex gibt, ist $C_3$ eindimensional. +Die Randabbildung $\partial_3$ hat die Matrix +\[ +\partial_3 += +\begin{pmatrix} +1\\ +-1\\ +1\\ +-1 +\end{pmatrix}. +\] +Die Zyklen $Z_2$ und die Ränder $B_2$ bilden also dieselbe Menge, auch +die Homologie-Gruppe $H_2$ ist $0$. + +Da es keine vierdimensionalen Simplizes gibt, ist $B_3=0$. +Die Zyklen $Z_3$ bestehen aus den Lösungen von $\partial_3w=0$, da +aber $\partial_3$ injektiv ist, ist $Z_3=0$. +Daher ist auch $H_3=0$. +\end{beispiel} + +\begin{beispiel} +Für dieses Beispiel entfernen wir das Innere des Tetraeders, es entsteht +ein Hohlraum. +Am Kettenkomplex der Triangulation ändert sich nur, dass $C_3$ jetzt +nur noch den $0$-Vektor enthält. +Das Bild $B_2=\operatorname{im}\partial_3$ wird damit auch $0$-dimensional, +während es im vorigen Beispiel eindimensional war. +Die einzige Änderung ist also in der Homologiegruppe +$H_2 = Z_2/B_2 = Z_2 / \{0\} \simeq \Bbbk$. +Die Homologiegruppe $H_2$ hat jetzt Dimension $1$ und zeigt damit den +Hohlraum an. +\end{beispiel} \subsection{Induzierte Abbildung \label{buch:subsection:induzierte-abbildung}} +Früher haben wurde eine Abbildung $f_*$ zwischen Kettenkomplexen $C_*$ und +$D_*$ so definiert, +dass sie mit den Randoperatoren verträglich sein muss. +Diese Forderung bewirkt, dass sich auch eine lineare Abbildung +\[ +H_k(f) \colon H_k(C) \to H_k(D) +\] +zwischen den Homologiegruppen ergibt, wie wir nun zeigen wollen. + +Um eine Abbildung von $H_k(C)$ nach $H_k(D)$ zu definieren, müssen wir +zu einem Element von $H_k(C)$ ein Bildelement konstruieren. +Ein Element in $H_k(C)$ ist eine Menge von Zyklen in $Z^C_k$, die sich +nur um einen Rand in $B_k$ unterscheiden. +Wir wählen also einen Zyklus $z\in Z_k$ und bilden ihn auf $f_k(z)$ ab. +Wegen $\partial^D_kf(z)=f\partial^C_kz = f(0) =0 $ ist auch $f_k(z)$ +ein Zyklus. +Wir müssen jetzt aber noch zeigen, dass eine andere Wahl des Zyklus +das gleiche Element in $H_k(D)$ ergibt. +Dazu genügt es zu sehen, dass sich $f(z)$ höchstens um einen Rand +ändert, wenn man $z$ um einen Rand ändert. +Sei also $b\in B^C_k$ ein Rand, es gibt also ein $w\in C_{k+1}$ mit +$\partial^C_{k+1}w=b$. +Dann gilt aber auch +\[ +f_k(z+b) += +f_k(z) + f_k(b) += +f_k(z) + f_k(\partial^C_{k+1}w) += +f_k(z) + \partial^D_{k+1}(f_k(w)). +\] +Der letzte Term ist ein Rand in $D_k$, somit ändert sich $f_k(z)$ nur +um diesen Rand, wenn man $z$ um einen Rand ändert. +$f_k(z)$ und $f_k(z+b)$ führen auf die selbe Homologieklasse. -\subsection{Homologie eines simplizialen Komplexes -\label{buch:subsection:simplizialekomplexe}} diff --git a/buch/chapters/95-homologie/komplex.tex b/buch/chapters/95-homologie/komplex.tex index 6dd8efb..fa2d8e1 100644 --- a/buch/chapters/95-homologie/komplex.tex +++ b/buch/chapters/95-homologie/komplex.tex @@ -6,9 +6,105 @@ \section{Kettenkomplexe \label{buch:section:komplex}} \rhead{Kettenkomplexe} +Die algebraische Struktur, die in Abschnitt~\ref{buch:subsection:triangulation} +konstruiert wurde, kann noch etwas abstrakter konstruiert werden. +Es ergibt sich das Konzept eines Kettenkomplexes. +Die Triangulation gibt also Anlass zu einem Kettenkomplex. +So lässt sich zu einem geometrischen Objekt ein algebraisches +Vergleichsobjekt konstruieren. +Im Idealfall lassens ich anschliessend geometrische Eigenschaften mit +algebraischen Rechnungen zum Beispiel in Vektorräumen mit Matrizen +beantworten. -\subsection{Randoperator von Simplexen -\label{buch:subsection:randoperator-von-simplexen}} +\subsection{Definition +\label{buch:subsection:kettenkomplex-definition}} +Die Operation $\partial$, die für Simplizes konstruiert worden ist, +war linear und hat die Eigenschaft $\partial^2$ gehabt. +Diese Eigenschaften reichen bereits für Definition eines Kettenkomplexes. + +\begin{definition} +Eine Folge $C_0,C_1,C_2,\dots$ von Vektorräumen über dem Körper $\Bbbk$ +mit einer Folge von linearen Abbildungen +$\partial_k\colon C_k \to C_{k-1}$, dem {\em Randoperator}, +heisst ein Kettenkomplex, wenn $\partial_{k-1}\partial_k=0$ gilt +für alle $k>0$. +\end{definition} + +Die aus den Triangulationen konstruieren Vektorräme von +Abschnitt~\ref{buch:subsection:triangulation} bilden einen +Kettenkomplex. + +XXX nachrechnen: $\partial^2 = 0$ ? + +\subsection{Abbildungen +\label{buch:subsection:abbildungen}} +Wenn man verschiedene geometrische Objekte mit Hilfe von Triangulationen +vergleichen will, dann muss man auch das Konzept der Abbildungen zwischen +den geometrischen Objekten in die Kettenkomplexe transportieren. + +Eine Abbildung zwischen Kettenkomplexen muss einerseits eine lineare +Abbildung der Vektorräume $C_k$ sein, andererseits muss sich eine +solche Abbildung mit dem Randoperator vertragen. +Wir definieren daher + +\begin{definition} +Eine Abbildung $f_*$ zwischen zwei Kettenkomplexe $(C_*,\partial^C_*)$ und +$(D_*,\partial^D_*)$ heisst eine Abbildung von Kettenkomplexen, wenn +für jedes $k$ +\begin{equation} +\partial^D_k +\circ +f_{k} += +f_{k+1} +\circ +\partial^C_k +\label{buch:komplex:abbildung} +\end{equation} +gilt. +\end{definition} + +Die Beziehung~\eqref{buch:komplex:abbildung} kann übersichtlich als +kommutatives Diagramm dargestellt werden. +\begin{equation} +\begin{tikzcd} +0 + & C_0 \arrow[l, "\partial_0^C"] + \arrow[d, "f_0"] + & C_1 \arrow[l,"\partial_1^C"] + \arrow[d, "f_1"] + & C_2 \arrow[l,"\partial_2^C"] + \arrow[d, "f_2"] + & \dots \arrow[l] + \arrow[l, "\partial_{k-1}^C"] + & C_k + \arrow[l, "\partial_k^C"] + \arrow[d, "f_k"] + & C_{k+1}\arrow[l, "\partial_{k+1}^C"] + \arrow[d, "f_{k+1}"] + & \dots +\\ +0 + & D_0 \arrow[l, "\partial_0^D"] + & D_1 \arrow[l,"\partial_1^D"] + & D_2 \arrow[l,"\partial_2^D"] + & \dots \arrow[l] + \arrow[l, "\partial_{k-1}^D"] + & D_k + \arrow[l, "\partial_k^D"] + & D_{k+1}\arrow[l, "\partial_{k+1}^D"] + & \dots +\end{tikzcd} +\label{buch:komplex:abbcd} +\end{equation} +Die Relation~\eqref{buch:komplex:abbildung} drückt aus, dass man jeden +den Pfeilen im Diagram~\eqref{buch:komplex:abbcd} folgen kann und +dabei zwischen zwei Vektorräumen unabhängig vom Weg die gleiche Abbildung +resultiert. + +Die Verfeinerung einer Triangulation erzeugt eine solche Abbildung von +Komplexen. + + +% XXX simpliziale Approximation -\subsection{Kettenkomplexe und Morphismen -\label{buch:subsection:kettenkomplex}} diff --git a/buch/chapters/95-homologie/simplex.tex b/buch/chapters/95-homologie/simplex.tex index 5ca2ca8..397ba07 100644 --- a/buch/chapters/95-homologie/simplex.tex +++ b/buch/chapters/95-homologie/simplex.tex @@ -233,6 +233,6 @@ Vorzeichen zu, die Matrix ist \subsection{Triangulation -\label{buch:subsection:}} +\label{buch:subsection:triangulation}} diff --git a/buch/papers/erdbeben/Gausskurve2.pdf b/buch/papers/erdbeben/Gausskurve2.pdf Binary files differindex bee3bc0..5e4afdf 100644 --- a/buch/papers/erdbeben/Gausskurve2.pdf +++ b/buch/papers/erdbeben/Gausskurve2.pdf diff --git a/buch/papers/erdbeben/Gausskurve2.tex b/buch/papers/erdbeben/Gausskurve2.tex index 44319c3..2441766 100644 --- a/buch/papers/erdbeben/Gausskurve2.tex +++ b/buch/papers/erdbeben/Gausskurve2.tex @@ -1,13 +1,12 @@ \documentclass{standalone} \usepackage{pgfplots} - +\usepackage{txfonts} \pgfplotsset{compat = newest} \begin{document} - -\begin{tikzpicture} +\begin{tikzpicture}[>=latex,thick] \begin{axis}[ diff --git a/buch/papers/erdbeben/Gausskurve3.pdf b/buch/papers/erdbeben/Gausskurve3.pdf Binary files differindex e86a403..b86023f 100644 --- a/buch/papers/erdbeben/Gausskurve3.pdf +++ b/buch/papers/erdbeben/Gausskurve3.pdf diff --git a/buch/papers/erdbeben/Gausskurve3.tex b/buch/papers/erdbeben/Gausskurve3.tex index 85455ef..032d6de 100644 --- a/buch/papers/erdbeben/Gausskurve3.tex +++ b/buch/papers/erdbeben/Gausskurve3.tex @@ -1,13 +1,12 @@ \documentclass{standalone} \usepackage{pgfplots} - +\usepackage{txfonts} \pgfplotsset{compat = newest} \begin{document} - -\begin{tikzpicture} +\begin{tikzpicture}[>=latex,thick] \begin{axis}[ diff --git a/buch/papers/erdbeben/main.tex b/buch/papers/erdbeben/main.tex index 95f1f4b..4167475 100644 --- a/buch/papers/erdbeben/main.tex +++ b/buch/papers/erdbeben/main.tex @@ -4,7 +4,7 @@ % (c) 2020 Hochschule Rapperswil % \chapter{Erdbebenmessung\label{chapter:erdbeben}} -\lhead{Thema} +\lhead{Erdbeben} \begin{refsection} \chapterauthor{Lukas Zogg und Fabio Veicelli} diff --git a/buch/papers/erdbeben/references.bib b/buch/papers/erdbeben/references.bib index 56ca24b..444c82d 100644 --- a/buch/papers/erdbeben/references.bib +++ b/buch/papers/erdbeben/references.bib @@ -1,22 +1,22 @@ %% This BibTeX bibliography file was created using BibDesk. %% https://bibdesk.sourceforge.io/ -%% Created for lukas zogg at 2021-07-17 16:48:19 +0200 +%% Created for lukas zogg at 2021-07-27 17:56:45 +0200 %% Saved with string encoding Unicode (UTF-8) -@article{aragher_understanding_2012, +@article{erdbeben:aragher_understanding_2012, author = {Faragher, Ramsey}, date-added = {2021-07-17 16:44:00 +0200}, date-modified = {2021-07-17 16:45:54 +0200}, - journal = { Signal Processing Magazine}, + journal = {Signal Processing Magazine}, month = {09}, number = {5}, pages = {128--132}, - title = {Understanding the Basis of the Kalman Filter Via a Simple and Intuitive Derivation }, + title = {Understanding the Basis of the Kalman Filter Via a Simple and Intuitive Derivation}, volume = {29}, year = {2012}, Bdsk-File-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxByLi4vLi4vLi4vLi4vLi4vLi4vRG93bmxvYWRzL1VuZGVyc3RhbmRpbmcgdGhlIEJhc2lzIG9mIHRoZSBLYWxtYW4gRmlsdGVyIFZpYSBhIFNpbXBsZSBhbmQgSW50dWl0aXZlIERlcml2YXRpb24ucGRmTxECbgAAAAACbgACAAAMTWFjaW50b3NoIEhEAAAAAAAAAAAAAAAAAAAAAAAAAEJEAAH/////H1VuZGVyc3RhbmRpbmcgdGhlICNGRkZGRkZGRi5wZGYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////8AAAAAAAAAAAAAAAAABgACAAAKIGN1AAAAAAAAAAAAAAAAAAlEb3dubG9hZHMAAAIAci86VXNlcnM6bHVrYXN6b2dnOkRvd25sb2FkczpVbmRlcnN0YW5kaW5nIHRoZSBCYXNpcyBvZiB0aGUgS2FsbWFuIEZpbHRlciBWaWEgYSBTaW1wbGUgYW5kIEludHVpdGl2ZSBEZXJpdmF0aW9uLnBkZgAOAK4AVgBVAG4AZABlAHIAcwB0AGEAbgBkAGkAbgBnACAAdABoAGUAIABCAGEAcwBpAHMAIABvAGYAIAB0AGgAZQAgAEsAYQBsAG0AYQBuACAARgBpAGwAdABlAHIAIABWAGkAYQAgAGEAIABTAGkAbQBwAGwAZQAgAGEAbgBkACAASQBuAHQAdQBpAHQAaQB2AGUAIABEAGUAcgBpAHYAYQB0AGkAbwBuAC4AcABkAGYADwAaAAwATQBhAGMAaQBuAHQAbwBzAGgAIABIAEQAEgBwVXNlcnMvbHVrYXN6b2dnL0Rvd25sb2Fkcy9VbmRlcnN0YW5kaW5nIHRoZSBCYXNpcyBvZiB0aGUgS2FsbWFuIEZpbHRlciBWaWEgYSBTaW1wbGUgYW5kIEludHVpdGl2ZSBEZXJpdmF0aW9uLnBkZgATAAEvAAAVAAIAEP//AAAACAANABoAJACZAAAAAAAAAgEAAAAAAAAABQAAAAAAAAAAAAAAAAAAAws=}} diff --git a/buch/papers/erdbeben/teil0.tex b/buch/papers/erdbeben/teil0.tex index 8ce8ff2..c099340 100644 --- a/buch/papers/erdbeben/teil0.tex +++ b/buch/papers/erdbeben/teil0.tex @@ -23,6 +23,7 @@ Die Masse schwing jedoch in seiner Eigendynamik weiter. Relativbewegung des Bodens kann damit als Auslenkung im Zeitverlauf gemessen werden. In modernen Seismographen wird die Bodenbewegung in alle Richtungen gemessen, sowohl Horizontal als auch Vertikal. Wir konstruieren uns eine einfachere Version eines Seismographen mit eine Gehäuse, an dem zwei Federn und eine Masse befestigt sind. +Der Seismograph ist in Abbildung ~\ref{erdbeben:Seismograph} ersichtlich. Ein Sensor unter der Masse misst die Position, bzw. die Auslenkung der Feder und der Masse. Dies bedeutet, unser Seismograph kann nur in eine Dimension Messwerte aufnehmen. @@ -30,52 +31,52 @@ Dies bedeutet, unser Seismograph kann nur in eine Dimension Messwerte aufnehmen. \begin{center} \includegraphics[width=5cm]{papers/erdbeben/Apperatur} \caption{Aufbau des Seismographen mit Gehäuse, Masse, Federn und Sensor} + \label{erdbeben:Seismograph} \end{center} \end{figure} \subsection{Ziel} Unser Seismograph misst nur die Position der Masse über die Zeit. -Wir wollen jedoch die Beschleunigung $a(t)$ des Boden bzw. die Kraft $f(t)$ welche auf das Gehäuse wirkt bestimmten. -Anhand dieser Beschleunigung bzw. der Krafteinwirkung durch die Bodenbewegung wird später das Bauwerk bemessen. +Wir wollen jedoch die Beschleunigung $a(t)$ des Boden, bzw. die Kraft $f(t)$, welche auf das Gehäuse wirkt, bestimmten. +Anhand dieser Beschleunigung, bzw. der Krafteinwirkung durch die Bodenbewegung, wird später das Bauwerk bemessen. Dies bedeutet, die für uns interessante Grösse $f(t)$ wird nicht durch einen Sensor erfasst. Jedoch können wir durch zweifaches ableiten der Positionsmessung $s(t)$ die Beschleunigung der Masse berechnen. Das heisst: Die Messung ist zweifach Integriert die Kraft $f(t)$ inklusive der Eigendynamik der Masse. -Um die Bewegung der Masse zu berechnen, müssen wir Gleichungen für unser System finden. +Um die Krafteinwirkung der Masse zu berechnen, müssen wir Gleichungen für unser System finden. \subsection{Systemgleichung} -Im Fall unseres Seismographen, kann die Differentialgleichung zweiter Ordnung einer gedämpften Schwingung am harmonischen Oszillator verwendet werden. -Diese lautet: +Im Paper~\cite{erdbeben:mendezmueller} wurde das System gleich definiert und vorgegangen. +Im Fall unseres Seismographen, handelt es sich um ein Feder-Masse-Pendel. +Dieser kann durch die Differentialgleichung zweiter Ordnung einer gedämpften Schwingung am harmonischen Oszillator beschrieben werden. +Die Gleichung lautet: \begin{equation} -m\ddot s + 2k \dot s + Ds = f +m\ddot s + 2k \dot s + Ds = f. \end{equation} -mit den Konstanten $m$ = Masse, $k$ = Dämpfungskonstante und $D$ = Federkonstante. -Da die DGL linear ist, kann sie in die kompaktere und einfachere Matrix-Form umgewandelt werden. Dazu wird die Differentialgleichung zweiter Ordnung substituiert: -\[ {s_1}=s \qquad -{s_2}=\dot s, \qquad\] -Somit entstehen die Gleichungen für die Position $s(t)$ der Masse : +wobei $m$ die Masse, $k$ die Dämpfungskonstante und $D$ die Federkonstante bezeichnet. +Da die Differentialgleichung linear ist, kann sie in die kompaktere und einfachere Matrix-Form umgewandelt werden. +Dazu verwenden wir die Subsitution: +\[
s_1 = s
\qquad \text{und} \qquad
s_2 = \dot s
.
\] +Somit entstehen die Gleichungen für die Position $ \dot s_1(t)$ der Masse : \[ \dot {s_1} = {s_2}\] und -\[ \dot s_2 = -\frac{D}{m} {s_1} -\frac{2k}{m} {s_2} + \frac{f} {m} \] für die Beschleunigung $a(t)$ der Masse. - +\[ \dot s_2 = -\frac{D}{m} {s_1} -\frac{2k}{m} {s_2} + \frac{f} {m} \] +für die Beschleunigung $\dot s_2(t)$ der Masse. Diese können wir nun in der Form -\[ {s_3}=-\frac{D}{m} {s_1} -\frac{2k}{m} {s_2} + \frac{f} {m} \] +\[ f =-\frac{D}{m} {s_1} -\frac{2k}{m} {s_2} + \frac{f} {m} \] auch als Matrix-Vektor-Gleichung darstellen. Dafür wird die Gleichung in die Zustände aufgeteilt. -Die für uns relevanten Zustände sind die Position der Masse, die Geschwindigkeit der Masse und die äussere Beschleunigung des ganzen System. -Dabei muss unterschieden werden, um welche Beschleunigung es sich handelt. -Das System beinhaltet sowohl eine Beschleunigung der Masse, innere Beschleunigung, als auch eine Beschleunigung der ganzen Apparatur, äussere Beschleunigung. -In unserem Fall wird die äusseren Beschleunigung gesucht, da diese der Erdbebenanregung gleich kommt. -\begin{equation} -\frac{d}{dt} \left(\begin{array}{c} {s_1} \\ {s_2} \end{array}\right) = \left( - \begin{array}{ccc} -0 & 1& 0 \\ -- \frac{D}{m} &-\frac{2k}{m} & \frac{1} {m}\\ -\end{array}\right) \left(\begin{array}{c} {s_1} \\ {s_2} \\ {s_3} \end{array}\right). -\end{equation} - -Durch Rücksubstituion ergibt sich: +Die für uns relevanten Zustände sind die Position der Masse, die Geschwindigkeit der Masse und die äussere Beschleunigung des ganzen Systems. + +Dabei muss unterschieden werden, um welche Beschleunigung es sich handelt. +Das System beinhaltet sowohl eine Beschleunigung der Masse (innere Beschleunigung) als auch eine Beschleunigung der ganzen Apparatur (äussere Beschleunigung). +In unserem Fall wird die äusseren Beschleunigung gesucht, da diese der Erdbebenanregung gleich kommt. +Dazu wird ein Zustandsvektor definiert: +\[ + \left(\begin{array}{c} {s_1} \\ {s_2} \\ {f} \end{array}\right). + \] +Durch Rücksubstituion ergibt sich uns folgende Systemgleichung in Matrix schreibweise, , wobei $\sot {s_1}= v$ ist: \begin{equation} -\frac{d}{dt} \left(\begin{array}{c} s(t) \\ v(t) \end{array}\right) = \left( +\frac{d}{dt} \left(\begin{array}{c} s(t) \\ v(t) \\ f(t) \end{array}\right) = \left( \begin{array}{ccc} 0 & 1& 0 \\ - \frac{D}{m} &-\frac{2k}{m} & \frac{1} {m}\\ diff --git a/buch/papers/erdbeben/teil1.tex b/buch/papers/erdbeben/teil1.tex index e07800f..6c334bf 100644 --- a/buch/papers/erdbeben/teil1.tex +++ b/buch/papers/erdbeben/teil1.tex @@ -14,6 +14,8 @@ \rhead{Kalman-Filter} \section{Kalman-Filter} +Interessante Grösse ist also Integral von Überlagerung zweier Kräfte. +Wir brauchen also dir zweite Ableitung von der Messung , ohne deren Eigendynamik. Da wir die äussere Kraft nicht direkt messen können, benötigen wir ein Werkzeug, welches aus der gemessenen Position, die Krafteinwirkung auf unsere System schätzt. Dies ist eine typische Anwendung für das Kalman-Filter. Unser Ziel ist es, anhand der Messung die eigentlich interessante Grösse $f$ zu bestimmen. @@ -23,8 +25,8 @@ Die Idee dahinter ist, dass das Kalman-Filter die nicht-deterministische Grösse Für mehrere Dimensionen (x,y,z) würde der Pythagoras für das System benötigt werden. Da sich der Pythagoras bekanntlich nicht linear verhält, kann kein lineares Kalman-Filter implementiert werden. Da das Kalman-Filter besonders effektiv und einfach für lineare Abläufe geeignet ist, würde eine zweidimensionale Betrachtung den Rahmen dieser Arbeit sprengen. -Für ein nicht-lineares System werden Extended Kalman-Filter benötigt, bei denen die System-Matrix (A) durch die Jacobi-Matrix des System ersetzt wird. Einfachheitshalber beschränken wir uns auf den linearen Fall, da dadurch die wesentlichen Punkte bereits aufgezeigt werden. +Für ein nicht-lineares System werden Extended Kalman-Filter benötigt, bei denen die System-Matrix (A) durch die Jacobi-Matrix des System ersetzt wird. \subsection{Geschichte} Das Kalman-Filter wurde 1960 von Rudolf Emil Kalman entdeckt und direkt von der NASA für die Appollo Mission benutzt. @@ -35,57 +37,60 @@ Das Filter schätzt den Zustand eines Systems anhand von Messungen und kann den Das Kalman-Filter schätzt den wahrscheinlichsten Wert zwischen Normalverteilungen. Dies bedeutet, das Filter schätzt nicht nur den Mittelwert, sondern auch die Standartabweichung. Da Normalverteilungen dadurch vollständig definiert sind, schätzt ein Kalman-Filter die gesamte Verteilungsfunktion des Zustandes. +In der Abbildung~\ref{erdbeben: Zwei Normalverteilungen} sind zwei Funktionen dargestellt. Die eine Funktion zeigt die errechnete Vorhersage des Zustands, bzw. deren Normalverteilung. Die andere Funktion zeigt die verrauschte Messung des nächsten Zustand, bzw. deren Normalverteilung. -Wie man am Beispiel der Gauss-Verteilungen unten sehen kann, ist sowohl der geschätzte Zustand als auch der gemessene Zustand normalverteilt und haben dementsprechend unterschiedliche Standardabweichungen $\sigma$ und Erwartungswerte $\mu$. - +Wie man am Beispiel der Gauss-Verteilungen in Abblidung~\ref{erdbeben: Zwei Normalverteilungen} sehen kann, ist sowohl der geschätzte Zustand als auch der gemessene Zustand normalverteilt und haben dementsprechend unterschiedliche Standardabweichungen $\sigma$ und Erwartungswerte $\mu$. Dies wird in~\cite{erdbeben:aragher_understanding_2012}beschrieben. \begin{figure} \begin{center} \includegraphics[width=5cm]{papers/erdbeben/Gausskurve2.pdf} \caption{Zwei Normalerteilungen; Die eine Funktion zeigt die Vorhersage, die andere die Messung} + \label{erdbeben: Zwei Normalverteilungen} \end{center} \end{figure} - - +Wir haben eine Vorhersage aus der Systemdynamik und eine Messung des Zustandes. +Diese widersprechen sich im Allgemeinen. +Jedoch wissen wir die Wahrscheinlichkeiten der beiden Aussagen. Um eine genauere Schätzung des Zustandes zu machen, wird nun ein Wert zwischen den beiden Verteilungen berechnet. Nun wird eine Eigenschaft der Normalverteilung ausgenutzt. Durch das Multiplizieren zweier Normalverteilungen entsteht eine neue Normalverteilung. Wir haben eine Normalverteilung der Vorhersage: - -\[ {y_1}(x;{\mu_1},{\sigma_1})=\frac{1}{\sqrt{2\pi\sigma_1^2}}\quad e^{-\frac{(x-{\mu_1})^2}{2{\sigma_1}^2}} \] +\[ +{y_1}(x;{\mu_1},{\sigma_1})=\frac{1}{\sqrt{2\pi\sigma_1^2}}\quad e^{-\frac{(x-{\mu_1})^2}{2{\sigma_1}^2}} +\] und der Messung: -\[ {y_2}(x;{\mu_2},{\sigma_2})=\frac{1}{\sqrt{2\pi\sigma_2^2}}\quad e^{-\frac{(x-{\mu_2})^2}{2{\sigma_2}^2}}. \] - - - -Diesen werden nun Multipliziert und durch deren Fläche geteilt um sie wieder zu Normieren: -\[ -{y_f}(x;{\mu_f},{\sigma_f})=\frac{ \frac{1}{\sqrt{2\pi\sigma_1^2}}e^{-\frac{(x-{\mu_1})^2}{2{\sigma_1}^2}} \cdot \frac{1}{\sqrt{2\pi\sigma_2^2}}e^{-\frac{(x-{\mu_2})^2}{2{\sigma_2}^2}}}{\int {y_1}\cdot{y_2} dx\,} - \] - +\[ +{y_2}(x;{\mu_2},{\sigma_2})=\frac{1}{\sqrt{2\pi\sigma_2^2}}\quad e^{-\frac{(x-{\mu_2})^2}{2{\sigma_2}^2}}. +\] +Diesen werden nun multipliziert und durch deren Fläche geteilt um sie wieder zu normieren, $\odot$ beschreibt dabei die Multiplikation und die Normierung auf den Flächeninhalt eins : +\begin{align*}
{y_f}(x; {\mu_f}, {\sigma_f}) = {y_1}(x;{ \mu_1},{ \sigma_1}) \odot {y_2}(x; {\mu_2}, {\sigma_2}) + &= + \frac{1}{\sqrt{2\pi\sigma_1^2}}\quad e^{-\frac{(x-{\mu_1})^2}{2{\sigma_1}^2}} \odot \frac{1}{\sqrt{2\pi\sigma_2^2}}\quad e^{-\frac{(x-{\mu_2})^2}{2{\sigma_2}^2}} + \\ + &=
\frac{ \frac{1}{\sqrt{2\pi\sigma_1^2}}e^{-\frac{(x-{\mu_1})^2}{2{\sigma_1}^2}} \cdot \frac{1}{\sqrt{2\pi\sigma_2^2}}e^{-\frac{(x-{\mu_2})^2}{2{\sigma_2}^2}}}{\int {y_1} {y_2} dx}.
\end{align*} Diese Kombination der beiden Verteilungen resultiert wiederum in einer Normalverteilung -\[ {y_f}(x; {\mu_f}, {\sigma_f}) = {y_1}(x;{ \mu_1},{ \sigma_1}) {\cdot y_2}(x; {\mu_2}, {\sigma_2}), \] mit Erwartungswert \[ \mu_f = \frac{\mu_1\sigma_2^2 + \mu_2 \sigma_1^2}{\sigma_1^2 + \sigma_2^2} \] und Varianz -\[ \sigma_f^2 = \frac{\sigma_1^2 \sigma_2^2}{\sigma_1^2 + \sigma_2^2}. \] - +\[ +\sigma_f^2 = \frac{\sigma_1^2 \sigma_2^2}{\sigma_1^2 + \sigma_2^2}. +\] Dadurch gleicht sich die neue Kurve den anderen an. Interessant daran ist, dass die fusionierte Kurve sich der genauere Normal-Verteilung anpasst. Ist ${\sigma_2}$ klein und ${\sigma_1}$ gross, so wird sich die fusionierte Kurve näher an ${y_2}(x;{\mu_2},{\sigma_2})$ begeben. -Sie ist also gewichtet und die best mögliche Schätzung. - - +Somit ist $\mu_f$ ist das gewichtete Mittel der beiden $\mu_{1,2}$, und die Varianzen sind die Gewichte! +Die neue Funktion ist die best mögliche Schätzung für zwei Verteilungen, welche den selben Zustand beschreiben. +Dies ist in der Abbildung~\ref{erdbeben:Gauss3} anhand der rote Funktion ersichtlich. \begin{figure} \begin{center} \includegraphics[width=5cm]{papers/erdbeben/Gausskurve3.pdf} \caption{Durch das Multiplizieren der blauen und der orangen Verteilung entsteht die die rote, optimale Funktion} + \label{erdbeben:Gauss3} \end{center} \end{figure} - - Was in zwei Dimensionen erklärt wurde, funktioniert auch in mehreren Dimensionen. Dieses Prinzip mach sich das Kalman Filter zu nutze, und wird von uns für die Erdbeben Berechnung genutzt. \section{Filter-Matrizen} +Da wir nun ein Werkzeug besitzen, dass die Beschleunigung, welche auf das Gehäuse wirkt, ermitteln kann, wird dieses nun Schritt für Schritt erklärt. Um den Kalman Filter zu starten, müssen gewisse Bedingungen definiert werden. In diesem Abschnitt werden die einzelnen Parameter und Matrizen erklärt und erläutert, wofür sie nützlich sind. @@ -94,8 +99,6 @@ In diesem Abschnitt werden die einzelnen Parameter und Matrizen erklärt und erl Das Filter benötigt eine Anfangsbedingung. In unserem Fall ist es die Ruhelage, die Masse bewegt sich nicht. Zudem erfährt die Apparatur keine äussere Kraft. - - \[ {x_0 }= \left( \begin{array}{c} {s_0}\\ {v_0}\\{f_0}\end{array}\right) = \left( \begin{array}{c} 0\\ 0\\ 0\end{array}\right) \] \subsubsection*{Anfangsfehler / Kovarianzmatrix $P$} @@ -108,7 +111,6 @@ Kovarianz: Cov(x, y) und Varianz: Var(x) = Cov(x, x) In unserem Fall ist der Anfangszustand gut bekannt. Wir gehen davon aus, dass das System in Ruhe und in Abwesenheit eines Erdbeben startet, somit kann die Matrix mit Nullen bestückt werden. Als Initialwert für die Kovarianzmatrix ergibt sich - \[ {P_0 }= \left( @@ -145,9 +147,9 @@ Die Matrix $\Phi$ beschreibt die Übergänge zwischen zeitlich aufeinanderfolgen \subsubsection*{Prozessrauschkovarianzmatrix $Q$} Die Prozessrauschmatrix teilt dem Filter mit, wie sich der Prozess verändert. -Kalman-Filter berücksichtigen sowohl Unsicherheiten wie Messfehler und -rauschen. -In der Matrix $Q$ geht es jedoch im die Unsicherheit die der Prozess mit sich bringt. -Bei unserem Modell könnte das beispielsweise ein Windstoss an die Masse sein. +Kalman-Filter berücksichtigen Unsicherheiten wie Messfehler und -rauschen. +In der Matrix $Q$ geht es jedoch um die Unsicherheit, die der Prozess mit sich bringt. +Bei unserem Modell könnte das beispielsweise ein Windstoss an die Masse sein oder auch die Ungenauigkeiten im Modell, wie die Annahme das dich die Kraft nicht ändert. Für uns wäre dies: \[ Q = \left( @@ -157,7 +159,6 @@ Q = \left( 0 & 0& {\sigma_f }^2\\ \end{array}\right) \] - Die Standabweichungen müssten statistisch ermittelt werden, da der Fehler nicht vom Sensor kommt und somit nicht vom Hersteller gegeben ist. Das Bedeutet wiederum dass $Q$ die Unsicherheit des Prozesses beschreibt und nicht die der Messung. @@ -165,13 +166,15 @@ Das Bedeutet wiederum dass $Q$ die Unsicherheit des Prozesses beschreibt und nic Die Messmatrix gibt an, welche Parameter gemessen werden. $H$ ist die Gleichung die für die Vorhersage der Messung. In unserem Falle ist es die Position der Massen. - -\[ H = (1, 0, 0) \] +\[ +H = (1, 0, 0) +\] \subsubsection*{Messrauschkovarianz $R$} Die Messrauschkovarianzmatrix beinhaltet, wie der Name schon sagt, das Rauschen der Messung. In unserem Fall wird nur die Position der Masse gemessen. Da wir keine anderen Sensoren haben ist $R$ lediglich: -\[ R= ({\sigma_{sensor}}^2). +\[ +R= ({\sigma_\mathrm{sensor}}^2). \] Diese Messrauchen wird meistens vom Sensorhersteller angegeben. Für unsere theoretische Apparatur wird hier ein kleiner Fehler eingesetzt da heutige Sensoren sehr genau messen können. @@ -182,19 +185,25 @@ Zuerst wird der nächste Zustand der Masse vorhergesagt, danach wird die Messung Das Filter berechnet aufgrund der aktuellen Schätzung eine Vorhersage. Diese wird, sobald verfügbar, mit der Messung verglichen. Aus dieser Differenz und den Unsicherheiten des Prozesses ($Q$) und der Messung ($R$) wird der wahrscheinlichste, neue Zustand geschätzt. +Dabei muss genau auf den Index geachtet werden. Nach dem Artikel~\cite{erdbeben:wikipedia} ist die Indexierung so genormt: +Der Zeitschritt wird mit $k$ definiert, $k-1$ ist somit ein Zeitschritt vor $k$. +Auf der linken Seite von | wird der aktuelle Zustand verlangt, bzw. ausgegeben, auf der rechten Seiten den bisherigen Zustand. +Dies bedeutet, dass die Notation $x_{n|m}$ die Schätzung von $x$ zum Zeitpunkt $n$ bis und mit zur Zeitpunkt $m \leq \ n$ präsentiert. \subsubsection*{Vorhersage} Im Filterschritt Vorhersage wird der nächste Zustand anhand des Anfangszustand und der Systemmatrix berechnet. Dies funktioniert mit dem Rechenschritt: -\[ -{x_{k-1}}=\Phi \cdot {x_{k-1}}= \exp(A\Delta t)\cdot{x_{k-1}}. - \] - -Die Kovarianz $P_{pred}$ wird ebenfalls neu berechnet. Da wir ein mehrdimensionales System haben, kommt noch die Prozessunsicherheit $Q$ dazu, so dass die Unsicherheit des Anfangsfehlers $P$ laufend verändert. +\[ +{x_{k|k-1}}=\Phi{x_{k-1|k-1}}= \exp(A\Delta t){x_{k-1|k-1}}. +\] +Die Kovarianz $P_{k|k-1}$ wird ebenfalls neu berechnet. Zudem kommt noch die Prozessunsicherheit $Q$ dazu, so dass die Unsicherheit des Anfangsfehlers $P$ laufend verändert. Dies funktioniert durch multiplizieren der Systemmatrix mit dem aktualisierten Anfangsfehler. Dazu wird noch die Prozessunsicherheit addiert, somit entsteht die Gleichung -\[ {P_{k-1}} = {\Phi_k} {P_{k-1}} {\Phi_k} ^T + {Q_{k-1}} .\] -Es vergeht genau $t$ Zeit, und dieser Vorgang wird wiederholt. +\[ +{P_{k|k-1}}=\Phi {P_{k-1|k-1}} {\Phi _{k}}^T + {Q_{k-1}}. +\] +Es vergeht genau $\Delta t$ Zeit, und dieser Vorgang wird wiederholt. +Das hochgestellte T bezeichnet die transponierte Matrix. Dabei wird in den späteren Schritten überprüft, wie genau die letzte Anpassung von $P$ zur Messung stimmt. Ist der Unterschied klein, wird die Kovarianz $P$ kleiner, ist der Unterschied gross, wird auch die Kovarianz grösser. Das Filter passt sich selber an und korrigiert sich bei grosser Abweichung. @@ -202,74 +211,83 @@ Das Filter passt sich selber an und korrigiert sich bei grosser Abweichung. \subsubsection*{Messen} Der Sensor wurde noch nicht benutz, doch genau der liefert Werte für das Filter. Die aktuellen Messwerte $z$ werden die Innovation $w$ mit dem Zustandsvektor $x$ und der Messmatrix $H$ zusammengerechnet. -Hier bei wird lediglich die Messung mit dem Fehler behaftet, und die Messmatrix $H$ mit der Vorhersage multipliziert - -\[{w_{k}}={z_{k}}-{H}\cdot{x_{k-1}}.\] - +Hier bei wird lediglich die Messung mit dem Fehler behaftet, und die Messmatrix $H$ mit der Vorhersage multipliziert. +\[ +{w_{k}}={z_{k}}-{H}{x_{k|k-1}}. +\] Die Innovation ist der Teil der Messung, die nicht durch die Systemdynamik erklärt werden kann. Die Hilfsgröße Innovation beschreibt, wie genau die Vorhersage den aktuellen Messwert mittels der Systemmatrix $\Phi$ beschreiben kann. Für eine schlechte Vorhersage wird die dazugehörige Innovation gross, für eine genaue Vorhersage dagegen klein sein. Entsprechende Korrekturen müssen dann gross bzw. nur gering ausfallen. -Innovation = Messung - Vorhersage. Dies ist intuitiv logisch, eine Innovation von 0 bedeutet, dass die Messung nichts Neues hervorbrachte. +Innovation = Messung - Vorhersage. Dies leuchtet ein, eine Innovation von 0 bedeutet, dass die Messung nichts Neues hervorbrachte. Im nächsten Schritt wir analysiert, mit welcher Kovarianz weiter gerechnet wird. Hierbei wird die Unsicherheit $P$, die Messmatrix $H$ und die Messunsicherheit $R$ miteinander verrechnet. \[ -{S_{k}}={H}{P_{k-1}}{H}^T+{R_{k}} - \] +{S_{k}}={H}{P_{k|k-1}}{H}^T+{R_{k}} +\] \subsubsection*{Aktualisieren} Im nächsten Schritt kommt nun die Wahrscheinlichkeit dazu. -\[ -{K_{k}}= {{P_{k-1}} \cdot {H_{k}^T}}\cdot {S_{k}}^{-1} - \] +\[{K_{k}}= {P_{k|k-1}} {H^T}{S_{k}^{-1}}\] Dieser Vorgang wird Kalman-Gain genannt. -Er sagt aus, welcher Kurve mehr Vertraut werden soll, dem Messwert oder der Systemdynamik. -Das Kalman-Gain wird geringer, wenn der Messwert dem vorhergesagten Systemzustand entspricht. -Sind die Messwerte komplett anders als die Vorhersage, werden die Elemente in der Matrix $K$ grösser. -Anhand der Informationen aus dem Kalman-Gain $K$ wird das System aktualisiert. +Das Kalman-Gain gibt dem Zustand die Gewichtung, bzw. wie die Vorhersage auf den Zustand passt. +Vereinfacht gesagt: Es wird das das Verhältnis zwischen der Unsicherheit der Vorhersage $P_k$ zu der zugehörigen Messunsicherheit $R_k$ gebildet. +In unserem Fall wird werden die Elemente der Kalman-Matrix vorweg berechnet, da das Kalman-Gain ohne Messungen auskommt. -\[ -{x_{k|k}}={x_{k-1}}+({K_{k}}\cdot {w_{k}}) - \] +Anhand der Informationen aus dem Kalman-Gain $K$ wird das System aktualisiert. +\[ +{x_{k|k}}={x_{k|k-1}}+{K_{k}}{w_{k}} +\] +Dabei wird der Unterschied zwischen dem erwarteten, errechneten, Zustand und dem gemessenen Zustand berechnet. Dazu kommt eine neue Kovarianz für den nächste Vorhersageschritt: - -\[ -{P_{k}}=(I-({K_{k}} \cdot {H})) \cdot {P_{k-1}} - \] - +\[ +{P_{k|k}}=(I-{K_{k}}{H}){P_{k|k-1}} +\] Der ganze Algorithmus und beginnt wieder mit der Vorhersage - -\[ -{x_{k-1}}=\Phi \cdot {x_{k-1}}= \exp(A\Delta t)\cdot{x_{k-1}}. - \] - +\[ +{x_{k|k-1}}=\Phi{x_{k-1|k-1}}= \exp(A\Delta t){x_{k|k-1}}. +\] \subsection{Zusammenfassung } Zusammenfassend kann das Kalman-Filter in offizieller Typus dargestellt werden. Dabei beginnt das Filter mit dem Anfangszustand für $k=0$ 1. Nächster Zustand vorhersagen -\[{x_{k-1}}={\Phi} \cdot {x_{k-1}}= \exp(A\Delta t)\cdot{x_{k-1}}.\] +\[ +{x_{k|k-1}}=\Phi{x_{k-1|k-1}}= \exp(A\Delta t){x_{k-1|k-1}}. +\] 2. Nächste Fehlerkovarianz vorhersagen -\[{P_{k-1}}={\Phi} {P_{k-1}} {\Phi _{k}}^T + {Q_{k-1}}.\] +\[ +{P_{k|k-1}}=\Phi {P_{k-1|k-1}} {\Phi _{k}}^T + {Q_{k-1}}. +\] 3. Zustand wird gemessen -\[{w_{k}}={z_{k}}-{H}\cdot{x_{k-1}}.\] +\[ +{w_{k}}={z_{k}}-{H}{x_{k|k-1}}. +\] 4. Innovation (= Messung - Vorhersage) -\[ {S_{k}}={H}{P_{k-1}}{H}^T+{R_{k}}\] +\[ +{S_{k}}={H}{P_{k|k-1}}{H}^T+{R_{k}} +\] 5. Das Kalman Filter anwenden -\[{K_{k}}= {P_{k-1}} \cdot {H^T}\cdot {S_{k}^{-1}}\] +\[ +{K_{k}}= {P_{k|k-1}} {H^T}{S_{k}^{-1}} +\] 6. Schätzung aktualisieren -\[{x_{k}}={x_{k-1}}+({K_{k}}\cdot {w_{k}}) \] +\[ +{x_{k|k}}={x_{k|k-1}}+{K_{k}}{w_{k}} +\] 7. Fehlerkovarianz aktualisieren -\[{P_{k}}=(I-({K_{k}}\cdot {H})) \cdot {P_{k-1}} \] +\[ +{P_{k|k}}=(I-{K_{k}}{H}){P_{k|k-1}} +\] 8. Die Outputs von $k$ werden die Inputs für ${k-1}$ und werden wieder im Schritt 1 verwendet diff --git a/buch/papers/multiplikation/Makefile b/buch/papers/multiplikation/Makefile index 8f04c2c..8f04c2c 100644..100755 --- a/buch/papers/multiplikation/Makefile +++ b/buch/papers/multiplikation/Makefile diff --git a/buch/papers/multiplikation/Makefile.inc b/buch/papers/multiplikation/Makefile.inc index b78d67e..074020f 100644..100755 --- a/buch/papers/multiplikation/Makefile.inc +++ b/buch/papers/multiplikation/Makefile.inc @@ -7,8 +7,7 @@ dependencies-multiplikation = \ papers/multiplikation/packages.tex \ papers/multiplikation/main.tex \ papers/multiplikation/references.bib \ - papers/multiplikation/teil0.tex \ - papers/multiplikation/teil1.tex \ - papers/multiplikation/teil2.tex \ - papers/multiplikation/teil3.tex + papers/multiplikation/einlteung.tex \ + papers/multiplikation/loesungsmethoden.tex \ + papers/multiplikation/problemstellung.tex diff --git a/buch/papers/multiplikation/code/Figure_1.png b/buch/papers/multiplikation/code/Figure_1.png Binary files differnew file mode 100755 index 0000000..9def15a --- /dev/null +++ b/buch/papers/multiplikation/code/Figure_1.png diff --git a/buch/papers/multiplikation/code/MM b/buch/papers/multiplikation/code/MM Binary files differnew file mode 100755 index 0000000..f07985f --- /dev/null +++ b/buch/papers/multiplikation/code/MM diff --git a/buch/papers/multiplikation/code/MM.c b/buch/papers/multiplikation/code/MM.c new file mode 100755 index 0000000..04c4dab --- /dev/null +++ b/buch/papers/multiplikation/code/MM.c @@ -0,0 +1,465 @@ +#include <stdio.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <time.h>
+#include <omp.h>
+#include "c_matrix.h"
+#include <gsl/gsl_cblas.h>
+#include <string.h>
+
+void MM(int *A, int *B, int *C, int n);
+void openMP_MM(int *A, int *B, int *C, int n);
+void winograd(int *A, int *B, int *C, int n);
+int winograd_inner(int *a, int *b, int n);
+void run_algo(void (*algo)(), char alog_name[], int print);
+void run_algo_cblas(int print);
+void MM_dc(int *A, int *B, int *C, int n);
+void strassen(int *A, int *B, int *C, int n);
+void printMatrix(int *C, int n);
+void printMatrix_double(double *C, int n);
+void split(int *in, int *out, int n, int col, int row);
+void join(int *in, int *out, int n, int col, int row);
+void add(int *A, int *B, int *C, int n);
+void sub(int *A, int *B, int *C, int n);
+void multiply(int *A, int *B, int *C, int n);
+
+int main() {
+ // omp_set_dynamic(0);
+ // omp_set_num_threads(4);
+// run_algo(openMP_MM, "openMP_MM",0);
+ run_algo(MM_dc, "MM_dc",0);
+ run_algo(strassen, "strassen",0);
+
+ run_algo(MM, "MM", 0);
+ // run_algo(winograd, "winograd", 0);
+ run_algo_cblas(0);
+
+ return 0;
+}
+
+void MM(int *A, int *B, int *C, int n) {
+ for (int i = 0; i < n; ++i) {
+ for (int j = 0; j < n; ++j) {
+ int sum = 0;
+ for (int k = 0; k < n; ++k) {
+ sum += (*((A + i * n) + k)) * (*((B + k * n) + j));
+ }
+ *((C + i * n) + j) = sum;
+ }
+ }
+}
+
+int winograd_inner(int *a, int *b, int n){
+ int ab = 0;
+ if(n%2==0)
+ {
+ int xi = 0;
+ int etha = 0;
+ for(int i = 0; i<n/2;++i)
+ {
+ xi += a[2*i]*a[2*i+1];
+ etha += b[2*i]*b[2*i+1];
+ ab += (a[2*i]+b[2*i+1])*(a[2*i+1]+b[2*i]);
+ }
+ ab = ab-etha-xi;
+ }
+ return ab;
+ }
+
+ void winograd(int *A, int *B, int *C, int n) {
+
+ int xi_array[n];
+ int etha_array[n];
+ int xi = 0;
+ int etha = 0;
+ int ab = 0;
+
+ for (int i = 0; i < n; ++i) {
+ xi = 0;
+ etha = 0;
+ for(int k = 0;k<n/2;++k)
+ {
+ xi += (*((A + i * n) + 2*k))*(*((A + i * n) + (2*k+1)));
+ etha += (*((B + 2*k * n) + i))*(*((B + (2*k+1) * n) + i));
+ }
+ xi_array[i] = xi;
+ etha_array[i] = etha;
+ }
+
+ for (int i = 0; i < n; ++i) {
+ for (int j = 0; j < n; ++j) {
+ ab = 0;
+ for(int k = 0;k<n/2;++k)
+ {
+ ab += ((*((A + i * n) + 2*k))+(*((B + (2*k+1) * n) + j)))*((*((A + i * n) + (2*k+1)))+(*((B + 2*k * n) + j)));
+ }
+ *((C + i * n) + j) = ab-etha_array[j]-xi_array[i];
+ }
+ }
+
+
+
+
+ // for (int i = 0; i < n; ++i) {
+ // int *a = (int*) malloc(n * sizeof(int));
+ // for(int k = 0; k<n; ++k)
+ // {
+ // a[k] = (*((A + i * n) + k));
+ // }
+ //
+ // for (int j = 0; j < n; ++j) {
+ // int *b = (int*) malloc(n * sizeof(int));
+ // for(int k = 0; k<n; ++k)
+ // {
+ // b[k] =(*((B + k * n) + j));
+ // }
+ // *((C + i * n) + j) = winograd_inner(a,b,n);
+ // }
+ // }
+ }
+
+
+void openMP_MM(int *A, int *B, int *C, int n) {
+
+ #pragma omp parallel for
+ for (int i = 0; i < n; ++i) {
+ for (int j = 0; j < n; ++j) {
+ int sum = 0;
+ for (int k = 0; k < n; ++k) {
+ sum += (*((A + i * n) + k)) * (*((B + k * n) + j));
+ }
+ *((C + i * n) + j) = sum;
+ }
+ }
+}
+
+void MM_dc(int *A, int *B, int *C, int n) {
+ if (n <= 2) {
+ MM((int*) A, (int*) B, (int*) C, n);
+ } else {
+ int *A11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *A12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *A21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *A22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ split((int*) A, (int*) A11, n / 2, 0, 0);
+ split((int*) A, (int*) A12, n / 2, 0, n / 2);
+ split((int*) A, (int*) A21, n / 2, n / 2, 0);
+ split((int*) A, (int*) A22, n / 2, n / 2, n / 2);
+ split((int*) B, (int*) B11, n / 2, 0, 0);
+ split((int*) B, (int*) B12, n / 2, 0, n / 2);
+ split((int*) B, (int*) B21, n / 2, n / 2, 0);
+ split((int*) B, (int*) B22, n / 2, n / 2, n / 2);
+
+ int *tmp1 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *tmp2 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *tmp3 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *tmp4 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *tmp5 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *tmp6 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *tmp7 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *tmp8 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ MM_dc((int*) A11, (int*) B11, (int*) tmp1, n / 2);
+ MM_dc((int*) A12, (int*) B21, (int*) tmp2, n / 2);
+ MM_dc((int*) A11, (int*) B12, (int*) tmp3, n / 2);
+ MM_dc((int*) A12, (int*) B22, (int*) tmp4, n / 2);
+ MM_dc((int*) A21, (int*) B11, (int*) tmp5, n / 2);
+ MM_dc((int*) A22, (int*) B21, (int*) tmp6, n / 2);
+ MM_dc((int*) A21, (int*) B12, (int*) tmp7, n / 2);
+ MM_dc((int*) A22, (int*) B22, (int*) tmp8, n / 2);
+
+ free(A11);
+ free(A12);
+ free(A21);
+ free(A22);
+ free(B11);
+ free(B12);
+ free(B21);
+ free(B22);
+
+ int *C11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *C12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *C21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *C22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ add((int*) tmp1, (int*) tmp2, (int*) C11, n / 2);
+ add((int*) tmp3, (int*) tmp4, (int*) C12, n / 2);
+ add((int*) tmp5, (int*) tmp6, (int*) C21, n / 2);
+ add((int*) tmp7, (int*) tmp8, (int*) C22, n / 2);
+
+ free(tmp1);
+ free(tmp2);
+ free(tmp3);
+ free(tmp4);
+ free(tmp5);
+ free(tmp6);
+ free(tmp7);
+ free(tmp8);
+
+ join((int*) C11, (int*) C, n / 2, 0, 0);
+ join((int*) C12, (int*) C, n / 2, 0, n / 2);
+ join((int*) C21, (int*) C, n / 2, n / 2, 0);
+ join((int*) C22, (int*) C, n / 2, n / 2, n / 2);
+
+ free(C11);
+ free(C12);
+ free(C21);
+ free(C22);
+
+ }
+}
+
+void strassen(int *A, int *B, int *C, int n) {
+ if (n <= 2) {
+
+ int P, Q, R, S, T, U, V;
+ P = ((*((A + 0 * n) + 0)) + (*((A + 1 * n) + 1)))
+ * ((*((B + 0 * n) + 0)) + (*((B + 1 * n) + 1)));
+ Q = ((*((A + 1 * n) + 0)) + (*((A + 1 * n) + 1)))
+ * ((*((B + 0 * n) + 0)));
+ R = ((*((A + 0 * n) + 0)))
+ * ((*((B + 0 * n) + 1)) - (*((B + 1 * n) + 1)));
+ S = ((*((A + 1 * n) + 1)))
+ * ((*((B + 1 * n) + 0)) - (*((B + 0 * n) + 0)));
+ T = ((*((A + 0 * n) + 0)) + (*((A + 0 * n) + 1)))
+ * ((*((B + 1 * n) + 1)));
+ U = ((*((A + 1 * n) + 0)) - (*((A + 0 * n) + 0)))
+ * ((*((B + 0 * n) + 0)) + (*((B + 0 * n) + 1)));
+ V = ((*((A + 0 * n) + 1)) - (*((A + 1 * n) + 1)))
+ * ((*((B + 1 * n) + 0)) + (*((B + 1 * n) + 1)));
+ (*((C + 0 * n) + 0)) = P + S - T + V;
+ (*((C + 0 * n) + 1)) = R + T;
+ (*((C + 1 * n) + 0)) = Q + S;
+ (*((C + 1 * n) + 1)) = P + R - Q + U;
+
+ } else {
+ int *A11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *A12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *A21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *A22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *B22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ split((int*) A, (int*) A11, n / 2, 0, 0);
+ split((int*) A, (int*) A12, n / 2, 0, n / 2);
+ split((int*) A, (int*) A21, n / 2, n / 2, 0);
+ split((int*) A, (int*) A22, n / 2, n / 2, n / 2);
+ split((int*) B, (int*) B11, n / 2, 0, 0);
+ split((int*) B, (int*) B12, n / 2, 0, n / 2);
+ split((int*) B, (int*) B21, n / 2, n / 2, 0);
+ split((int*) B, (int*) B22, n / 2, n / 2, n / 2);
+
+ int *P = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *Q = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *R = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *S = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *T = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *U = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *V = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ int *addA = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *addB = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ add((int*) A11, (int*) A22, (int*) addA, n / 2);
+ add((int*) B11, (int*) B22, (int*) addB, n / 2);
+ strassen((int*) addA, (int*) addB, (int*) P, n / 2);
+
+ add((int*) A21, (int*) A22, (int*) addA, n / 2);
+ strassen((int*) addA, (int*) B11, (int*) Q, n / 2);
+
+ sub((int*) B12, (int*) B22, (int*) addB, n / 2);
+ strassen((int*) A11, (int*) addB, (int*) R, n / 2);
+
+ sub((int*) B21, (int*) B11, (int*) addB, n / 2);
+ strassen((int*) A22, (int*) addB, (int*) S, n / 2);
+
+ add((int*) A11, (int*) A12, (int*) addA, n / 2);
+ strassen((int*) addA, (int*) B22, (int*) T, n / 2);
+
+ sub((int*) A21, (int*) A11, (int*) addA, n / 2);
+ add((int*) B11, (int*) B12, (int*) addB, n / 2);
+ strassen((int*) addA, (int*) addB, (int*) U, n / 2);
+
+ sub((int*) A12, (int*) A22, (int*) addA, n / 2);
+ add((int*) B21, (int*) B22, (int*) addB, n / 2);
+ strassen((int*) addA, (int*) addB, (int*) V, n / 2);
+
+ free(A11);
+ free(A12);
+ free(A21);
+ free(A22);
+ free(B11);
+ free(B12);
+ free(B21);
+ free(B22);
+ free(addA);
+ free(addB);
+
+ int *C11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *C12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *C21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *C22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ int *resAdd1 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+ int *resAdd2 = (int*) malloc(n / 2 * n / 2 * sizeof(int));
+
+ add((int*) R, (int*) T, (int*) C12, n / 2);
+ add((int*) Q, (int*) S, (int*) C21, n / 2);
+
+ add((int*) P, (int*) S, (int*) resAdd1, n / 2);
+ add((int*) resAdd1, (int*) V, (int*) resAdd2, n / 2);
+ sub((int*) resAdd2, (int*) T, (int*) C11, n / 2);
+
+ add((int*) P, (int*) R, (int*) resAdd1, n / 2);
+ add((int*) resAdd1, (int*) U, (int*) resAdd2, n / 2);
+ sub((int*) resAdd2, (int*) Q, (int*) C22, n / 2);
+
+ free(P);
+ free(Q);
+ free(R);
+ free(S);
+ free(T);
+ free(U);
+ free(V);
+ free(resAdd1);
+ free(resAdd2);
+
+ join((int*) C11, (int*) C, n / 2, 0, 0);
+ join((int*) C12, (int*) C, n / 2, 0, n / 2);
+ join((int*) C21, (int*) C, n / 2, n / 2, 0);
+ join((int*) C22, (int*) C, n / 2, n / 2, n / 2);
+
+ free(C11);
+ free(C12);
+ free(C21);
+ free(C22);
+ }
+}
+
+void add(int *A, int *B, int *C, int n) {
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ *((C + i * n) + j) = *((A + i * n) + j) + *((B + i * n) + j);
+ }
+ }
+}
+
+void sub(int *A, int *B, int *C, int n) {
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ *((C + i * n) + j) = *((A + i * n) + j) - *((B + i * n) + j);
+ }
+ }
+}
+
+void multiply(int *A, int *B, int *C, int n) {
+ int mul;
+
+ for (int i = 0; i < n; ++i) {
+ for (int j = 0; j < n; ++j) {
+ mul = (*((A + i * n) + j)) * (*((B + i * n) + j));
+ *((C + i * n) + j) = mul;
+ }
+ }
+}
+
+void split(int *in, int *out, int n, int col, int row) {
+ for (int i1 = 0, i2 = col; i1 < n; i1++, i2++)
+ for (int j1 = 0, j2 = row; j1 < n; j1++, j2++) {
+ *((out + i1 * n) + j1) = *((in + i2 * n * 2) + j2);
+
+ }
+}
+
+void join(int *in, int *out, int n, int col, int row) {
+ for (int i1 = 0, i2 = col; i1 < n; i1++, i2++)
+ for (int j1 = 0, j2 = row; j1 < n; j1++, j2++)
+ *((out + i2 * n * 2) + j2) = *((in + i1 * n) + j1);
+}
+
+void printMatrix(int *C, int n) {
+ for (int i = 0; i < n; ++i) {
+ for (int j = 0; j < n; ++j) {
+ printf("%d ", *((C + i * n) + j));
+ }
+ printf("\n");
+ }
+}
+
+void printMatrix_double(double *C, int n) {
+ for (int i = 0; i < n; ++i) {
+ for (int j = 0; j < n; ++j) {
+ printf("%.0f ", *((C + i * n) + j));
+ }
+ printf("\n");
+ }
+}
+
+void run_algo(void (*algo)(), char alog_name[], int print)
+{
+ FILE *fptr;
+
+ char fileName[40] = "meas/";
+ strcat(fileName, alog_name);
+ strcat(fileName, ".txt");
+ fptr = fopen(fileName, "w");
+
+
+ for(int i=0; i<n_arrays; ++i)
+ {
+ for(int j = 0; j<1; ++j)
+ {
+ int *C = (int*) malloc(n[i] * n[i] * sizeof(int));
+ double dtime = omp_get_wtime();
+ algo(Ap[i], Bp[i], (int*) C, n[i]);
+ dtime = omp_get_wtime() - dtime;
+ // printf("The %s program took %f seconds to execute \n", alog_name, dtime);
+ fprintf(fptr, "%f,%d\n", dtime, n[i]);
+
+ if(print==1)
+ {
+ printMatrix((int*)C, n[i]);
+ }
+ free(C);
+ }
+ }
+ fclose(fptr);
+
+}
+
+void run_algo_cblas(int print)
+{
+
+ FILE *fptr;
+
+ fptr = fopen("meas/blas.txt", "w");
+ for(int i=0; i<n_arrays; ++i)
+ {
+ for(int j = 0; j<1; ++j)
+ {
+ double *dC = (double*) malloc(n[i] * n[i] * sizeof(double));
+ double dtime = omp_get_wtime();
+ cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n[i], n[i], n[i], 1.0, dAp[i], n[i],
+ dBp[i], n[i], 0.0, dC, n[i]);
+ dtime = omp_get_wtime() - dtime;
+ // printf("The cblas program took %f seconds to execute \n", dtime);
+ fprintf(fptr, "%f,%d\n",dtime, n[i]);
+
+ if(print==1)
+ {
+ printMatrix_double( (double*)dC, n[i]);
+ }
+
+ free(dC);
+ }
+ }
+ fclose(fptr);
+
+}
diff --git a/buch/papers/multiplikation/code/MM.py b/buch/papers/multiplikation/code/MM.py new file mode 100644 index 0000000..626b82d --- /dev/null +++ b/buch/papers/multiplikation/code/MM.py @@ -0,0 +1,311 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Fri Mar 19 07:31:29 2021 + +@author: nunigan +""" +import numpy as np +import time +import matplotlib.pyplot as plt +from scipy.optimize import curve_fit +import tikzplotlib +def MM(A, B): + n = np.shape(A)[0] + C = np.zeros((n, n)) + for i in range(n): + for j in range(n): + C[i, j] = 0 + for k in range(n): + C[i, j] += A[i, k]*B[k, j] + return C + + +def MM_dc(A, B): + n = np.shape(A)[0] + if(n <= 2): + C = np.zeros((n, n)) + C[0, 0] = A[0, 0]*B[0, 0]+A[0, 1]*B[1, 0] + C[0, 1] = A[0, 0]*B[0, 1]+A[0, 1]*B[1, 1] + C[1, 0] = A[1, 0]*B[0, 0]+A[1, 1]*B[1, 0] + C[1, 1] = A[1, 0]*B[0, 1]+A[1, 1]*B[1, 1] + return C + else: + A11, A12, A21, A22 = A[:n//2, :n//2], A[:n//2, n//2:], A[n//2:, :n//2], A[n//2:, n//2:] + B11, B12, B21, B22 = B[:n//2, :n//2], B[:n//2, n//2:], B[n//2:, :n//2], B[n//2:, n//2:] + C11 = MM_dc(A11, B11) + MM_dc(A12, B21) + C12 = MM_dc(A11, B12) + MM_dc(A12, B22) + C21 = MM_dc(A21, B11) + MM_dc(A22, B21) + C22 = MM_dc(A21, B12) + MM_dc(A22, B22) + C = np.vstack((np.hstack((C11, C12)), np.hstack((C21, C22)))) + return C + + +def strassen(A, B): + n = np.shape(A)[0] + if(n <= 2): + C = np.zeros((n, n)) + P = (A[0, 0]+A[1, 1])*(B[0, 0]+B[1, 1]) + Q = (A[1, 0]+A[1, 1])*B[0, 0] + R = A[0, 0]*(B[0, 1]-B[1, 1]) + S = A[1, 1]*(B[1, 0]-B[0, 0]) + T = (A[0, 0]+A[0, 1])*B[1, 1] + U = (A[1, 0]-A[0, 0])*(B[0, 0]+B[0, 1]) + V = (A[0, 1]-A[1, 1])*(B[1, 0]+B[1, 1]) + C[0, 0] = P+S-T+V + C[0, 1] = R+T + C[1, 0] = Q+S + C[1, 1] = P+R-Q+U + return C + else: + m = n//2 + A11, A12, A21, A22 = A[:m, :m], A[:m, m:], A[m:, :m], A[m:, m:] + B11, B12, B21, B22 = B[:m, :m], B[:m, m:], B[m:, :m], B[m:, m:] + P = strassen((A11+A22),(B11+B22)) + Q = strassen((A21+A22),B11) + R = strassen(A11,(B12-B22)) + S = strassen(A22,(B21-B11)) + T = strassen((A11+A12),B22) + U = strassen((A21-A11),(B11+B12)) + V = strassen((A12-A22),(B21+B22)) + + C11 = P+S-T+V + C12 = R+T + C21 = Q+S + C22 = P+R-Q+U + + C = np.vstack((np.hstack((C11, C12)), np.hstack((C21, C22)))) + return C + +def winograd_inner(a, b): + n = np.shape(a)[0] + if n%2 == 0: + xi = np.sum(a[::2]*a[1::2]) + etha = np.sum(b[::2]*b[1::2]) + # print("xi = {}, etha = {}".format(xi, etha)) + ab = np.sum((a[::2]+b[1::2])*(a[1::2]+b[::2]))-xi-etha + else: + xi = np.sum(a[0:-1:2]*a[1::2]) + etha = np.sum(b[0:-1:2]*b[1::2]) + ab = np.sum((a[0:-1:2]+b[1::2])*(a[1::2]+b[0:-1:2]))-xi-etha+a[-1]*b[-1] + return ab + +def winograd(A, B): + m,n = np.shape(A) + n2,p = np.shape(B) + C = np.zeros((m,p)) + for i in range(np.shape(A)[0]): + for j in range(np.shape(B)[1]): + C[i,j] = winograd_inner(A[i,:], B[:,j]) + return C + +def winograd2(A, B): + m,n = np.shape(A) + n2,p = np.shape(B) + C = np.zeros((m,p)) + xi = np.zeros((m)) + eta = np.zeros((p)) + ab = 0 + for i in range(m): + for j in range(n//2): + xi[i] += A[i,2*j]*A[i,2*j+1] + + for i in range(p): + for j in range(n//2): + eta[i] += B[2*j,i]*B[2*j+1,i] + + if n%2==0: + for i in range(m): + for j in range(p): + ab = 0 + for k in range(n//2): + ab += (A[i,2*k]+B[2*k+1,j])*(A[i,2*k+1]+B[2*k,j]) + C[i,j] = ab-eta[j]-xi[i] + else: + for i in range(m): + for j in range(p): + ab = 0 + for k in range(n//2): + ab += (A[i,2*k]+B[2*k+1,j])*(A[i,2*k+1]+B[2*k,j]) + C[i,j] = ab-eta[j]-xi[i]+A[i,-1]*B[-1,j] + + return C + +def test_perfomance(n): + t_mm = [] + t_mm_dc = [] + t_mm_strassen = [] + t_wino = [] + t_np = [] + + for i in n: + A = np.random.randn(i, i) + B = np.random.randn(i, i) + # A = np.random.randint(-100, 100,(i, i)) + # B = np.random.randint(-100, 100,(i, i)) + + start = time.time() + C3 = strassen(A, B) + t_mm_strassen.append(time.time() - start) + + start = time.time() + C1 = MM(A, B) + t_mm.append(time.time() - start) + + start = time.time() + C2 = MM_dc(A, B) + t_mm_dc.append(time.time() - start) + + start = time.time() + C4 = winograd2(A, B) + t_wino.append(time.time() - start) + + start = time.time() + C = A@B + t_np.append(time.time() - start) + + plt.figure(figsize=(13,8)) + plt.rcParams['font.family'] = 'STIXGeneral' + plt.rc('axes', labelsize=23) + plt.rc('xtick', labelsize=23) + plt.rc('ytick', labelsize=23) + plt.plot(n, t_mm, label='Standard', lw=5) + plt.plot(n, t_mm_dc, label='Divide and conquer', lw=5) + plt.plot(n, t_mm_strassen, label='Strassen', lw=5) + plt.plot(n, t_wino, label='Winograd', lw=5) + plt.plot(n, t_np, label='NumPy A@B', lw=5) + plt.legend() + plt.xlabel("n") + plt.ylabel("time (s)") + plt.grid(True) + plt.tight_layout() + # plt.yscale('log') + plt.legend(fontsize=19) + plt.savefig('meas_' + str(max(n))+ '.pdf') + arr = np.array([n, t_mm, t_mm_dc, t_mm_strassen, t_wino, t_np]) + np.savetxt('meas_' + str(max(n))+ '.txt',arr) + return arr + + +def plot(num): + arr = np.loadtxt('meas_{}.txt'.format(num)) + n, t_mm, t_mm_dc, t_mm_strassen, t_wino, t_np = arr + plt.figure(figsize=(13,8)) + plt.rcParams['font.family'] = 'STIXGeneral' + plt.rc('axes', labelsize=23) + plt.rc('xtick', labelsize=23) + plt.rc('ytick', labelsize=23) + plt.plot(n, t_mm, label='3 For Loops', lw=5) + plt.plot(n, t_mm_dc, label='Divide and Conquer', lw=5) + plt.plot(n, t_mm_strassen, label='Strassen', lw=5) + # plt.plot(n, t_wino, label='Winograd', lw=5) + plt.plot(n, t_np, label='NumPy A@B', lw=5) + plt.legend() + plt.xlabel("n") + plt.ylabel("time (s)") + plt.grid(True) + plt.tight_layout() + # plt.yscale('log') + plt.legend(fontsize=19) + plt.savefig('meas_' + str(num)+ '.pdf') + return arr + +def plot_c_res(ave, num): + MM = np.loadtxt("meas/MM.txt", delimiter=',') + # winograd = np.loadtxt("meas/winograd.txt", delimiter=',') + blas = np.loadtxt("meas/blas.txt", delimiter=',') + MM_dc = np.loadtxt("meas/MM_dc.txt", delimiter=',') + strassen = np.loadtxt("meas/strassen.txt", delimiter=',') + + MM_t = MM[:,0] + MM_n = MM[:,1] + MM_t = np.mean(MM_t.reshape(-1,ave),axis=1) + MM_n = np.mean(MM_n.reshape(-1,ave),axis=1) + + MM_dc_t = MM_dc[:,0] + MM_dc_n = MM_dc[:,1] + MM_dc_t = np.mean(MM_dc_t.reshape(-1,ave),axis=1) + MM_dc_n = np.mean(MM_dc_n.reshape(-1,ave),axis=1) + + strassen_t = strassen[:,0] + strassen_n = strassen[:,1] + strassen_t = np.mean(strassen_t.reshape(-1,ave),axis=1) + strassen_n = np.mean(strassen_n.reshape(-1,ave),axis=1) + + # winograd_t = winograd[:,0] + # winograd_n = winograd[:,1] + # winograd_t = np.mean(winograd_t.reshape(-1,ave),axis=1) + # winograd_n = np.mean(winograd_n.reshape(-1,ave),axis=1) + + blas_t = blas[:,0] + blas_n = blas[:,1] + blas_t = np.mean(blas_t.reshape(-1,ave),axis=1) + blas_n = np.mean(blas_n.reshape(-1,ave),axis=1) + + def func(x, a,b): + return b*x**a + + # popt, pcov = curve_fit(func, blas_n, blas_t) + # popt1, pcov2 = curve_fit(func, blas_n, winograd_t) + # popt2, pcov2 = curve_fit(func, blas_n, MM_t) + + plt.figure(figsize=(13,8)) + plt.rcParams['font.family'] = 'STIXGeneral' + plt.rc('axes', labelsize=23) + plt.rc('xtick', labelsize=23) + plt.rc('ytick', labelsize=23) + plt.plot(MM_n, MM_t, label='3 For Loops', lw=5) + # plt.plot(winograd_n, winograd_t, label='Winograd MM', lw=5) + plt.plot(blas_n, blas_t, label='Blas', lw=5) + plt.plot(strassen_n, strassen_t, label='Strassen', lw=5) + plt.plot(MM_dc_n, MM_dc_t, label='Divide and Conquer', lw=5) + plt.xlabel("n") + plt.ylabel("time (s)") + plt.grid(True) + plt.tight_layout() + plt.legend(fontsize=19) + plt.savefig('c_meas_' + str(num)+ '.pdf') + + # plt.plot(blas_n, func(blas_n, *popt), 'r-', label='fit blas: a=%5.5f, b=%5.10f' % tuple(popt)) + # plt.plot(blas_n, func(blas_n, *popt1), 'r-', label='fit winograd: a=%5.5f, b=%5.10f' % tuple(popt1)) + # plt.plot(blas_n, func(blas_n, *popt2), 'r-', label='fit MM: a=%5.5f, b=%5.10f' % tuple(popt2)) + + plt.legend() + + +# test%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if __name__ == '__main__': + plot_c_res(1, 4096) + + + # plot(8) + # n = np.logspace(1,10,10,base=2,dtype=(np.int)) + # n = np.arange(1,50,2) + A = np.random.randint(-10, 10, (5,3)) + B = np.random.randint(-10, 10, (3,5)) + + C = winograd2(A, B) + C_test = A@B + print(C) + print(C_test) + # print(np.equal(C, C_test)) + + # t_np = test_perfomance(n) + # C = strassen(A, B) + # C_test = A@B + + + # plot_c_res() + # def func(x, a): + # return x**a + + # popt, pcov = curve_fit(func, n, t_np, bounds=(2, 3)) + + + # plt.figure() + # plt.plot(n, t_np, 'b-', label='data') + # plt.plot(n, func(n, *popt), 'r-', label='fit: a=%5.3f' % tuple(popt)) + # plt.xlabel('x') + # plt.ylabel('y') + # plt.legend() +
\ No newline at end of file diff --git a/buch/papers/multiplikation/code/__pycache__/MM.cpython-38.pyc b/buch/papers/multiplikation/code/__pycache__/MM.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..7768772 --- /dev/null +++ b/buch/papers/multiplikation/code/__pycache__/MM.cpython-38.pyc diff --git a/buch/papers/multiplikation/code/c_matrix.h b/buch/papers/multiplikation/code/c_matrix.h new file mode 100644 index 0000000..13df55d --- /dev/null +++ b/buch/papers/multiplikation/code/c_matrix.h @@ -0,0 +1,101 @@ +/* Seminar Matrizen, autogenerated File, Michael Schmid, 30/05/2021, 22:00:57 */ + +#include <stdint.h> +const int A0[][2] = + { + {-15,68}, + {49,86} + }; +const int B0[][2] = + { + {33,73}, + {38,-76} + }; +const double dB0[][2] = + { + {33,73}, + {38,-76} + }; +const double dA0[][2] = + { + {-15,68}, + {49,86} + }; +const int A1[][4] = + { + {75,-38,-32,-65}, + {37,74,-31,29}, + {15,-62,-20,-20}, + {-31,-35,-89,47} + }; +const int B1[][4] = + { + {71,90,78,-98}, + {4,63,12,-47}, + {11,-44,75,-69}, + {95,-15,64,23} + }; +const double dB1[][4] = + { + {71,90,78,-98}, + {4,63,12,-47}, + {11,-44,75,-69}, + {95,-15,64,23} + }; +const double dA1[][4] = + { + {75,-38,-32,-65}, + {37,74,-31,29}, + {15,-62,-20,-20}, + {-31,-35,-89,47} + }; +const int A2[][8] = + { + {80,42,3,-16,6,55,87,16}, + {-99,-14,21,-1,-94,-56,91,10}, + {-47,-55,-59,62,12,-53,87,-65}, + {-60,94,-67,23,-62,33,-63,-72}, + {12,-75,16,21,22,-37,1,16}, + {-100,-99,82,-66,2,64,-13,44}, + {59,-100,-90,8,36,-24,18,88}, + {73,-58,75,-100,-19,-29,85,-19} + }; +const int B2[][8] = + { + {-61,88,69,49,-53,47,73,45}, + {16,14,-88,-11,-67,-73,-20,43}, + {-60,-63,26,32,-29,18,-44,-69}, + {1,21,21,38,7,-100,-61,-76}, + {-90,95,-99,88,49,-80,27,-36}, + {24,-12,-47,-7,29,15,52,37}, + {-98,-76,29,76,-41,-75,97,79}, + {62,-90,-35,-14,-30,-42,-95,52} + }; +const double dB2[][8] = + { + {-61,88,69,49,-53,47,73,45}, + {16,14,-88,-11,-67,-73,-20,43}, + {-60,-63,26,32,-29,18,-44,-69}, + {1,21,21,38,7,-100,-61,-76}, + {-90,95,-99,88,49,-80,27,-36}, + {24,-12,-47,-7,29,15,52,37}, + {-98,-76,29,76,-41,-75,97,79}, + {62,-90,-35,-14,-30,-42,-95,52} + }; +const double dA2[][8] = + { + {80,42,3,-16,6,55,87,16}, + {-99,-14,21,-1,-94,-56,91,10}, + {-47,-55,-59,62,12,-53,87,-65}, + {-60,94,-67,23,-62,33,-63,-72}, + {12,-75,16,21,22,-37,1,16}, + {-100,-99,82,-66,2,64,-13,44}, + {59,-100,-90,8,36,-24,18,88}, + {73,-58,75,-100,-19,-29,85,-19} + }; +const int *Ap[3] = {(int*) A0,(int*) A1,(int*) A2}; +const int *Bp[3] = {(int*) B0,(int*) B1,(int*) B2}; +const double *dAp[3] = {(double*) dA0,(double*) dA1,(double*) dA2}; +const double *dBp[3] = {(double*) dB0,(double*) dB1,(double*) dB2}; +int n[3] = {2,4,8}; +int n_arrays = 3; diff --git a/buch/papers/multiplikation/code/c_meas_1024.pdf b/buch/papers/multiplikation/code/c_meas_1024.pdf Binary files differnew file mode 100644 index 0000000..95b68b5 --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_1024.pdf diff --git a/buch/papers/multiplikation/code/c_meas_128.pdf b/buch/papers/multiplikation/code/c_meas_128.pdf Binary files differnew file mode 100644 index 0000000..56b9200 --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_128.pdf diff --git a/buch/papers/multiplikation/code/c_meas_16.pdf b/buch/papers/multiplikation/code/c_meas_16.pdf Binary files differnew file mode 100644 index 0000000..2edc82d --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_16.pdf diff --git a/buch/papers/multiplikation/code/c_meas_2048.pdf b/buch/papers/multiplikation/code/c_meas_2048.pdf Binary files differnew file mode 100644 index 0000000..caba698 --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_2048.pdf diff --git a/buch/papers/multiplikation/code/c_meas_256.pdf b/buch/papers/multiplikation/code/c_meas_256.pdf Binary files differnew file mode 100644 index 0000000..383ae86 --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_256.pdf diff --git a/buch/papers/multiplikation/code/c_meas_32.pdf b/buch/papers/multiplikation/code/c_meas_32.pdf Binary files differnew file mode 100644 index 0000000..180fd22 --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_32.pdf diff --git a/buch/papers/multiplikation/code/c_meas_4096.pdf b/buch/papers/multiplikation/code/c_meas_4096.pdf Binary files differnew file mode 100644 index 0000000..547d794 --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_4096.pdf diff --git a/buch/papers/multiplikation/code/c_meas_512.pdf b/buch/papers/multiplikation/code/c_meas_512.pdf Binary files differnew file mode 100644 index 0000000..5e8894e --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_512.pdf diff --git a/buch/papers/multiplikation/code/c_meas_64.pdf b/buch/papers/multiplikation/code/c_meas_64.pdf Binary files differnew file mode 100644 index 0000000..8ff905c --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_64.pdf diff --git a/buch/papers/multiplikation/code/c_meas_8.pdf b/buch/papers/multiplikation/code/c_meas_8.pdf Binary files differnew file mode 100644 index 0000000..9682aca --- /dev/null +++ b/buch/papers/multiplikation/code/c_meas_8.pdf diff --git a/buch/papers/multiplikation/code/helper_class.py b/buch/papers/multiplikation/code/helper_class.py new file mode 100755 index 0000000..485fa76 --- /dev/null +++ b/buch/papers/multiplikation/code/helper_class.py @@ -0,0 +1,105 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Fri Mar 12 09:02:48 2021 + +@author: nunigan +""" + +from datetime import datetime +import numpy as np + +class Helper(): + def __init__(self): + pass + + def write_c_matrix(self, n_array): + + with open('c_matrix.h', 'w') as file: + file.writelines('/* Seminar Matrizen, autogenerated File, Michael Schmid, {} */ \n \n'.format(datetime.now().strftime("%d/%m/%Y, %H:%M:%S"))) + + file.writelines('#include <stdint.h> \n') + + + + for k, n in enumerate(n_array): + A = np.random.randint(-100,100,(n,n)) + B = np.random.randint(-100,100,(n,n)) + file.writelines('const int A{}[][{}] = \n'.format(k, n)) + file.writelines(' {\n') + for i in range(n): + file.writelines(' {') + for j in range(n): + if j == n-1: + file.writelines('{}'.format(A[i,j])) + else: + file.writelines('{},'.format(A[i,j])) + if i == n-1: + file.writelines('}\n') + else: + file.writelines('},\n') + + file.writelines(' };\n') + + file.writelines('const int B{}[][{}] = \n'.format(k,n)) + file.writelines(' {\n') + for i in range(n): + file.writelines(' {') + for j in range(n): + if j == n-1: + file.writelines('{}'.format(B[i,j])) + else: + file.writelines('{},'.format(B[i,j])) + if i == n-1: + file.writelines('}\n') + else: + file.writelines('},\n') + + file.writelines(' };\n') + + file.writelines('const double dB{}[][{}] = \n'.format(k,n)) + file.writelines(' {\n') + for i in range(n): + file.writelines(' {') + for j in range(n): + if j == n-1: + file.writelines('{}'.format(B[i,j])) + else: + file.writelines('{},'.format(B[i,j])) + if i == n-1: + file.writelines('}\n') + else: + file.writelines('},\n') + + file.writelines(' };\n') + + file.writelines('const double dA{}[][{}] = \n'.format(k,n)) + file.writelines(' {\n') + for i in range(n): + file.writelines(' {') + for j in range(n): + if j == n-1: + file.writelines('{}'.format(A[i,j])) + else: + file.writelines('{},'.format(A[i,j])) + if i == n-1: + file.writelines('}\n') + else: + file.writelines('},\n') + + file.writelines(' };\n') + + file.writelines('const int *Ap[{}] = {{{}}}; \n'.format(len(n_array),",".join(['(int*) A'+str(element) for element in np.arange(len(n_array))]))) + file.writelines('const int *Bp[{}] = {{{}}}; \n'.format(len(n_array),",".join(['(int*) B'+str(element) for element in np.arange(len(n_array))]))) + file.writelines('const double *dAp[{}] = {{{}}}; \n'.format(len(n_array),",".join(['(double*) dA'+str(element) for element in np.arange(len(n_array))]))) + file.writelines('const double *dBp[{}] = {{{}}}; \n'.format(len(n_array),",".join(['(double*) dB'+str(element) for element in np.arange(len(n_array))]))) + file.writelines('int n[{}] = {{{}}}; \n'.format(len(n_array),",".join([str(element) for element in n_array]))) + file.writelines('int n_arrays = {};\n'.format(len(n_array))) + +# test%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if __name__ == '__main__': + + helper = Helper() + # n = np.arange(2,10) + n = np.logspace(1,3,3,base=2,dtype=(np.int)) + C = helper.write_c_matrix(n) diff --git a/buch/papers/multiplikation/code/meas/MM.txt b/buch/papers/multiplikation/code/meas/MM.txt new file mode 100644 index 0000000..1a0cd5d --- /dev/null +++ b/buch/papers/multiplikation/code/meas/MM.txt @@ -0,0 +1,12 @@ +0.000000,2 +0.000000,4 +0.000002,8 +0.000011,16 +0.000080,32 +0.000653,64 +0.005397,128 +0.045147,256 +0.487710,512 +3.964180,1024 +128.863544,2048 +996.370209,4096 diff --git a/buch/papers/multiplikation/code/meas/MM_dc.txt b/buch/papers/multiplikation/code/meas/MM_dc.txt new file mode 100644 index 0000000..0d5580a --- /dev/null +++ b/buch/papers/multiplikation/code/meas/MM_dc.txt @@ -0,0 +1,12 @@ +0.000006,2 +0.000007,4 +0.000035,8 +0.000228,16 +0.001310,32 +0.007204,64 +0.034338,128 +0.267511,256 +2.131212,512 +17.177403,1024 +146.112874,2048 +1156.777565,4096 diff --git a/buch/papers/multiplikation/code/meas/blas.txt b/buch/papers/multiplikation/code/meas/blas.txt new file mode 100644 index 0000000..6b7cd0b --- /dev/null +++ b/buch/papers/multiplikation/code/meas/blas.txt @@ -0,0 +1,12 @@ +0.000001,2 +0.000000,4 +0.000001,8 +0.000003,16 +0.000021,32 +0.000164,64 +0.001240,128 +0.009657,256 +0.072523,512 +0.735149,1024 +6.895747,2048 +56.812183,4096 diff --git a/buch/papers/multiplikation/code/meas/strassen.txt b/buch/papers/multiplikation/code/meas/strassen.txt new file mode 100644 index 0000000..89cf41a --- /dev/null +++ b/buch/papers/multiplikation/code/meas/strassen.txt @@ -0,0 +1,12 @@ +0.000000,2 +0.000003,4 +0.000010,8 +0.000086,16 +0.000476,32 +0.003366,64 +0.025547,128 +0.184593,256 +1.248713,512 +9.007700,1024 +61.079879,2048 +424.493037,4096 diff --git a/buch/papers/multiplikation/code/meas/test/4096/MM.txt b/buch/papers/multiplikation/code/meas/test/4096/MM.txt new file mode 100644 index 0000000..25e40e1 --- /dev/null +++ b/buch/papers/multiplikation/code/meas/test/4096/MM.txt @@ -0,0 +1,12 @@ +0.000000,2 +0.000000,4 +0.000002,8 +0.000011,16 +0.000100,32 +0.000712,64 +0.005498,128 +0.046711,256 +0.489233,512 +4.006544,1024 +124.427496,2048 +993.405615,4096 diff --git a/buch/papers/multiplikation/code/meas/test/4096/strassen.txt b/buch/papers/multiplikation/code/meas/test/4096/strassen.txt new file mode 100644 index 0000000..eb2a496 --- /dev/null +++ b/buch/papers/multiplikation/code/meas/test/4096/strassen.txt @@ -0,0 +1,12 @@ +0.000007,2 +0.000007,4 +0.000029,8 +0.000199,16 +0.001414,32 +0.007583,64 +0.028096,128 +0.171662,256 +1.198323,512 +8.421896,1024 +58.803644,2048 +415.115401,4096 diff --git a/buch/papers/multiplikation/code/meas/test/MM.txt b/buch/papers/multiplikation/code/meas/test/MM.txt new file mode 100644 index 0000000..e0754ab --- /dev/null +++ b/buch/papers/multiplikation/code/meas/test/MM.txt @@ -0,0 +1,14900 @@ +0.000004,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000001,8 +0.000001,8 +0.000002,8 +0.000002,8 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000006,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000013,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000008,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000016,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000007,14 +0.000011,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000025,16 +0.000011,16 +0.000020,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000010,16 +0.000016,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000015,18 +0.000014,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000015,18 +0.000014,18 +0.000021,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000030,20 +0.000029,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000030,20 +0.000030,20 +0.000029,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000048,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000020,20 +0.000027,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000033,22 +0.000040,22 +0.000045,22 +0.000046,22 +0.000041,22 +0.000040,22 +0.000040,22 +0.000040,22 +0.000042,22 +0.000040,22 +0.000043,22 +0.000030,22 +0.000036,22 +0.000026,22 +0.000037,22 +0.000049,22 +0.000036,22 +0.000046,22 +0.000047,22 +0.000049,22 +0.000037,22 +0.000035,22 +0.000037,22 +0.000050,22 +0.000055,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000036,22 +0.000036,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000026,22 +0.000036,22 +0.000046,22 +0.000062,22 +0.000047,22 +0.000036,22 +0.000047,22 +0.000041,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000050,24 +0.000053,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000055,24 +0.000058,26 +0.000055,26 +0.000077,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000052,26 +0.000043,26 +0.000043,26 +0.000066,26 +0.000061,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000054,28 +0.000054,28 +0.000053,28 +0.000053,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000065,28 +0.000066,28 +0.000058,28 +0.000097,28 +0.000084,28 +0.000073,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000053,28 +0.000054,28 +0.000054,28 +0.000073,28 +0.000054,28 +0.000053,28 +0.000054,28 +0.000054,28 +0.000053,28 +0.000073,28 +0.000054,28 +0.000064,28 +0.000063,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000073,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000082,28 +0.000063,28 +0.000083,28 +0.000063,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000069,30 +0.000066,30 +0.000066,30 +0.000074,30 +0.000103,30 +0.000108,30 +0.000107,30 +0.000112,30 +0.000111,30 +0.000087,30 +0.000105,30 +0.000076,30 +0.000066,30 +0.000107,30 +0.000119,30 +0.000105,30 +0.000117,30 +0.000077,30 +0.000077,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000079,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000069,30 +0.000077,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000096,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000085,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000089,30 +0.000066,30 +0.000066,30 +0.000066,30 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000079,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000102,32 +0.000091,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000090,32 +0.000119,32 +0.000129,32 +0.000134,32 +0.000095,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000100,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000102,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000100,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000100,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000114,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000080,32 +0.000098,34 +0.000096,34 +0.000106,34 +0.000124,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000134,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000131,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000119,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000154,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000116,36 +0.000153,36 +0.000133,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000123,36 +0.000142,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000150,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000113,36 +0.000143,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000143,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000143,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000145,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000161,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000180,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000141,38 +0.000143,38 +0.000168,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000168,40 +0.000164,40 +0.000165,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000166,40 +0.000164,40 +0.000268,40 +0.000164,40 +0.000164,40 +0.000165,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000188,40 +0.000183,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000174,40 +0.000293,40 +0.000184,40 +0.000164,40 +0.000164,40 +0.000170,40 +0.000234,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000195,40 +0.000174,40 +0.000164,40 +0.000214,40 +0.000234,40 +0.000203,40 +0.000164,40 +0.000183,40 +0.000183,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000186,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000164,40 +0.000190,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000200,42 +0.000198,42 +0.000215,42 +0.000258,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000231,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000201,42 +0.000252,42 +0.000189,42 +0.000189,42 +0.000347,42 +0.000296,42 +0.000208,42 +0.000194,42 +0.000195,42 +0.000213,42 +0.000215,42 +0.000323,42 +0.000235,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000199,42 +0.000220,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000199,42 +0.000240,42 +0.000189,42 +0.000222,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000209,42 +0.000199,42 +0.000194,42 +0.000194,42 +0.000194,42 +0.000194,42 +0.000194,42 +0.000194,42 +0.000194,42 +0.000194,42 +0.000194,42 +0.000202,42 +0.000223,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000189,42 +0.000222,44 +0.000216,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000288,44 +0.000228,44 +0.000216,44 +0.000217,44 +0.000254,44 +0.000216,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000216,44 +0.000268,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000256,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000254,44 +0.000255,44 +0.000217,44 +0.000216,44 +0.000216,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000240,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000245,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000216,44 +0.000217,44 +0.000217,44 +0.000217,44 +0.000250,46 +0.000246,46 +0.000246,46 +0.000249,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000257,46 +0.000275,46 +0.000303,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000285,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000250,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000252,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000253,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000253,46 +0.000257,46 +0.000277,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000285,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000246,46 +0.000250,46 +0.000286,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000286,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000279,48 +0.000279,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000284,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000284,48 +0.000280,48 +0.000280,48 +0.000290,48 +0.000311,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000318,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000281,48 +0.000279,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000283,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000281,48 +0.000321,48 +0.000280,48 +0.000332,48 +0.000316,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000279,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000280,48 +0.000334,48 +0.000343,48 +0.000319,50 +0.000338,50 +0.000315,50 +0.000431,50 +0.000315,50 +0.000335,50 +0.000315,50 +0.000446,50 +0.000315,50 +0.000315,50 +0.000351,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000359,50 +0.000315,50 +0.000343,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000355,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000352,50 +0.000315,50 +0.000315,50 +0.000325,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000326,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000354,50 +0.000339,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000343,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000334,50 +0.000376,50 +0.000317,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000315,50 +0.000319,50 +0.000315,50 +0.000359,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000362,52 +0.000353,52 +0.000354,52 +0.000356,52 +0.000392,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000354,52 +0.000354,52 +0.000358,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000354,52 +0.000355,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000354,52 +0.000357,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000354,52 +0.000362,52 +0.000356,52 +0.000354,52 +0.000353,52 +0.000392,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000358,52 +0.000353,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000354,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000355,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000358,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000353,52 +0.000355,52 +0.000409,54 +0.000395,54 +0.000395,54 +0.000405,54 +0.000423,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000400,54 +0.000394,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000396,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000394,54 +0.000395,54 +0.000395,54 +0.000396,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000394,54 +0.000395,54 +0.000395,54 +0.000398,54 +0.000395,54 +0.000403,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000434,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000397,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000399,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000395,54 +0.000421,54 +0.000395,54 +0.000395,54 +0.000473,54 +0.000404,54 +0.000419,54 +0.000415,54 +0.000419,54 +0.000408,54 +0.000443,54 +0.000419,54 +0.000395,54 +0.000419,54 +0.000434,54 +0.000409,54 +0.000467,54 +0.000462,54 +0.000429,54 +0.000395,54 +0.000440,54 +0.000415,54 +0.000395,54 +0.000497,54 +0.000415,54 +0.000395,54 +0.000436,54 +0.000395,54 +0.000395,54 +0.000431,54 +0.000395,54 +0.000444,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000469,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000463,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000448,56 +0.000439,56 +0.000439,56 +0.000523,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000472,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000535,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000461,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000450,56 +0.000439,56 +0.000468,56 +0.000478,56 +0.000439,56 +0.000439,56 +0.000440,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000441,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000461,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000457,56 +0.000451,56 +0.000451,56 +0.000448,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000439,56 +0.000470,56 +0.000439,56 +0.000439,56 +0.000537,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000512,58 +0.000500,58 +0.000497,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000529,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000491,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000511,58 +0.000496,58 +0.000487,58 +0.000487,58 +0.000526,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000492,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000489,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000489,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000491,58 +0.000487,58 +0.000495,58 +0.000487,58 +0.000487,58 +0.000526,58 +0.000487,58 +0.000487,58 +0.000489,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000521,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000487,58 +0.000545,58 +0.000521,58 +0.000511,58 +0.000557,58 +0.000544,58 +0.000531,58 +0.000500,58 +0.000498,58 +0.000539,58 +0.000521,58 +0.000517,58 +0.000549,58 +0.000508,58 +0.000576,60 +0.000609,60 +0.000601,60 +0.000538,60 +0.000538,60 +0.000582,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000543,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000540,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000542,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000546,60 +0.000538,60 +0.000579,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000569,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000570,60 +0.000567,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000542,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000546,60 +0.000538,60 +0.000541,60 +0.000577,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000543,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000540,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000542,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000548,60 +0.000609,60 +0.000538,60 +0.000570,60 +0.000538,60 +0.000558,60 +0.000558,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000538,60 +0.000542,60 +0.000538,60 +0.000597,62 +0.000593,62 +0.000593,62 +0.000595,62 +0.000593,62 +0.000594,62 +0.000593,62 +0.000592,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000597,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000633,62 +0.000595,62 +0.000601,62 +0.000593,62 +0.000632,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000598,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000595,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000594,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000597,62 +0.000593,62 +0.000601,62 +0.000593,62 +0.000632,62 +0.000593,62 +0.000595,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000597,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000606,62 +0.000668,62 +0.000617,62 +0.000617,62 +0.000637,62 +0.000607,62 +0.000634,62 +0.000625,62 +0.000608,62 +0.000667,62 +0.000634,62 +0.000653,62 +0.000683,62 +0.000625,62 +0.000593,62 +0.000593,62 +0.000635,62 +0.000593,62 +0.000593,62 +0.000633,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000593,62 +0.000613,62 +0.000677,62 +0.000746,62 +0.000613,62 +0.000749,62 +0.000623,62 +0.000612,62 +0.000593,62 +0.000632,62 +0.000593,62 +0.000612,62 +0.000658,64 +0.000681,64 +0.000651,64 +0.000697,64 +0.000650,64 +0.000650,64 +0.000671,64 +0.000650,64 +0.000650,64 +0.000680,64 +0.000650,64 +0.000650,64 +0.000651,64 +0.000650,64 +0.000651,64 +0.000673,64 +0.000732,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000654,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000659,64 +0.000653,64 +0.000690,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000655,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000652,64 +0.000651,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000654,64 +0.000650,64 +0.000670,64 +0.000670,64 +0.000650,64 +0.000709,64 +0.000663,64 +0.000689,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000655,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000652,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000654,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000652,64 +0.000658,64 +0.000650,64 +0.000689,64 +0.000650,64 +0.000650,64 +0.000655,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000652,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000650,64 +0.000654,64 +0.000650,64 +0.000650,64 +0.000651,64 +0.000651,64 +0.000650,64 +0.000725,66 +0.000713,66 +0.000722,66 +0.000713,66 +0.000752,66 +0.000713,66 +0.000718,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000759,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000717,66 +0.000713,66 +0.000812,66 +0.000736,66 +0.000740,66 +0.000776,66 +0.000755,66 +0.000738,66 +0.000766,66 +0.000775,66 +0.000797,66 +0.000776,66 +0.000829,66 +0.000722,66 +0.000713,66 +0.000713,66 +0.000736,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000859,66 +0.000825,66 +0.000713,66 +0.000713,66 +0.000733,66 +0.000757,66 +0.000713,66 +0.000733,66 +0.000765,66 +0.000772,66 +0.000894,66 +0.000713,66 +0.000713,66 +0.000752,66 +0.000731,66 +0.000754,66 +0.000723,66 +0.000713,66 +0.000734,66 +0.000713,66 +0.000713,66 +0.000749,66 +0.000793,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000840,66 +0.000768,66 +0.000752,66 +0.000756,66 +0.000713,66 +0.000724,66 +0.000781,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000736,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000736,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000744,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000713,66 +0.000712,66 +0.000745,66 +0.000713,66 +0.000752,66 +0.000713,66 +0.000713,66 +0.000719,66 +0.000713,66 +0.000789,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000785,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000783,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000780,68 +0.000787,68 +0.000817,68 +0.000778,68 +0.000778,68 +0.000783,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000780,68 +0.000779,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000780,68 +0.000779,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000782,68 +0.000778,68 +0.000787,68 +0.000778,68 +0.000817,68 +0.000781,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000783,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000780,68 +0.000778,68 +0.000845,68 +0.000822,68 +0.000813,68 +0.000832,68 +0.000826,68 +0.000902,68 +0.000890,68 +0.000835,68 +0.000799,68 +0.000868,68 +0.000778,68 +0.000778,68 +0.000816,68 +0.000778,68 +0.000779,68 +0.000778,68 +0.000778,68 +0.000813,68 +0.000798,68 +0.000778,68 +0.000778,68 +0.000798,68 +0.000820,68 +0.000778,68 +0.000779,68 +0.000778,68 +0.000787,68 +0.000841,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000783,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000780,68 +0.000846,68 +0.000778,68 +0.000778,68 +0.000778,68 +0.000786,68 +0.000779,68 +0.000778,68 +0.000779,68 +0.000790,68 +0.000864,70 +0.000887,70 +0.000848,70 +0.000895,70 +0.000856,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000850,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000849,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000863,70 +0.000848,70 +0.000887,70 +0.000848,70 +0.000848,70 +0.000852,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000854,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000850,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000852,70 +0.000857,70 +0.000848,70 +0.000887,70 +0.000848,70 +0.000850,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000896,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000850,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000848,70 +0.000852,70 +0.000848,70 +0.000857,70 +0.000887,70 +0.000848,70 +0.000851,70 +0.001152,70 +0.000848,70 +0.000848,70 +0.000880,70 +0.001018,70 +0.000848,70 +0.001016,70 +0.000885,70 +0.000848,70 +0.000935,70 +0.000894,70 +0.000883,70 +0.000921,70 +0.000926,70 +0.000922,70 +0.001052,70 +0.000956,70 +0.000883,70 +0.001083,70 +0.000970,70 +0.001244,70 +0.000980,70 +0.000928,70 +0.000927,70 +0.000914,70 +0.000951,70 +0.000948,70 +0.000969,70 +0.000974,70 +0.000970,70 +0.001081,70 +0.001080,70 +0.000962,70 +0.000948,70 +0.000948,70 +0.000946,70 +0.000934,70 +0.000946,70 +0.001066,72 +0.001042,72 +0.001018,72 +0.001084,72 +0.001068,72 +0.001038,72 +0.001056,72 +0.001073,72 +0.001119,72 +0.001100,72 +0.001092,72 +0.001032,72 +0.001029,72 +0.001016,72 +0.001057,72 +0.001057,72 +0.001057,72 +0.001068,72 +0.001039,72 +0.001038,72 +0.001066,72 +0.001032,72 +0.001037,72 +0.001037,72 +0.001135,72 +0.001046,72 +0.001085,72 +0.001089,72 +0.001054,72 +0.001079,72 +0.001024,72 +0.001033,72 +0.001036,72 +0.001050,72 +0.000921,72 +0.001033,72 +0.001062,72 +0.000960,72 +0.000921,72 +0.001050,72 +0.001081,72 +0.001111,72 +0.001031,72 +0.001009,72 +0.001014,72 +0.000946,72 +0.001031,72 +0.000950,72 +0.001043,72 +0.000921,72 +0.000921,72 +0.001055,72 +0.000958,72 +0.001054,72 +0.001056,72 +0.000921,72 +0.000980,72 +0.001135,72 +0.001088,72 +0.001116,72 +0.000955,72 +0.000921,72 +0.001174,72 +0.000941,72 +0.000967,72 +0.001058,72 +0.000921,72 +0.000921,72 +0.000947,72 +0.001054,72 +0.000941,72 +0.001007,72 +0.001018,72 +0.001027,72 +0.000987,72 +0.001003,72 +0.001095,72 +0.000942,72 +0.001094,72 +0.000921,72 +0.000971,72 +0.000921,72 +0.000921,72 +0.000942,72 +0.000965,72 +0.000921,72 +0.000921,72 +0.000921,72 +0.000921,72 +0.000966,72 +0.000941,72 +0.000921,72 +0.000941,72 +0.000996,72 +0.000921,72 +0.000921,72 +0.000921,72 +0.000967,72 +0.000921,72 +0.000921,72 +0.001012,74 +0.001031,74 +0.000999,74 +0.001078,74 +0.000998,74 +0.001047,74 +0.000999,74 +0.000999,74 +0.000999,74 +0.001067,74 +0.001024,74 +0.000998,74 +0.000999,74 +0.001002,74 +0.000998,74 +0.000998,74 +0.000998,74 +0.001007,74 +0.000998,74 +0.000998,74 +0.000998,74 +0.001001,74 +0.000998,74 +0.000999,74 +0.001053,74 +0.001033,74 +0.001023,74 +0.000999,74 +0.000998,74 +0.001003,74 +0.000999,74 +0.000999,74 +0.000998,74 +0.001000,74 +0.000999,74 +0.000998,74 +0.000998,74 +0.001005,74 +0.000999,74 +0.000998,74 +0.000998,74 +0.001000,74 +0.001022,74 +0.001024,74 +0.000999,74 +0.001007,74 +0.000999,74 +0.000999,74 +0.000998,74 +0.001000,74 +0.000998,74 +0.000998,74 +0.000999,74 +0.001000,74 +0.000999,74 +0.000999,74 +0.000999,74 +0.001002,74 +0.001021,74 +0.000998,74 +0.001023,74 +0.001002,74 +0.000998,74 +0.000998,74 +0.000998,74 +0.001005,74 +0.000999,74 +0.000999,74 +0.000998,74 +0.001000,74 +0.000998,74 +0.000999,74 +0.001075,74 +0.001077,74 +0.001043,74 +0.001087,74 +0.001126,74 +0.001090,74 +0.001029,74 +0.001098,74 +0.001032,74 +0.000999,74 +0.000998,74 +0.001048,74 +0.001004,74 +0.000999,74 +0.000999,74 +0.000999,74 +0.001006,74 +0.000999,74 +0.000999,74 +0.001023,74 +0.001028,74 +0.000999,74 +0.000998,74 +0.000999,74 +0.001007,74 +0.000998,74 +0.000998,74 +0.000998,74 +0.001095,76 +0.001081,76 +0.001153,76 +0.001081,76 +0.001095,76 +0.001081,76 +0.001081,76 +0.001111,76 +0.001116,76 +0.001082,76 +0.001080,76 +0.001091,76 +0.001080,76 +0.001081,76 +0.001081,76 +0.001083,76 +0.001081,76 +0.001081,76 +0.001082,76 +0.001277,76 +0.001102,76 +0.001101,76 +0.001132,76 +0.001106,76 +0.001081,76 +0.001105,76 +0.001081,76 +0.001081,76 +0.001081,76 +0.001104,76 +0.001081,76 +0.001080,76 +0.001081,76 +0.001109,76 +0.001081,76 +0.001081,76 +0.001109,76 +0.001103,76 +0.001105,76 +0.001081,76 +0.001089,76 +0.001081,76 +0.001081,76 +0.001080,76 +0.001082,76 +0.001081,76 +0.001081,76 +0.001102,76 +0.001081,76 +0.001081,76 +0.001081,76 +0.001085,76 +0.001080,76 +0.001103,76 +0.001104,76 +0.001107,76 +0.001081,76 +0.001081,76 +0.001089,76 +0.001174,76 +0.001081,76 +0.001081,76 +0.001330,76 +0.001080,76 +0.001081,76 +0.001148,76 +0.001121,76 +0.001161,76 +0.001117,76 +0.001203,76 +0.001255,76 +0.001144,76 +0.001592,76 +0.002119,76 +0.002177,76 +0.001425,76 +0.001322,76 +0.001309,76 +0.001290,76 +0.001266,76 +0.001303,76 +0.001343,76 +0.001229,76 +0.001141,76 +0.001222,76 +0.001349,76 +0.001260,76 +0.001221,76 +0.001172,76 +0.001276,76 +0.001166,76 +0.001110,76 +0.001237,76 +0.001164,76 +0.001207,76 +0.001205,76 +0.001145,76 +0.001226,76 +0.001109,76 +0.001230,76 +0.001250,78 +0.001198,78 +0.001318,78 +0.001202,78 +0.001205,78 +0.001384,78 +0.001220,78 +0.001353,78 +0.001168,78 +0.001194,78 +0.001167,78 +0.001167,78 +0.001167,78 +0.001215,78 +0.001167,78 +0.001167,78 +0.001201,78 +0.001167,78 +0.001167,78 +0.001239,78 +0.001190,78 +0.001191,78 +0.001168,78 +0.001204,78 +0.001167,78 +0.001167,78 +0.001198,78 +0.001167,78 +0.001177,78 +0.001198,78 +0.001167,78 +0.001167,78 +0.001167,78 +0.001221,78 +0.001190,78 +0.001194,78 +0.001362,78 +0.001167,78 +0.001167,78 +0.001210,78 +0.001167,78 +0.001167,78 +0.001167,78 +0.001204,78 +0.001167,78 +0.001167,78 +0.001283,78 +0.001278,78 +0.001323,78 +0.001268,78 +0.001204,78 +0.001262,78 +0.001289,78 +0.001167,78 +0.001167,78 +0.001167,78 +0.001202,78 +0.001309,78 +0.001167,78 +0.001206,78 +0.001167,78 +0.001167,78 +0.001423,78 +0.001194,78 +0.001167,78 +0.001167,78 +0.001211,78 +0.001168,78 +0.001168,78 +0.001192,78 +0.001251,78 +0.001167,78 +0.001332,78 +0.001199,78 +0.001190,78 +0.001189,78 +0.001204,78 +0.001191,78 +0.001167,78 +0.001212,78 +0.001167,78 +0.001167,78 +0.001207,78 +0.001167,78 +0.001167,78 +0.001167,78 +0.001201,78 +0.001167,78 +0.001167,78 +0.001239,78 +0.001167,78 +0.001192,78 +0.001184,78 +0.001186,78 +0.001168,78 +0.001167,78 +0.001173,78 +0.001168,78 +0.001167,78 +0.001169,78 +0.001268,80 +0.001257,80 +0.001261,80 +0.001279,80 +0.001282,80 +0.001257,80 +0.001261,80 +0.001257,80 +0.001257,80 +0.001263,80 +0.001257,80 +0.001257,80 +0.001259,80 +0.001257,80 +0.001287,80 +0.001268,80 +0.001257,80 +0.001297,80 +0.001284,80 +0.001257,80 +0.001257,80 +0.001259,80 +0.001257,80 +0.001257,80 +0.001256,80 +0.001263,80 +0.001257,80 +0.001257,80 +0.001259,80 +0.001353,80 +0.001333,80 +0.001366,80 +0.001305,80 +0.001357,80 +0.001332,80 +0.001365,80 +0.001257,80 +0.001291,80 +0.001257,80 +0.001257,80 +0.001282,80 +0.001257,80 +0.001278,80 +0.001294,80 +0.001280,80 +0.001257,80 +0.001286,80 +0.001257,80 +0.001257,80 +0.001280,80 +0.001257,80 +0.001330,80 +0.001257,80 +0.001302,80 +0.001257,80 +0.001257,80 +0.001283,80 +0.001281,80 +0.001257,80 +0.001261,80 +0.001257,80 +0.001257,80 +0.001297,80 +0.001306,80 +0.001257,80 +0.001300,80 +0.001267,80 +0.001257,80 +0.001323,80 +0.001278,80 +0.001280,80 +0.001281,80 +0.001257,80 +0.001257,80 +0.001274,80 +0.001266,80 +0.001257,80 +0.001257,80 +0.001259,80 +0.001257,80 +0.001257,80 +0.001260,80 +0.001278,80 +0.001353,80 +0.001274,80 +0.001259,80 +0.001257,80 +0.001263,80 +0.001257,80 +0.001257,80 +0.001259,80 +0.001257,80 +0.001257,80 +0.001261,80 +0.001434,80 +0.001276,80 +0.001527,80 +0.001383,80 +0.001498,80 +0.001345,80 +0.001604,82 +0.001498,82 +0.001578,82 +0.001498,82 +0.001565,82 +0.001591,82 +0.001523,82 +0.001503,82 +0.001502,82 +0.001531,82 +0.001463,82 +0.001638,82 +0.001432,82 +0.001530,82 +0.001492,82 +0.001578,82 +0.001501,82 +0.001977,82 +0.001577,82 +0.001540,82 +0.001526,82 +0.001540,82 +0.001564,82 +0.001492,82 +0.001627,82 +0.001528,82 +0.001529,82 +0.001539,82 +0.001479,82 +0.001453,82 +0.001450,82 +0.001442,82 +0.001445,82 +0.001457,82 +0.001457,82 +0.001469,82 +0.001572,82 +0.001430,82 +0.001776,82 +0.001605,82 +0.001509,82 +0.001503,82 +0.001509,82 +0.001536,82 +0.001509,82 +0.001493,82 +0.001517,82 +0.001511,82 +0.001508,82 +0.001513,82 +0.001536,82 +0.001484,82 +0.001468,82 +0.001473,82 +0.001476,82 +0.001487,82 +0.001474,82 +0.001489,82 +0.001553,82 +0.001523,82 +0.001489,82 +0.001544,82 +0.001542,82 +0.001464,82 +0.001463,82 +0.001469,82 +0.001482,82 +0.001511,82 +0.001423,82 +0.001497,82 +0.001488,82 +0.001635,82 +0.001456,82 +0.001527,82 +0.001452,82 +0.001566,82 +0.001485,82 +0.001559,82 +0.001428,82 +0.001697,82 +0.001431,82 +0.001431,82 +0.001410,82 +0.001421,82 +0.001736,82 +0.001462,82 +0.001439,82 +0.001382,82 +0.001366,82 +0.001766,82 +0.001578,82 +0.001466,82 +0.001366,82 +0.001556,82 +0.001485,82 +0.001559,82 +0.001420,82 +0.001509,82 +0.001448,82 +0.001433,82 +0.001505,84 +0.001708,84 +0.001583,84 +0.001532,84 +0.001867,84 +0.001624,84 +0.001513,84 +0.001615,84 +0.001491,84 +0.001673,84 +0.001537,84 +0.001602,84 +0.001517,84 +0.001776,84 +0.001573,84 +0.001652,84 +0.001731,84 +0.001606,84 +0.001568,84 +0.001583,84 +0.001534,84 +0.001584,84 +0.001581,84 +0.001996,84 +0.001828,84 +0.001970,84 +0.001907,84 +0.001872,84 +0.001870,84 +0.001966,84 +0.001880,84 +0.001653,84 +0.001818,84 +0.001933,84 +0.001632,84 +0.001582,84 +0.001560,84 +0.001675,84 +0.001603,84 +0.001697,84 +0.001657,84 +0.001648,84 +0.001725,84 +0.001654,84 +0.001623,84 +0.001516,84 +0.001491,84 +0.001517,84 +0.001491,84 +0.001679,84 +0.001637,84 +0.001610,84 +0.001630,84 +0.001572,84 +0.001564,84 +0.001569,84 +0.001545,84 +0.001588,84 +0.001658,84 +0.001571,84 +0.001573,84 +0.001709,84 +0.001576,84 +0.001554,84 +0.001481,84 +0.001796,84 +0.001491,84 +0.001621,84 +0.001545,84 +0.001453,84 +0.001494,84 +0.001452,84 +0.001563,84 +0.001522,84 +0.001584,84 +0.001637,84 +0.001725,84 +0.001619,84 +0.001604,84 +0.001670,84 +0.001588,84 +0.001708,84 +0.001615,84 +0.001452,84 +0.001606,84 +0.001490,84 +0.001604,84 +0.001579,84 +0.001527,84 +0.001452,84 +0.001499,84 +0.001452,84 +0.001465,84 +0.001486,84 +0.001555,84 +0.001452,84 +0.001526,84 +0.001675,84 +0.001599,84 +0.001499,84 +0.001638,86 +0.001737,86 +0.001600,86 +0.001737,86 +0.001559,86 +0.001559,86 +0.001749,86 +0.001691,86 +0.001658,86 +0.001558,86 +0.001590,86 +0.001558,86 +0.001559,86 +0.001587,86 +0.001558,86 +0.001680,86 +0.001558,86 +0.001579,86 +0.001627,86 +0.001597,86 +0.001789,86 +0.001558,86 +0.001558,86 +0.001584,86 +0.001559,86 +0.001583,86 +0.001558,86 +0.001703,86 +0.001776,86 +0.001597,86 +0.001583,86 +0.001558,86 +0.001559,86 +0.001690,86 +0.001600,86 +0.001592,86 +0.001559,86 +0.001559,86 +0.001683,86 +0.001761,86 +0.001623,86 +0.001558,86 +0.001558,86 +0.001584,86 +0.001558,86 +0.001581,86 +0.001796,86 +0.001659,86 +0.001857,86 +0.001810,86 +0.001826,86 +0.001671,86 +0.001702,86 +0.001696,86 +0.001702,86 +0.001628,86 +0.001734,86 +0.001704,86 +0.001711,86 +0.001851,86 +0.001669,86 +0.001721,86 +0.001756,86 +0.001707,86 +0.001834,86 +0.001838,86 +0.001635,86 +0.001871,86 +0.001859,86 +0.001666,86 +0.001666,86 +0.001657,86 +0.001668,86 +0.001654,86 +0.001675,86 +0.001891,86 +0.001799,86 +0.001804,86 +0.001750,86 +0.001787,86 +0.001738,86 +0.001770,86 +0.001625,86 +0.001771,86 +0.001757,86 +0.001690,86 +0.001711,86 +0.001751,86 +0.001820,86 +0.001612,86 +0.001733,86 +0.001706,86 +0.001678,86 +0.001699,86 +0.001700,86 +0.001734,86 +0.001750,86 +0.001779,86 +0.001700,86 +0.001779,86 +0.001813,88 +0.001813,88 +0.001888,88 +0.001836,88 +0.001887,88 +0.001911,88 +0.001892,88 +0.001787,88 +0.001867,88 +0.001848,88 +0.001905,88 +0.001843,88 +0.001897,88 +0.002130,88 +0.004302,88 +0.001848,88 +0.001766,88 +0.001722,88 +0.001804,88 +0.001802,88 +0.001815,88 +0.001818,88 +0.001847,88 +0.001865,88 +0.001767,88 +0.001776,88 +0.001751,88 +0.001773,88 +0.001744,88 +0.001782,88 +0.001919,88 +0.002034,88 +0.001918,88 +0.001979,88 +0.001885,88 +0.001895,88 +0.001865,88 +0.001859,88 +0.001773,88 +0.001917,88 +0.001851,88 +0.001844,88 +0.001803,88 +0.001832,88 +0.001774,88 +0.001863,88 +0.001940,88 +0.001916,88 +0.001999,88 +0.001922,88 +0.001866,88 +0.001984,88 +0.001864,88 +0.001809,88 +0.001784,88 +0.001841,88 +0.001970,88 +0.001865,88 +0.001875,88 +0.001867,88 +0.001998,88 +0.001879,88 +0.001818,88 +0.001863,88 +0.001943,88 +0.002102,88 +0.001872,88 +0.001922,88 +0.001922,88 +0.001738,88 +0.001803,88 +0.001777,88 +0.001788,88 +0.002044,88 +0.002014,88 +0.001786,88 +0.001942,88 +0.001800,88 +0.001764,88 +0.001819,88 +0.001800,88 +0.001826,88 +0.001763,88 +0.001832,88 +0.001832,88 +0.001867,88 +0.001826,88 +0.001783,88 +0.001833,88 +0.001755,88 +0.001767,88 +0.001849,88 +0.001800,88 +0.001838,88 +0.002000,88 +0.001914,88 +0.001889,88 +0.001822,88 +0.001900,88 +0.001868,88 +0.002045,90 +0.002083,90 +0.001996,90 +0.002012,90 +0.001956,90 +0.001960,90 +0.001994,90 +0.001975,90 +0.002229,90 +0.001996,90 +0.001926,90 +0.002033,90 +0.001940,90 +0.001917,90 +0.001934,90 +0.001913,90 +0.001920,90 +0.001983,90 +0.001978,90 +0.002018,90 +0.001928,90 +0.001949,90 +0.001948,90 +0.001969,90 +0.002095,90 +0.001965,90 +0.002043,90 +0.001930,90 +0.001987,90 +0.001946,90 +0.001935,90 +0.001928,90 +0.001970,90 +0.001996,90 +0.001952,90 +0.002076,90 +0.002171,90 +0.002512,90 +0.002524,90 +0.002317,90 +0.002413,90 +0.002428,90 +0.002173,90 +0.002052,90 +0.002012,90 +0.001995,90 +0.001990,90 +0.002001,90 +0.001979,90 +0.001961,90 +0.002068,90 +0.001985,90 +0.001988,90 +0.002031,90 +0.002024,90 +0.002012,90 +0.001985,90 +0.001977,90 +0.002043,90 +0.002001,90 +0.002052,90 +0.002040,90 +0.002011,90 +0.002026,90 +0.001964,90 +0.002007,90 +0.001987,90 +0.001951,90 +0.001966,90 +0.002065,90 +0.001977,90 +0.001908,90 +0.001914,90 +0.002070,90 +0.002188,90 +0.002242,90 +0.002210,90 +0.002093,90 +0.002013,90 +0.001985,90 +0.001969,90 +0.001980,90 +0.001984,90 +0.001978,90 +0.001962,90 +0.001997,90 +0.001951,90 +0.001964,90 +0.001948,90 +0.001950,90 +0.001944,90 +0.002016,90 +0.001914,90 +0.001957,90 +0.001954,90 +0.001952,90 +0.001933,90 +0.001929,90 +0.001929,90 +0.001955,90 +0.002176,92 +0.002076,92 +0.002074,92 +0.002073,92 +0.002086,92 +0.002072,92 +0.002070,92 +0.002071,92 +0.002150,92 +0.002102,92 +0.002085,92 +0.002072,92 +0.002090,92 +0.002103,92 +0.002081,92 +0.002080,92 +0.002178,92 +0.002117,92 +0.002096,92 +0.002074,92 +0.002081,92 +0.002049,92 +0.001983,92 +0.001978,92 +0.001988,92 +0.002048,92 +0.002083,92 +0.001966,92 +0.001939,92 +0.001905,92 +0.001938,92 +0.001905,92 +0.001998,92 +0.001988,92 +0.001990,92 +0.001956,92 +0.001944,92 +0.001905,92 +0.001940,92 +0.001905,92 +0.001931,92 +0.002051,92 +0.001932,92 +0.001916,92 +0.001945,92 +0.001934,92 +0.001905,92 +0.001934,92 +0.001905,92 +0.001959,92 +0.001905,92 +0.001956,92 +0.002195,92 +0.002039,92 +0.002183,92 +0.001987,92 +0.002163,92 +0.002143,92 +0.002184,92 +0.002212,92 +0.002241,92 +0.002146,92 +0.002183,92 +0.002171,92 +0.002169,92 +0.002408,92 +0.002204,92 +0.002163,92 +0.002097,92 +0.002111,92 +0.002057,92 +0.002114,92 +0.002097,92 +0.002273,92 +0.002191,92 +0.002150,92 +0.002058,92 +0.002047,92 +0.002057,92 +0.002034,92 +0.001942,92 +0.002168,92 +0.002163,92 +0.003191,92 +0.002162,92 +0.002106,92 +0.002028,92 +0.002057,92 +0.002162,92 +0.002098,92 +0.002227,92 +0.002239,92 +0.002172,92 +0.002044,92 +0.002031,92 +0.002021,92 +0.002299,92 +0.002519,92 +0.002628,92 +0.002104,92 +0.002270,94 +0.002232,94 +0.002239,94 +0.002805,94 +0.002718,94 +0.002506,94 +0.002880,94 +0.002652,94 +0.002438,94 +0.002516,94 +0.002958,94 +0.002180,94 +0.002139,94 +0.002145,94 +0.002162,94 +0.002192,94 +0.002308,94 +0.002193,94 +0.003367,94 +0.002772,94 +0.002902,94 +0.002238,94 +0.002120,94 +0.002267,94 +0.002291,94 +0.002955,94 +0.002548,94 +0.002764,94 +0.002785,94 +0.002638,94 +0.002414,94 +0.002271,94 +0.002242,94 +0.002232,94 +0.002199,94 +0.002193,94 +0.002248,94 +0.002287,94 +0.002269,94 +0.002258,94 +0.002242,94 +0.002174,94 +0.002188,94 +0.002180,94 +0.002209,94 +0.002219,94 +0.002284,94 +0.002228,94 +0.002259,94 +0.002227,94 +0.002286,94 +0.002191,94 +0.002205,94 +0.002281,94 +0.002241,94 +0.002187,94 +0.002224,94 +0.002170,94 +0.002151,94 +0.002234,94 +0.002278,94 +0.002294,94 +0.002267,94 +0.002179,94 +0.002405,94 +0.002226,94 +0.002247,94 +0.002268,94 +0.002221,94 +0.002960,94 +0.003003,94 +0.002788,94 +0.002929,94 +0.002821,94 +0.003428,94 +0.002702,94 +0.002226,94 +0.002220,94 +0.002311,94 +0.002193,94 +0.002503,94 +0.002530,94 +0.002313,94 +0.002327,94 +0.002228,94 +0.002315,94 +0.002801,94 +0.003093,94 +0.002355,94 +0.002123,94 +0.002102,94 +0.002036,94 +0.002268,94 +0.002291,94 +0.002212,94 +0.002548,94 +0.002096,94 +0.002070,94 +0.002223,94 +0.003631,94 +0.003131,96 +0.002345,96 +0.002444,96 +0.002200,96 +0.002164,96 +0.002201,96 +0.002165,96 +0.002459,96 +0.002256,96 +0.002386,96 +0.002270,96 +0.002165,96 +0.002200,96 +0.002165,96 +0.002303,96 +0.002474,96 +0.002570,96 +0.002492,96 +0.002222,96 +0.002253,96 +0.002445,96 +0.002405,96 +0.002374,96 +0.002388,96 +0.002320,96 +0.002348,96 +0.002412,96 +0.002335,96 +0.002826,96 +0.002458,96 +0.002369,96 +0.002287,96 +0.002271,96 +0.002221,96 +0.002232,96 +0.002600,96 +0.002674,96 +0.002477,96 +0.002204,96 +0.002200,96 +0.002249,96 +0.002207,96 +0.002188,96 +0.003085,96 +0.002353,96 +0.002224,96 +0.002199,96 +0.002165,96 +0.002200,96 +0.002524,96 +0.002687,96 +0.002478,96 +0.002204,96 +0.002224,96 +0.002204,96 +0.002476,96 +0.002659,96 +0.002713,96 +0.002460,96 +0.002290,96 +0.002394,96 +0.002247,96 +0.002490,96 +0.002873,96 +0.002604,96 +0.002406,96 +0.002254,96 +0.002250,96 +0.002389,96 +0.002253,96 +0.002941,96 +0.002625,96 +0.002418,96 +0.002181,96 +0.002247,96 +0.002221,96 +0.002249,96 +0.002854,96 +0.002349,96 +0.002397,96 +0.002164,96 +0.002199,96 +0.002287,96 +0.002282,96 +0.002452,96 +0.002915,96 +0.002363,96 +0.002283,96 +0.002221,96 +0.002247,96 +0.002222,96 +0.002580,96 +0.002344,96 +0.002385,96 +0.002205,96 +0.002164,96 +0.002200,96 +0.002164,96 +0.002477,96 +0.002228,96 +0.002862,98 +0.002740,98 +0.002681,98 +0.002558,98 +0.003056,98 +0.003342,98 +0.002864,98 +0.003272,98 +0.003514,98 +0.002586,98 +0.002846,98 +0.003309,98 +0.002700,98 +0.002704,98 +0.002443,98 +0.002605,98 +0.003502,98 +0.003117,98 +0.002557,98 +0.002528,98 +0.002538,98 +0.002366,98 +0.002391,98 +0.003854,98 +0.003106,98 +0.002539,98 +0.002463,98 +0.002305,98 +0.003020,98 +0.002789,98 +0.002425,98 +0.002469,98 +0.002396,98 +0.002366,98 +0.002765,98 +0.002778,98 +0.002635,98 +0.002610,98 +0.002480,98 +0.002392,98 +0.002396,98 +0.002714,98 +0.002756,98 +0.002841,98 +0.004154,98 +0.002943,98 +0.002630,98 +0.002467,98 +0.003615,98 +0.003165,98 +0.002790,98 +0.002379,98 +0.003336,98 +0.002897,98 +0.003019,98 +0.002448,98 +0.002841,98 +0.002532,98 +0.002560,98 +0.002856,98 +0.003478,98 +0.003149,98 +0.002553,98 +0.002413,98 +0.002631,98 +0.003139,98 +0.002597,98 +0.002427,98 +0.002502,98 +0.002393,98 +0.002618,98 +0.002441,98 +0.002753,98 +0.003863,98 +0.003689,98 +0.002348,98 +0.002846,98 +0.002731,98 +0.002495,98 +0.002508,98 +0.002396,98 +0.002401,98 +0.002703,98 +0.002545,98 +0.002685,98 +0.002514,98 +0.002346,98 +0.002623,98 +0.002410,98 +0.002921,98 +0.003268,98 +0.002623,98 +0.002346,98 +0.002697,98 +0.002615,98 +0.002521,98 +0.003498,98 +0.003344,98 +0.003301,98 +0.002581,98 +0.002742,100 +0.002698,100 +0.003454,100 +0.002797,100 +0.002585,100 +0.002507,100 +0.002585,100 +0.002588,100 +0.003374,100 +0.002645,100 +0.002527,100 +0.002447,100 +0.002799,100 +0.002665,100 +0.003417,100 +0.002694,100 +0.002484,100 +0.002548,100 +0.002658,100 +0.002574,100 +0.003506,100 +0.002723,100 +0.002596,100 +0.002688,100 +0.002624,100 +0.002649,100 +0.003460,100 +0.002747,100 +0.002662,100 +0.002631,100 +0.002617,100 +0.002584,100 +0.002649,100 +0.002590,100 +0.002796,100 +0.002484,100 +0.002778,100 +0.002643,100 +0.002649,100 +0.002754,100 +0.002555,100 +0.002564,100 +0.002531,100 +0.004300,100 +0.002859,100 +0.002562,100 +0.002571,100 +0.002561,100 +0.002549,100 +0.002654,100 +0.002806,100 +0.002635,100 +0.002647,100 +0.002842,100 +0.002732,100 +0.002691,100 +0.004549,100 +0.003644,100 +0.003237,100 +0.003062,100 +0.003510,100 +0.002940,100 +0.002762,100 +0.002677,100 +0.002640,100 +0.002693,100 +0.002635,100 +0.002778,100 +0.004505,100 +0.002998,100 +0.003058,100 +0.002824,100 +0.002817,100 +0.002728,100 +0.002627,100 +0.002649,100 +0.002588,100 +0.003822,100 +0.003904,100 +0.003254,100 +0.003074,100 +0.003190,100 +0.003889,100 +0.003142,100 +0.002844,100 +0.002776,100 +0.002816,100 +0.003645,100 +0.003645,100 +0.002665,100 +0.002592,100 +0.002575,100 +0.002658,100 +0.003486,100 +0.002725,100 +0.002622,100 +0.002620,100 +0.002645,100 +0.002613,100 +0.002580,100 +0.002724,102 +0.003303,102 +0.003048,102 +0.002780,102 +0.002951,102 +0.004601,102 +0.003367,102 +0.003190,102 +0.003475,102 +0.003924,102 +0.003630,102 +0.002814,102 +0.002834,102 +0.002798,102 +0.002829,102 +0.003342,102 +0.003120,102 +0.002870,102 +0.002729,102 +0.002820,102 +0.003945,102 +0.003139,102 +0.003297,102 +0.002713,102 +0.002807,102 +0.002903,102 +0.003155,102 +0.003056,102 +0.002928,102 +0.002823,102 +0.002892,102 +0.003179,102 +0.002805,102 +0.002963,102 +0.003007,102 +0.002791,102 +0.002833,102 +0.003276,102 +0.003000,102 +0.002734,102 +0.002885,102 +0.002941,102 +0.003071,102 +0.003235,102 +0.003131,102 +0.002980,102 +0.003010,102 +0.002969,102 +0.002932,102 +0.003002,102 +0.002888,102 +0.002757,102 +0.002811,102 +0.002874,102 +0.002963,102 +0.002898,102 +0.002741,102 +0.002809,102 +0.002712,102 +0.003060,102 +0.003273,102 +0.003245,102 +0.003031,102 +0.002997,102 +0.003172,102 +0.002861,102 +0.002823,102 +0.002939,102 +0.002998,102 +0.002820,102 +0.002794,102 +0.003012,102 +0.002913,102 +0.002679,102 +0.002762,102 +0.002738,102 +0.002825,102 +0.002687,102 +0.002860,102 +0.002803,102 +0.002834,102 +0.002665,102 +0.002883,102 +0.002636,102 +0.002978,102 +0.002732,102 +0.002656,102 +0.002633,102 +0.002697,102 +0.002831,102 +0.002744,102 +0.002656,102 +0.002900,102 +0.002691,102 +0.002800,102 +0.002862,102 +0.003009,102 +0.002916,102 +0.002882,102 +0.002770,102 +0.003104,104 +0.004950,104 +0.005103,104 +0.004573,104 +0.004026,104 +0.003457,104 +0.003062,104 +0.003048,104 +0.002974,104 +0.003241,104 +0.003673,104 +0.002939,104 +0.002939,104 +0.002946,104 +0.003087,104 +0.003103,104 +0.003060,104 +0.003008,104 +0.003019,104 +0.003130,104 +0.003015,104 +0.003053,104 +0.002991,104 +0.003000,104 +0.003002,104 +0.002993,104 +0.003105,104 +0.003042,104 +0.003033,104 +0.003031,104 +0.003215,104 +0.002948,104 +0.002988,104 +0.003126,104 +0.003376,104 +0.003281,104 +0.003323,104 +0.003151,104 +0.003025,104 +0.002992,104 +0.002998,104 +0.003124,104 +0.003087,104 +0.003148,104 +0.003070,104 +0.003095,104 +0.003224,104 +0.003072,104 +0.002990,104 +0.003106,104 +0.003007,104 +0.003000,104 +0.003089,104 +0.002909,104 +0.002937,104 +0.003134,104 +0.003013,104 +0.003071,104 +0.003501,104 +0.003272,104 +0.002931,104 +0.002971,104 +0.003224,104 +0.003673,104 +0.004977,104 +0.005140,104 +0.004520,104 +0.003520,104 +0.003634,104 +0.003674,104 +0.003072,104 +0.004450,104 +0.005067,104 +0.003972,104 +0.003040,104 +0.004208,104 +0.003163,104 +0.003146,104 +0.003114,104 +0.003184,104 +0.004320,104 +0.004138,104 +0.003283,104 +0.003101,104 +0.003353,104 +0.003452,104 +0.003375,104 +0.003198,104 +0.002984,104 +0.002996,104 +0.003103,104 +0.003065,104 +0.002990,104 +0.003533,104 +0.002977,104 +0.003177,104 +0.003234,104 +0.003008,104 +0.002749,104 +0.002798,104 +0.003047,106 +0.003276,106 +0.003251,106 +0.002976,106 +0.002943,106 +0.002945,106 +0.003244,106 +0.003172,106 +0.003055,106 +0.002941,106 +0.002908,106 +0.003125,106 +0.003282,106 +0.003298,106 +0.002979,106 +0.002907,106 +0.002947,106 +0.003287,106 +0.003200,106 +0.003031,106 +0.002942,106 +0.002940,106 +0.003263,106 +0.003190,106 +0.003135,106 +0.003207,106 +0.003102,106 +0.003048,106 +0.003238,106 +0.004084,106 +0.003262,106 +0.002951,106 +0.003074,106 +0.003253,106 +0.003276,106 +0.002987,106 +0.002948,106 +0.002943,106 +0.003273,106 +0.003223,106 +0.003069,106 +0.002946,106 +0.002907,106 +0.003239,106 +0.003170,106 +0.003175,106 +0.002966,106 +0.002907,106 +0.002944,106 +0.003637,106 +0.003381,106 +0.003021,106 +0.002907,106 +0.002945,106 +0.003403,106 +0.003164,106 +0.003231,106 +0.003006,106 +0.003251,106 +0.003278,106 +0.003057,106 +0.003331,106 +0.003197,106 +0.003204,106 +0.003135,106 +0.003388,106 +0.003199,106 +0.003293,106 +0.003074,106 +0.003239,106 +0.003718,106 +0.003302,106 +0.003199,106 +0.003224,106 +0.003473,106 +0.004491,106 +0.003305,106 +0.002990,106 +0.003136,106 +0.003739,106 +0.003203,106 +0.003375,106 +0.003028,106 +0.003151,106 +0.003945,106 +0.003031,106 +0.003347,106 +0.003095,106 +0.003152,106 +0.003090,106 +0.003259,106 +0.003189,106 +0.002980,106 +0.002939,106 +0.002946,106 +0.003175,106 +0.003065,106 +0.003058,106 +0.002943,106 +0.002907,106 +0.003187,108 +0.003114,108 +0.003144,108 +0.003167,108 +0.003105,108 +0.003137,108 +0.003077,108 +0.003091,108 +0.003151,108 +0.003082,108 +0.003082,108 +0.003137,108 +0.003076,108 +0.003128,108 +0.003080,108 +0.003082,108 +0.003117,108 +0.003076,108 +0.003171,108 +0.003267,108 +0.003295,108 +0.003273,108 +0.003076,108 +0.003203,108 +0.003136,108 +0.003176,108 +0.003111,108 +0.003154,108 +0.003122,108 +0.003130,108 +0.003084,108 +0.003076,108 +0.003118,108 +0.003448,108 +0.003253,108 +0.003176,108 +0.003076,108 +0.003272,108 +0.003213,108 +0.003440,108 +0.003461,108 +0.003272,108 +0.003390,108 +0.003595,108 +0.003716,108 +0.003763,108 +0.003569,108 +0.003491,108 +0.004074,108 +0.004008,108 +0.003675,108 +0.003863,108 +0.004063,108 +0.004119,108 +0.003293,108 +0.003363,108 +0.003859,108 +0.004069,108 +0.003520,108 +0.003406,108 +0.003918,108 +0.003379,108 +0.003471,108 +0.003419,108 +0.003413,108 +0.003456,108 +0.003645,108 +0.003479,108 +0.003432,108 +0.003446,108 +0.003743,108 +0.003456,108 +0.003485,108 +0.003335,108 +0.003717,108 +0.003818,108 +0.004702,108 +0.003204,108 +0.003619,108 +0.004511,108 +0.003444,108 +0.003417,108 +0.003457,108 +0.003391,108 +0.004317,108 +0.003866,108 +0.003940,108 +0.004001,108 +0.004094,108 +0.003464,108 +0.003306,108 +0.003358,108 +0.004539,108 +0.003901,108 +0.003670,108 +0.003260,108 +0.003190,108 +0.003597,108 +0.003501,108 +0.003408,108 +0.003429,110 +0.003429,110 +0.003797,110 +0.004116,110 +0.004120,110 +0.003768,110 +0.004135,110 +0.003665,110 +0.003478,110 +0.003370,110 +0.003650,110 +0.003790,110 +0.003530,110 +0.003283,110 +0.003287,110 +0.003979,110 +0.003637,110 +0.003364,110 +0.003284,110 +0.003276,110 +0.003956,110 +0.003654,110 +0.003303,110 +0.003277,110 +0.003401,110 +0.003906,110 +0.003552,110 +0.003310,110 +0.003291,110 +0.003906,110 +0.003494,110 +0.004124,110 +0.004018,110 +0.003607,110 +0.004405,110 +0.003534,110 +0.003367,110 +0.003302,110 +0.004091,110 +0.003674,110 +0.003433,110 +0.003281,110 +0.003282,110 +0.004209,110 +0.004076,110 +0.003343,110 +0.003248,110 +0.003524,110 +0.004683,110 +0.003419,110 +0.003310,110 +0.003274,110 +0.003638,110 +0.004112,110 +0.003305,110 +0.003293,110 +0.003420,110 +0.004203,110 +0.003878,110 +0.003977,110 +0.003768,110 +0.004266,110 +0.003622,110 +0.003306,110 +0.003291,110 +0.003711,110 +0.004202,110 +0.003488,110 +0.003287,110 +0.003288,110 +0.004122,110 +0.003463,110 +0.003373,110 +0.003309,110 +0.003280,110 +0.003765,110 +0.003592,110 +0.003307,110 +0.003268,110 +0.003380,110 +0.003534,110 +0.003634,110 +0.003308,110 +0.003291,110 +0.003403,110 +0.003537,110 +0.003463,110 +0.004221,110 +0.003886,110 +0.003534,110 +0.003454,110 +0.003349,110 +0.003297,110 +0.003337,110 +0.003307,110 +0.003330,110 +0.003333,110 +0.003292,110 +0.003253,110 +0.003314,110 +0.003456,112 +0.003488,112 +0.003424,112 +0.003424,112 +0.003485,112 +0.003424,112 +0.003509,112 +0.003465,112 +0.003487,112 +0.003426,112 +0.003655,112 +0.003506,112 +0.003448,112 +0.003691,112 +0.003444,112 +0.003525,112 +0.004253,112 +0.004014,112 +0.003595,112 +0.003568,112 +0.003467,112 +0.003682,112 +0.003663,112 +0.003452,112 +0.003849,112 +0.003829,112 +0.003802,112 +0.004047,112 +0.003946,112 +0.003842,112 +0.003872,112 +0.003809,112 +0.003732,112 +0.003750,112 +0.003766,112 +0.003737,112 +0.003740,112 +0.003876,112 +0.003732,112 +0.003700,112 +0.004181,112 +0.004431,112 +0.004791,112 +0.004435,112 +0.004282,112 +0.004833,112 +0.003635,112 +0.003641,112 +0.004416,112 +0.004212,112 +0.003849,112 +0.003800,112 +0.004405,112 +0.004508,112 +0.003790,112 +0.003760,112 +0.004236,112 +0.004309,112 +0.004036,112 +0.004067,112 +0.004138,112 +0.004338,112 +0.003998,112 +0.003950,112 +0.004470,112 +0.004087,112 +0.003750,112 +0.003674,112 +0.004195,112 +0.003909,112 +0.003730,112 +0.003789,112 +0.003871,112 +0.004001,112 +0.003885,112 +0.003800,112 +0.003805,112 +0.003705,112 +0.003966,112 +0.003826,112 +0.003758,112 +0.004308,112 +0.004099,112 +0.003878,112 +0.003669,112 +0.004048,112 +0.003747,112 +0.004013,112 +0.003836,112 +0.004167,112 +0.004281,112 +0.003775,112 +0.003679,112 +0.003618,112 +0.004103,112 +0.004505,112 +0.003802,112 +0.003920,112 +0.004098,112 +0.003758,112 +0.004096,114 +0.004092,114 +0.004524,114 +0.003986,114 +0.004240,114 +0.004373,114 +0.004719,114 +0.004651,114 +0.004453,114 +0.004648,114 +0.004415,114 +0.004713,114 +0.004440,114 +0.004585,114 +0.004241,114 +0.003937,114 +0.003874,114 +0.004223,114 +0.004237,114 +0.004248,114 +0.003954,114 +0.004599,114 +0.003933,114 +0.004173,114 +0.003968,114 +0.004382,114 +0.004115,114 +0.004127,114 +0.004023,114 +0.004088,114 +0.004349,114 +0.004448,114 +0.004103,114 +0.004327,114 +0.004140,114 +0.004051,114 +0.004106,114 +0.004270,114 +0.004178,114 +0.004092,114 +0.004039,114 +0.003899,114 +0.004260,114 +0.004283,114 +0.004056,114 +0.004069,114 +0.004379,114 +0.004036,114 +0.004061,114 +0.004247,114 +0.003940,114 +0.004357,114 +0.004266,114 +0.004872,114 +0.004120,114 +0.004111,114 +0.004133,114 +0.004764,114 +0.004693,114 +0.004351,114 +0.004444,114 +0.004386,114 +0.004131,114 +0.004052,114 +0.003993,114 +0.004490,114 +0.004194,114 +0.004035,114 +0.004154,114 +0.004109,114 +0.004098,114 +0.004010,114 +0.004149,114 +0.004626,114 +0.004505,114 +0.003911,114 +0.004349,114 +0.004280,114 +0.004227,114 +0.003865,114 +0.004203,114 +0.004726,114 +0.004246,114 +0.004057,114 +0.004151,114 +0.004506,114 +0.004091,114 +0.004129,114 +0.003975,114 +0.004005,114 +0.004205,114 +0.004115,114 +0.004046,114 +0.004115,114 +0.004059,114 +0.003898,114 +0.003900,114 +0.004033,114 +0.003874,114 +0.003878,114 +0.004165,116 +0.004023,116 +0.003963,116 +0.003937,116 +0.003927,116 +0.003950,116 +0.004177,116 +0.003951,116 +0.003834,116 +0.003977,116 +0.003862,116 +0.003893,116 +0.003824,116 +0.003883,116 +0.004006,116 +0.004065,116 +0.003836,116 +0.003913,116 +0.003836,116 +0.003851,116 +0.003851,116 +0.003833,116 +0.003878,116 +0.003807,116 +0.003856,116 +0.003801,116 +0.003897,116 +0.003805,116 +0.003903,116 +0.003825,116 +0.003925,116 +0.003808,116 +0.003824,116 +0.003827,116 +0.003812,116 +0.003879,116 +0.003935,116 +0.003904,116 +0.003808,116 +0.003932,116 +0.003906,116 +0.004212,116 +0.003857,116 +0.004047,116 +0.003861,116 +0.003930,116 +0.003859,116 +0.003830,116 +0.003823,116 +0.003885,116 +0.003844,116 +0.003812,116 +0.003804,116 +0.003832,116 +0.003877,116 +0.003803,116 +0.003807,116 +0.003801,116 +0.003831,116 +0.003943,116 +0.003805,116 +0.003826,116 +0.003802,116 +0.003859,116 +0.003803,116 +0.003913,116 +0.003920,116 +0.004088,116 +0.003964,116 +0.003828,116 +0.003826,116 +0.003879,116 +0.003828,116 +0.003809,116 +0.003812,116 +0.003832,116 +0.003845,116 +0.003829,116 +0.003806,116 +0.003802,116 +0.003875,116 +0.003803,116 +0.003804,116 +0.003800,116 +0.003830,116 +0.003849,116 +0.003802,116 +0.003805,116 +0.003802,116 +0.003875,116 +0.003802,116 +0.003932,116 +0.003888,116 +0.004108,116 +0.003871,116 +0.003825,116 +0.003979,116 +0.003924,116 +0.003832,116 +0.003967,116 +0.004099,118 +0.004075,118 +0.004074,118 +0.004004,118 +0.004010,118 +0.004033,118 +0.004051,118 +0.004004,118 +0.004004,118 +0.004007,118 +0.004094,118 +0.004050,118 +0.004003,118 +0.004006,118 +0.004077,118 +0.004006,118 +0.004087,118 +0.004210,118 +0.004358,118 +0.004105,118 +0.004024,118 +0.004011,118 +0.004085,118 +0.004140,118 +0.004008,118 +0.004016,118 +0.004140,118 +0.004010,118 +0.004005,118 +0.004004,118 +0.004075,118 +0.004006,118 +0.004006,118 +0.004004,118 +0.004124,118 +0.004004,118 +0.004149,118 +0.004055,118 +0.004022,118 +0.004042,118 +0.004037,118 +0.004253,118 +0.004472,118 +0.004140,118 +0.004036,118 +0.004067,118 +0.004177,118 +0.004095,118 +0.004128,118 +0.004145,118 +0.004078,118 +0.004070,118 +0.004007,118 +0.004009,118 +0.004034,118 +0.004069,118 +0.004007,118 +0.004009,118 +0.004007,118 +0.004071,118 +0.004006,118 +0.004003,118 +0.004006,118 +0.004093,118 +0.004039,118 +0.004071,118 +0.004192,118 +0.004376,118 +0.004032,118 +0.004024,118 +0.004029,118 +0.004094,118 +0.004011,118 +0.004007,118 +0.004009,118 +0.004075,118 +0.004004,118 +0.004006,118 +0.004004,118 +0.004078,118 +0.004024,118 +0.004006,118 +0.004003,118 +0.004033,118 +0.004112,118 +0.004038,118 +0.004023,118 +0.004035,118 +0.004048,118 +0.004004,118 +0.004159,118 +0.004318,118 +0.004226,118 +0.004037,118 +0.004078,118 +0.004100,118 +0.004078,118 +0.004041,118 +0.004005,118 +0.004013,118 +0.004287,120 +0.004207,120 +0.004205,120 +0.004205,120 +0.004275,120 +0.004208,120 +0.004204,120 +0.004206,120 +0.004272,120 +0.004207,120 +0.004204,120 +0.004236,120 +0.004244,120 +0.004211,120 +0.004343,120 +0.004570,120 +0.004448,120 +0.004240,120 +0.004242,120 +0.004260,120 +0.004269,120 +0.004209,120 +0.004207,120 +0.004272,120 +0.004207,120 +0.004203,120 +0.004206,120 +0.004277,120 +0.004204,120 +0.004205,120 +0.004203,120 +0.004275,120 +0.004203,120 +0.004205,120 +0.004223,120 +0.004274,120 +0.004203,120 +0.004205,120 +0.004403,120 +0.004593,120 +0.004256,120 +0.004269,120 +0.004335,120 +0.004336,120 +0.004315,120 +0.004269,120 +0.004230,120 +0.004365,120 +0.004229,120 +0.004224,120 +0.004224,120 +0.004274,120 +0.004204,120 +0.004206,120 +0.004233,120 +0.004246,120 +0.004391,120 +0.004207,120 +0.004236,120 +0.004243,120 +0.004206,120 +0.004343,120 +0.004532,120 +0.004434,120 +0.004247,120 +0.004307,120 +0.004299,120 +0.004225,120 +0.004233,120 +0.004225,120 +0.004294,120 +0.004319,120 +0.004244,120 +0.004232,120 +0.004317,120 +0.004256,120 +0.004245,120 +0.004250,120 +0.004315,120 +0.004206,120 +0.004204,120 +0.004205,120 +0.004273,120 +0.004206,120 +0.004238,120 +0.004449,120 +0.004641,120 +0.004204,120 +0.004205,120 +0.004224,120 +0.004247,120 +0.004204,120 +0.004205,120 +0.004233,120 +0.004265,120 +0.004204,120 +0.004205,120 +0.004231,120 +0.004290,120 +0.004203,120 +0.004448,122 +0.004493,122 +0.004564,122 +0.004424,122 +0.004419,122 +0.004477,122 +0.004420,122 +0.004419,122 +0.004614,122 +0.004852,122 +0.004420,122 +0.004643,122 +0.004469,122 +0.004523,122 +0.004598,122 +0.004456,122 +0.004554,122 +0.004446,122 +0.004423,122 +0.004419,122 +0.004492,122 +0.004420,122 +0.004420,122 +0.004452,122 +0.004460,122 +0.004424,122 +0.004421,122 +0.004471,122 +0.004488,122 +0.004445,122 +0.004588,122 +0.004816,122 +0.004674,122 +0.004440,122 +0.004448,122 +0.004523,122 +0.004466,122 +0.004424,122 +0.004470,122 +0.004481,122 +0.004423,122 +0.004464,122 +0.004488,122 +0.004422,122 +0.004427,122 +0.004422,122 +0.004530,122 +0.004423,122 +0.004420,122 +0.004422,122 +0.004537,122 +0.004419,122 +0.004470,122 +0.004943,122 +0.004728,122 +0.004450,122 +0.004420,122 +0.004705,122 +0.004813,122 +0.004763,122 +0.004560,122 +0.004446,122 +0.004525,122 +0.004445,122 +0.004512,122 +0.004572,122 +0.004654,122 +0.004420,122 +0.004476,122 +0.004561,122 +0.004623,122 +0.004454,122 +0.004489,122 +0.004460,122 +0.004494,122 +0.004738,122 +0.004682,122 +0.004465,122 +0.004475,122 +0.004489,122 +0.004479,122 +0.004420,122 +0.004420,122 +0.004477,122 +0.004420,122 +0.004442,122 +0.004431,122 +0.004486,122 +0.004441,122 +0.004464,122 +0.004468,122 +0.004420,122 +0.004422,122 +0.004419,122 +0.004512,122 +0.004420,122 +0.004425,122 +0.004646,122 +0.004711,122 +0.004576,122 +0.004711,124 +0.004750,124 +0.004739,124 +0.004677,124 +0.004678,124 +0.004712,124 +0.004638,124 +0.004635,124 +0.004690,124 +0.004638,124 +0.004636,124 +0.004637,124 +0.004684,124 +0.004695,124 +0.004646,124 +0.004648,124 +0.004681,124 +0.004635,124 +0.004683,124 +0.004996,124 +0.004826,124 +0.004724,124 +0.004688,124 +0.004707,124 +0.004640,124 +0.004642,124 +0.004685,124 +0.004681,124 +0.004666,124 +0.004638,124 +0.004685,124 +0.004640,124 +0.004692,124 +0.004689,124 +0.004635,124 +0.004641,124 +0.004636,124 +0.004689,124 +0.004661,124 +0.004636,124 +0.004882,124 +0.004919,124 +0.004701,124 +0.004638,124 +0.004705,124 +0.004638,124 +0.004636,124 +0.004647,124 +0.004680,124 +0.004636,124 +0.005736,124 +0.004788,124 +0.004636,124 +0.004643,124 +0.004678,124 +0.004667,124 +0.004638,124 +0.004635,124 +0.004687,124 +0.004641,124 +0.004636,124 +0.004925,124 +0.005010,124 +0.004684,124 +0.004679,124 +0.004749,124 +0.004758,124 +0.004657,124 +0.004758,124 +0.004704,124 +0.004636,124 +0.004638,124 +0.004706,124 +0.004639,124 +0.004636,124 +0.004667,124 +0.004699,124 +0.004636,124 +0.004670,124 +0.004706,124 +0.004659,124 +0.004635,124 +0.004787,124 +0.005047,124 +0.004857,124 +0.004656,124 +0.004749,124 +0.004659,124 +0.004636,124 +0.004662,124 +0.004766,124 +0.004687,124 +0.004664,124 +0.004730,124 +0.004661,124 +0.004636,124 +0.004642,124 +0.004704,124 +0.004640,124 +0.004638,124 +0.004915,126 +0.004906,126 +0.004864,126 +0.004917,126 +0.005215,126 +0.005071,126 +0.004884,126 +0.005222,126 +0.004990,126 +0.005259,126 +0.005390,126 +0.005463,126 +0.005577,126 +0.005841,126 +0.005507,126 +0.005470,126 +0.005750,126 +0.007375,126 +0.006174,126 +0.006265,126 +0.005507,126 +0.005868,126 +0.009030,126 +0.007537,126 +0.007350,126 +0.005591,126 +0.005574,126 +0.007123,126 +0.005460,126 +0.005456,126 +0.007157,126 +0.005286,126 +0.005380,126 +0.006827,126 +0.005305,126 +0.005246,126 +0.006802,126 +0.005030,126 +0.008349,126 +0.008952,126 +0.004990,126 +0.004984,126 +0.004962,126 +0.004979,126 +0.005130,126 +0.004950,126 +0.005002,126 +0.004897,126 +0.004938,126 +0.004991,126 +0.004948,126 +0.005013,126 +0.004889,126 +0.004946,126 +0.004927,126 +0.004868,126 +0.006621,126 +0.008387,126 +0.004923,126 +0.004954,126 +0.004954,126 +0.004868,126 +0.005026,126 +0.004867,126 +0.004864,126 +0.004906,126 +0.004905,126 +0.004864,126 +0.004866,126 +0.004947,126 +0.004884,126 +0.004866,126 +0.004942,126 +0.004866,126 +0.004867,126 +0.005186,126 +0.008795,126 +0.005915,126 +0.004976,126 +0.004869,126 +0.004885,126 +0.004933,126 +0.004925,126 +0.004887,126 +0.004868,126 +0.004964,126 +0.004888,126 +0.004887,126 +0.004947,126 +0.004867,126 +0.004949,126 +0.004907,126 +0.004930,126 +0.004866,126 +0.004866,126 +0.007738,126 +0.007211,126 +0.004975,126 +0.004872,126 +0.004864,126 +0.005386,128 +0.005457,128 +0.005374,128 +0.005376,128 +0.005440,128 +0.005372,128 +0.005418,128 +0.005458,128 +0.005413,128 +0.005375,128 +0.005435,128 +0.005372,128 +0.005376,128 +0.007662,128 +0.008165,128 +0.005499,128 +0.005405,128 +0.005429,128 +0.005458,128 +0.005401,128 +0.005376,128 +0.005431,128 +0.005375,128 +0.005376,128 +0.005431,128 +0.005375,128 +0.005376,128 +0.005392,128 +0.005415,128 +0.005377,128 +0.005393,128 +0.008756,128 +0.007322,128 +0.005482,128 +0.005442,128 +0.005407,128 +0.005487,128 +0.005377,128 +0.005396,128 +0.005436,128 +0.005373,128 +0.005375,128 +0.005435,128 +0.005373,128 +0.005418,128 +0.005435,128 +0.005373,128 +0.005376,128 +0.006360,128 +0.009397,128 +0.005654,128 +0.005469,128 +0.005642,128 +0.005554,128 +0.005407,128 +0.005405,128 +0.005435,128 +0.005401,128 +0.005411,128 +0.005434,128 +0.005408,128 +0.005464,128 +0.005396,128 +0.005417,128 +0.005377,128 +0.005395,128 +0.008415,128 +0.007413,128 +0.005487,128 +0.005378,128 +0.005376,128 +0.005459,128 +0.005373,128 +0.005375,128 +0.005466,128 +0.005374,128 +0.005660,128 +0.006978,128 +0.005549,128 +0.005383,128 +0.005587,128 +0.006194,128 +0.005526,128 +0.008246,128 +0.008427,128 +0.005702,128 +0.005406,128 +0.005692,128 +0.005657,128 +0.005604,128 +0.005617,128 +0.005458,128 +0.005567,128 +0.005881,128 +0.005510,128 +0.005733,128 +0.005493,128 +0.005481,128 +0.005583,128 +0.005448,128 +0.007634,130 +0.008371,130 +0.005475,130 +0.005438,130 +0.005381,130 +0.005505,130 +0.005396,130 +0.005344,130 +0.005421,130 +0.005375,130 +0.005337,130 +0.005420,130 +0.005397,130 +0.005339,130 +0.005418,130 +0.005390,130 +0.005344,130 +0.005521,130 +0.007434,130 +0.008883,130 +0.005438,130 +0.005415,130 +0.005448,130 +0.005405,130 +0.005400,130 +0.005437,130 +0.005424,130 +0.005340,130 +0.005439,130 +0.005372,130 +0.005340,130 +0.005378,130 +0.005383,130 +0.005380,130 +0.005378,130 +0.006334,130 +0.009437,130 +0.005541,130 +0.005377,130 +0.005616,130 +0.005437,130 +0.005339,130 +0.005600,130 +0.005439,130 +0.005337,130 +0.005339,130 +0.005459,130 +0.005337,130 +0.005339,130 +0.005439,130 +0.005337,130 +0.005341,130 +0.005442,130 +0.007503,130 +0.008373,130 +0.005348,130 +0.005343,130 +0.005455,130 +0.005339,130 +0.005364,130 +0.005397,130 +0.005379,130 +0.005341,130 +0.005378,130 +0.005380,130 +0.005342,130 +0.005357,130 +0.005421,130 +0.005341,130 +0.005337,130 +0.005517,130 +0.008094,130 +0.007734,130 +0.005471,130 +0.006000,130 +0.006253,130 +0.005450,130 +0.005444,130 +0.005474,130 +0.005337,130 +0.005420,130 +0.005439,130 +0.005398,130 +0.005341,130 +0.005421,130 +0.005338,130 +0.005342,130 +0.005425,130 +0.006189,130 +0.009636,130 +0.005515,130 +0.005400,130 +0.005429,130 +0.005374,130 +0.005482,130 +0.005847,130 +0.005396,130 +0.005360,130 +0.005418,130 +0.005342,130 +0.005615,132 +0.005666,132 +0.005921,132 +0.005611,132 +0.005735,132 +0.005710,132 +0.010125,132 +0.006354,132 +0.005653,132 +0.005672,132 +0.005607,132 +0.005646,132 +0.005715,132 +0.006172,132 +0.006019,132 +0.005687,132 +0.005589,132 +0.005627,132 +0.005667,132 +0.005585,132 +0.005590,132 +0.005691,132 +0.007254,132 +0.009219,132 +0.005691,132 +0.005624,132 +0.005865,132 +0.005591,132 +0.005606,132 +0.005692,132 +0.005588,132 +0.005589,132 +0.005665,132 +0.005587,132 +0.005611,132 +0.005685,132 +0.005606,132 +0.005592,132 +0.005745,132 +0.007300,132 +0.009084,132 +0.005619,132 +0.005597,132 +0.005708,132 +0.005624,132 +0.005675,132 +0.005747,132 +0.005725,132 +0.005683,132 +0.005650,132 +0.005598,132 +0.005613,132 +0.005687,132 +0.005588,132 +0.005605,132 +0.005759,132 +0.007564,132 +0.008772,132 +0.005623,132 +0.005671,132 +0.005660,132 +0.005645,132 +0.005625,132 +0.005628,132 +0.005589,132 +0.005606,132 +0.005635,132 +0.005744,132 +0.005645,132 +0.005590,132 +0.005586,132 +0.005669,132 +0.005738,132 +0.007667,132 +0.008944,132 +0.005686,132 +0.005690,132 +0.006929,132 +0.010806,132 +0.010826,132 +0.010964,132 +0.010989,132 +0.010404,132 +0.008319,132 +0.005731,132 +0.008331,132 +0.008752,132 +0.005674,132 +0.005879,132 +0.005639,132 +0.005672,132 +0.005971,132 +0.005622,132 +0.005645,132 +0.005624,132 +0.005586,132 +0.005622,132 +0.005624,132 +0.005585,132 +0.005644,132 +0.005968,134 +0.006600,134 +0.010243,134 +0.005955,134 +0.006033,134 +0.005905,134 +0.005864,134 +0.005923,134 +0.005841,134 +0.005846,134 +0.005925,134 +0.005844,134 +0.005881,134 +0.005923,134 +0.005842,134 +0.005863,134 +0.005983,134 +0.006247,134 +0.010562,134 +0.006022,134 +0.005924,134 +0.005888,134 +0.005843,134 +0.005924,134 +0.005841,134 +0.005843,134 +0.005926,134 +0.005840,134 +0.005844,134 +0.005922,134 +0.005846,134 +0.005840,134 +0.005944,134 +0.005923,134 +0.009654,134 +0.007257,134 +0.005909,134 +0.005901,134 +0.005865,134 +0.005921,134 +0.005845,134 +0.005841,134 +0.005926,134 +0.005883,134 +0.005865,134 +0.005927,134 +0.005846,134 +0.005843,134 +0.005923,134 +0.005908,134 +0.008324,134 +0.008524,134 +0.005931,134 +0.005912,134 +0.005887,134 +0.006011,134 +0.005851,134 +0.005841,134 +0.005926,134 +0.005842,134 +0.005844,134 +0.005920,134 +0.005845,134 +0.005842,134 +0.005939,134 +0.005904,134 +0.007211,134 +0.009723,134 +0.005917,134 +0.005949,134 +0.005866,134 +0.005883,134 +0.005884,134 +0.005840,134 +0.005925,134 +0.005842,134 +0.005845,134 +0.005928,134 +0.005843,134 +0.005844,134 +0.005949,134 +0.005903,134 +0.005978,134 +0.010587,134 +0.006265,134 +0.005974,134 +0.005847,134 +0.005888,134 +0.005879,134 +0.005845,134 +0.005881,134 +0.005883,134 +0.005842,134 +0.005926,134 +0.005844,134 +0.005844,134 +0.005926,134 +0.005949,134 +0.005843,134 +0.009580,134 +0.007544,136 +0.006259,136 +0.006137,136 +0.006177,136 +0.006148,136 +0.006099,136 +0.006257,136 +0.006103,136 +0.006102,136 +0.006180,136 +0.006124,136 +0.006101,136 +0.006234,136 +0.006189,136 +0.007276,136 +0.010162,136 +0.006208,136 +0.006129,136 +0.006098,136 +0.006184,136 +0.006101,136 +0.006133,136 +0.006182,136 +0.006138,136 +0.006145,136 +0.006140,136 +0.006122,136 +0.006238,136 +0.006165,136 +0.006100,136 +0.009424,136 +0.007949,136 +0.006220,136 +0.006165,136 +0.006179,136 +0.006205,136 +0.006099,136 +0.006204,136 +0.006101,136 +0.006102,136 +0.006177,136 +0.006145,136 +0.006163,136 +0.006159,136 +0.006162,136 +0.006208,136 +0.010491,136 +0.007331,136 +0.006136,136 +0.006138,136 +0.006207,136 +0.006110,136 +0.006183,136 +0.006164,136 +0.006098,136 +0.006185,136 +0.006101,136 +0.006102,136 +0.006207,136 +0.006182,136 +0.006102,136 +0.009914,136 +0.007608,136 +0.006170,136 +0.006119,136 +0.006205,136 +0.006101,136 +0.006102,136 +0.006182,136 +0.006102,136 +0.006121,136 +0.006210,136 +0.006097,136 +0.006181,136 +0.006171,136 +0.006104,136 +0.007201,136 +0.010121,136 +0.006260,136 +0.006129,136 +0.006142,136 +0.006253,136 +0.006098,136 +0.006221,136 +0.006100,136 +0.006102,136 +0.006218,136 +0.006102,136 +0.006113,136 +0.006188,136 +0.006159,136 +0.006146,136 +0.009205,136 +0.008398,136 +0.006163,136 +0.006129,136 +0.006238,136 +0.006110,136 +0.006101,136 +0.006184,136 +0.006475,138 +0.006483,138 +0.006375,138 +0.006380,138 +0.006462,138 +0.006437,138 +0.006422,138 +0.008880,138 +0.009047,138 +0.006436,138 +0.006377,138 +0.006463,138 +0.006380,138 +0.006415,138 +0.006424,138 +0.006379,138 +0.006465,138 +0.006380,138 +0.006375,138 +0.006458,138 +0.006482,138 +0.006478,138 +0.009612,138 +0.008407,138 +0.006416,138 +0.006408,138 +0.006474,138 +0.006380,138 +0.006463,138 +0.006381,138 +0.006463,138 +0.006476,138 +0.006379,138 +0.006420,138 +0.006414,138 +0.006450,138 +0.006463,138 +0.010245,138 +0.007760,138 +0.006435,138 +0.006458,138 +0.006458,138 +0.006388,138 +0.006456,138 +0.006402,138 +0.006378,138 +0.006481,138 +0.006399,138 +0.006458,138 +0.006480,138 +0.006398,138 +0.006459,138 +0.010950,138 +0.006932,138 +0.006438,138 +0.006532,138 +0.006417,138 +0.006415,138 +0.006459,138 +0.006376,138 +0.006423,138 +0.006416,138 +0.006381,138 +0.006499,138 +0.006475,138 +0.006380,138 +0.006794,138 +0.011207,138 +0.006485,138 +0.006396,138 +0.006503,138 +0.006445,138 +0.006410,138 +0.006490,138 +0.006439,138 +0.006463,138 +0.006386,138 +0.006378,138 +0.006462,138 +0.006463,138 +0.006458,138 +0.007488,138 +0.010416,138 +0.006409,138 +0.006401,138 +0.006456,138 +0.006436,138 +0.006480,138 +0.006379,138 +0.006380,138 +0.006474,138 +0.006375,138 +0.006423,138 +0.006417,138 +0.006450,138 +0.006461,138 +0.007113,138 +0.011225,138 +0.006471,138 +0.006478,138 +0.006769,140 +0.006656,140 +0.006753,140 +0.006655,140 +0.006738,140 +0.006691,140 +0.006655,140 +0.006737,140 +0.006713,140 +0.006737,140 +0.006694,140 +0.011793,140 +0.006709,140 +0.006807,140 +0.006790,140 +0.006687,140 +0.006729,140 +0.006655,140 +0.006696,140 +0.006692,140 +0.006655,140 +0.006736,140 +0.006710,140 +0.006765,140 +0.006694,140 +0.010488,140 +0.008057,140 +0.006740,140 +0.006800,140 +0.006695,140 +0.006780,140 +0.006676,140 +0.006678,140 +0.006751,140 +0.006655,140 +0.006747,140 +0.006761,140 +0.006656,140 +0.006732,140 +0.009127,140 +0.009353,140 +0.006724,140 +0.006806,140 +0.006677,140 +0.006760,140 +0.006654,140 +0.006715,140 +0.006734,140 +0.006651,140 +0.006733,140 +0.006684,140 +0.006766,140 +0.006730,140 +0.007838,140 +0.010583,140 +0.006669,140 +0.006790,140 +0.006676,140 +0.006704,140 +0.006691,140 +0.006655,140 +0.006734,140 +0.006676,140 +0.006805,140 +0.006760,140 +0.006711,140 +0.006734,140 +0.006655,140 +0.011768,140 +0.006691,140 +0.006817,140 +0.006717,140 +0.006691,140 +0.006778,140 +0.006655,140 +0.006731,140 +0.006655,140 +0.006719,140 +0.006782,140 +0.006765,140 +0.006796,140 +0.006700,140 +0.010922,140 +0.007698,140 +0.006781,140 +0.006674,140 +0.006694,140 +0.006740,140 +0.006651,140 +0.006738,140 +0.006656,140 +0.006655,140 +0.006736,140 +0.006822,140 +0.006776,140 +0.006673,140 +0.009524,140 +0.008979,140 +0.006754,140 +0.006715,140 +0.007035,142 +0.007048,142 +0.006946,142 +0.007020,142 +0.007048,142 +0.007000,142 +0.007080,142 +0.007065,142 +0.007026,142 +0.006946,142 +0.011171,142 +0.007917,142 +0.007063,142 +0.007218,142 +0.007036,142 +0.006964,142 +0.007092,142 +0.007063,142 +0.008122,142 +0.007109,142 +0.007142,142 +0.007097,142 +0.006951,142 +0.008729,142 +0.010398,142 +0.007144,142 +0.007088,142 +0.006942,142 +0.007028,142 +0.006949,142 +0.007069,142 +0.007492,142 +0.007120,142 +0.007258,142 +0.007069,142 +0.007050,142 +0.006944,142 +0.010432,142 +0.009191,142 +0.007110,142 +0.007057,142 +0.007094,142 +0.006976,142 +0.007043,142 +0.006947,142 +0.006946,142 +0.007023,142 +0.007052,142 +0.007024,142 +0.006946,142 +0.008870,142 +0.010285,142 +0.007081,142 +0.006970,142 +0.007068,142 +0.007010,142 +0.007010,142 +0.007087,142 +0.006966,142 +0.007024,142 +0.006985,142 +0.007014,142 +0.007026,142 +0.006945,142 +0.010603,142 +0.008532,142 +0.007087,142 +0.006987,142 +0.007045,142 +0.006968,142 +0.007052,142 +0.007006,142 +0.006958,142 +0.007029,142 +0.007006,142 +0.007024,142 +0.006943,142 +0.006946,142 +0.012083,142 +0.007096,142 +0.006994,142 +0.006994,142 +0.007034,142 +0.007008,142 +0.007026,142 +0.006946,142 +0.006985,142 +0.006985,142 +0.007024,142 +0.007025,142 +0.006942,142 +0.008762,142 +0.010367,142 +0.007151,142 +0.006977,142 +0.007046,142 +0.006955,142 +0.006988,142 +0.006987,142 +0.006944,142 +0.007327,144 +0.007334,144 +0.007310,144 +0.007232,144 +0.007268,144 +0.012184,144 +0.007532,144 +0.007281,144 +0.007333,144 +0.007233,144 +0.007237,144 +0.007310,144 +0.007274,144 +0.007310,144 +0.007298,144 +0.007331,144 +0.007454,144 +0.007391,144 +0.011581,144 +0.007960,144 +0.007244,144 +0.007270,144 +0.007314,144 +0.007273,144 +0.007328,144 +0.007248,144 +0.007312,144 +0.007335,144 +0.007310,144 +0.007232,144 +0.007269,144 +0.010878,144 +0.008735,144 +0.007287,144 +0.007312,144 +0.007293,144 +0.007232,144 +0.007358,144 +0.007243,144 +0.007335,144 +0.007291,144 +0.007310,144 +0.007231,144 +0.007227,144 +0.010332,144 +0.009383,144 +0.007242,144 +0.007305,144 +0.007304,144 +0.007293,144 +0.007309,144 +0.007232,144 +0.007310,144 +0.007312,144 +0.007339,144 +0.007228,144 +0.007231,144 +0.009600,144 +0.010036,144 +0.007243,144 +0.007316,144 +0.007283,144 +0.007262,144 +0.007314,144 +0.007254,144 +0.007333,144 +0.007283,144 +0.007355,144 +0.007228,144 +0.007274,144 +0.007931,144 +0.012148,144 +0.007279,144 +0.007336,144 +0.007293,144 +0.007232,144 +0.007309,144 +0.007231,144 +0.007310,144 +0.007292,144 +0.007352,144 +0.007228,144 +0.007375,144 +0.009157,144 +0.010462,144 +0.007231,144 +0.007276,144 +0.007271,144 +0.007230,144 +0.007311,144 +0.007231,144 +0.007312,144 +0.007291,144 +0.007270,144 +0.007267,144 +0.007231,144 +0.008402,144 +0.011334,144 +0.007284,144 +0.007240,144 +0.007692,146 +0.007635,146 +0.007671,146 +0.007604,146 +0.007675,146 +0.007674,146 +0.007691,146 +0.007592,146 +0.008196,146 +0.011100,146 +0.009205,146 +0.007645,146 +0.007745,146 +0.007741,146 +0.007693,146 +0.007592,146 +0.007713,146 +0.007721,146 +0.007635,146 +0.007631,146 +0.007589,146 +0.008456,146 +0.011895,146 +0.007599,146 +0.007672,146 +0.007591,146 +0.007850,146 +0.007654,146 +0.007612,146 +0.007675,146 +0.007654,146 +0.007694,146 +0.007590,146 +0.007653,146 +0.011486,146 +0.008898,146 +0.007667,146 +0.007743,146 +0.007588,146 +0.007674,146 +0.007592,146 +0.007675,146 +0.007653,146 +0.007671,146 +0.007592,146 +0.007812,146 +0.008585,146 +0.011660,146 +0.007667,146 +0.007763,146 +0.007664,146 +0.007691,146 +0.007589,146 +0.007630,146 +0.007656,146 +0.007675,146 +0.007671,146 +0.007592,146 +0.007714,146 +0.011731,146 +0.008435,146 +0.007684,146 +0.007714,146 +0.007672,146 +0.007723,146 +0.007733,146 +0.007689,146 +0.007660,146 +0.007674,146 +0.007592,146 +0.007674,146 +0.008910,146 +0.011245,146 +0.007650,146 +0.007695,146 +0.007592,146 +0.007752,146 +0.007666,146 +0.007710,146 +0.007593,146 +0.007711,146 +0.007716,146 +0.007592,146 +0.007674,146 +0.012258,146 +0.007952,146 +0.007695,146 +0.007613,146 +0.007652,146 +0.007758,146 +0.007596,146 +0.007690,146 +0.007652,146 +0.007679,146 +0.007635,146 +0.007674,146 +0.008160,146 +0.012631,146 +0.008593,146 +0.007761,146 +0.007959,148 +0.007968,148 +0.007851,148 +0.007933,148 +0.007973,148 +0.007929,148 +0.008064,148 +0.007951,148 +0.009425,148 +0.011397,148 +0.007870,148 +0.007970,148 +0.007905,148 +0.007930,148 +0.007850,148 +0.007932,148 +0.007918,148 +0.007932,148 +0.007850,148 +0.007933,148 +0.008677,148 +0.012120,148 +0.007928,148 +0.007977,148 +0.007935,148 +0.007924,148 +0.007869,148 +0.007936,148 +0.007914,148 +0.007929,148 +0.007850,148 +0.007940,148 +0.008258,148 +0.012461,148 +0.007890,148 +0.007965,148 +0.007929,148 +0.007910,148 +0.007851,148 +0.007914,148 +0.007934,148 +0.007977,148 +0.007850,148 +0.007929,148 +0.007850,148 +0.012867,148 +0.007892,148 +0.007950,148 +0.007874,148 +0.007932,148 +0.007872,148 +0.007944,148 +0.007951,148 +0.007930,148 +0.007850,148 +0.007911,148 +0.007851,148 +0.012936,148 +0.007927,148 +0.007969,148 +0.007873,148 +0.007961,148 +0.007850,148 +0.007933,148 +0.007970,148 +0.007910,148 +0.007927,148 +0.007972,148 +0.007849,148 +0.012914,148 +0.007896,148 +0.007971,148 +0.007897,148 +0.007961,148 +0.007914,148 +0.007989,148 +0.007942,148 +0.007972,148 +0.007896,148 +0.007957,148 +0.007873,148 +0.012887,148 +0.007898,148 +0.007967,148 +0.007851,148 +0.007972,148 +0.007890,148 +0.007907,148 +0.007930,148 +0.007909,148 +0.007850,148 +0.007909,148 +0.007851,148 +0.012450,148 +0.008353,148 +0.007964,148 +0.007935,148 +0.007967,148 +0.007860,148 +0.008012,148 +0.008326,150 +0.008283,150 +0.008174,150 +0.008234,150 +0.008176,150 +0.013231,150 +0.008333,150 +0.008238,150 +0.008228,150 +0.008234,150 +0.008227,150 +0.008236,150 +0.008307,150 +0.008221,150 +0.008196,150 +0.008215,150 +0.009105,150 +0.013067,150 +0.009257,150 +0.008500,150 +0.008297,150 +0.008421,150 +0.008322,150 +0.008274,150 +0.008333,150 +0.008374,150 +0.008256,150 +0.008175,150 +0.013310,150 +0.008296,150 +0.008247,150 +0.008317,150 +0.008242,150 +0.008293,150 +0.008203,150 +0.008344,150 +0.008177,150 +0.008256,150 +0.008198,150 +0.010603,150 +0.010949,150 +0.008287,150 +0.008198,150 +0.008256,150 +0.008192,150 +0.008240,150 +0.008258,150 +0.008269,150 +0.008235,150 +0.008241,150 +0.008175,150 +0.013210,150 +0.008325,150 +0.008201,150 +0.008306,150 +0.008176,150 +0.008239,150 +0.008211,150 +0.008391,150 +0.008218,150 +0.008248,150 +0.008181,150 +0.009482,150 +0.011948,150 +0.008287,150 +0.008195,150 +0.008310,150 +0.008197,150 +0.008256,150 +0.008283,150 +0.008265,150 +0.008176,150 +0.008239,150 +0.008176,150 +0.012253,150 +0.009329,150 +0.008246,150 +0.008255,150 +0.008195,150 +0.008235,150 +0.008176,150 +0.008328,150 +0.008177,150 +0.008353,150 +0.008176,150 +0.008301,150 +0.013030,150 +0.008253,150 +0.008203,150 +0.008289,150 +0.008261,150 +0.008237,150 +0.008196,150 +0.008282,150 +0.008176,150 +0.008215,150 +0.008199,150 +0.011124,150 +0.010348,150 +0.008221,150 +0.008590,152 +0.008528,152 +0.008581,152 +0.008496,152 +0.008618,152 +0.008500,152 +0.008539,152 +0.008495,152 +0.009897,152 +0.012220,152 +0.008549,152 +0.008580,152 +0.008496,152 +0.008536,152 +0.008536,152 +0.008594,152 +0.008504,152 +0.008537,152 +0.008508,152 +0.008783,152 +0.013258,152 +0.008581,152 +0.008518,152 +0.008561,152 +0.008531,152 +0.008556,152 +0.008678,152 +0.008503,152 +0.008537,152 +0.008538,152 +0.008536,152 +0.013405,152 +0.009086,152 +0.008519,152 +0.008583,152 +0.008531,152 +0.008603,152 +0.008575,152 +0.008543,152 +0.008708,152 +0.008499,152 +0.008728,152 +0.013398,152 +0.008614,152 +0.008541,152 +0.008572,152 +0.008527,152 +0.008578,152 +0.008571,152 +0.008540,152 +0.008496,152 +0.008633,152 +0.008537,152 +0.012668,152 +0.009393,152 +0.008538,152 +0.008580,152 +0.008513,152 +0.008534,152 +0.008556,152 +0.008553,152 +0.008498,152 +0.008536,152 +0.008495,152 +0.011647,152 +0.010350,152 +0.008567,152 +0.008598,152 +0.008497,152 +0.008541,152 +0.008564,152 +0.008630,152 +0.008497,152 +0.008536,152 +0.008499,152 +0.010562,152 +0.011428,152 +0.008526,152 +0.008558,152 +0.008550,152 +0.008571,152 +0.008993,152 +0.009109,152 +0.008602,152 +0.008796,152 +0.008519,152 +0.010517,152 +0.011600,152 +0.008552,152 +0.008619,152 +0.008497,152 +0.008579,152 +0.008496,152 +0.008652,152 +0.008569,152 +0.008620,152 +0.008498,152 +0.009709,152 +0.012485,152 +0.008564,152 +0.009016,154 +0.008902,154 +0.008946,154 +0.008847,154 +0.008991,154 +0.008844,154 +0.008929,154 +0.008883,154 +0.011722,154 +0.011108,154 +0.008916,154 +0.008952,154 +0.008897,154 +0.008927,154 +0.008921,154 +0.008936,154 +0.008879,154 +0.008908,154 +0.008925,154 +0.013578,154 +0.009007,154 +0.008936,154 +0.008911,154 +0.008889,154 +0.008881,154 +0.009014,154 +0.008844,154 +0.008920,154 +0.008842,154 +0.008925,154 +0.013867,154 +0.008872,154 +0.008942,154 +0.008897,154 +0.008921,154 +0.008842,154 +0.008996,154 +0.009369,154 +0.009038,154 +0.008919,154 +0.009989,154 +0.013399,154 +0.008900,154 +0.008974,154 +0.008902,154 +0.008949,154 +0.008947,154 +0.008939,154 +0.009119,154 +0.008847,154 +0.008954,154 +0.013207,154 +0.009464,154 +0.008922,154 +0.008902,154 +0.008945,154 +0.008842,154 +0.009057,154 +0.008846,154 +0.008920,154 +0.008889,154 +0.008921,154 +0.013838,154 +0.008916,154 +0.008943,154 +0.008860,154 +0.008921,154 +0.008842,154 +0.009052,154 +0.008841,154 +0.008921,154 +0.008842,154 +0.010556,154 +0.012137,154 +0.008893,154 +0.009020,154 +0.008856,154 +0.008920,154 +0.008948,154 +0.009503,154 +0.008969,154 +0.008888,154 +0.008961,154 +0.012439,154 +0.010243,154 +0.008968,154 +0.008888,154 +0.008947,154 +0.008843,154 +0.008980,154 +0.008842,154 +0.008925,154 +0.008843,154 +0.008920,154 +0.013791,154 +0.008942,154 +0.008941,154 +0.008903,154 +0.008926,154 +0.008848,154 +0.009499,156 +0.009334,156 +0.009283,156 +0.009266,156 +0.011629,156 +0.011676,156 +0.009271,156 +0.009246,156 +0.009345,156 +0.009240,156 +0.009374,156 +0.009283,156 +0.009286,156 +0.009184,156 +0.009266,156 +0.014065,156 +0.009249,156 +0.009320,156 +0.009289,156 +0.009245,156 +0.009339,156 +0.009187,156 +0.009283,156 +0.009188,156 +0.009263,156 +0.013484,156 +0.009916,156 +0.009344,156 +0.009206,156 +0.009293,156 +0.009184,156 +0.009405,156 +0.009270,156 +0.009185,156 +0.009287,156 +0.011293,156 +0.012023,156 +0.009330,156 +0.009187,156 +0.009264,156 +0.009192,156 +0.009396,156 +0.009184,156 +0.009284,156 +0.009228,156 +0.009224,156 +0.014616,156 +0.009291,156 +0.009270,156 +0.009321,156 +0.009187,156 +0.009374,156 +0.009282,156 +0.009344,156 +0.009185,156 +0.009271,156 +0.013772,156 +0.009505,156 +0.009288,156 +0.009205,156 +0.009265,156 +0.009332,156 +0.009187,156 +0.009263,156 +0.009286,156 +0.009381,156 +0.010971,156 +0.012399,156 +0.009319,156 +0.009214,156 +0.009270,156 +0.009185,156 +0.009331,156 +0.009207,156 +0.009204,156 +0.009225,156 +0.009189,156 +0.014033,156 +0.009291,156 +0.009208,156 +0.009224,156 +0.009228,156 +0.009336,156 +0.009186,156 +0.009225,156 +0.009186,156 +0.009245,156 +0.012972,156 +0.010474,156 +0.009281,156 +0.009432,156 +0.009240,156 +0.009350,156 +0.009186,156 +0.009249,156 +0.009185,156 +0.009224,156 +0.010326,156 +0.013002,156 +0.009279,156 +0.009701,158 +0.009625,158 +0.009621,158 +0.009726,158 +0.009628,158 +0.009543,158 +0.009582,158 +0.010835,158 +0.013186,158 +0.009713,158 +0.009620,158 +0.009625,158 +0.009666,158 +0.009545,158 +0.009610,158 +0.009585,158 +0.009679,158 +0.010873,158 +0.013045,158 +0.009651,158 +0.009623,158 +0.009568,158 +0.009643,158 +0.009545,158 +0.009583,158 +0.009542,158 +0.009586,158 +0.010793,158 +0.013279,158 +0.009682,158 +0.009608,158 +0.009561,158 +0.009687,158 +0.009548,158 +0.009582,158 +0.009545,158 +0.009612,158 +0.010642,158 +0.013318,158 +0.009618,158 +0.009640,158 +0.009560,158 +0.009687,158 +0.009544,158 +0.009582,158 +0.009546,158 +0.009582,158 +0.009657,158 +0.014768,158 +0.009654,158 +0.009671,158 +0.009584,158 +0.009713,158 +0.009808,158 +0.009650,158 +0.009599,158 +0.009547,158 +0.009723,158 +0.009852,158 +0.009656,158 +0.009584,158 +0.009627,158 +0.009685,158 +0.009587,158 +0.009604,158 +0.009544,158 +0.009607,158 +0.009562,158 +0.009986,158 +0.009774,158 +0.009682,158 +0.011187,158 +0.009877,158 +0.009714,158 +0.009629,158 +0.009544,158 +0.009622,158 +0.009546,158 +0.009776,158 +0.009973,158 +0.009588,158 +0.010187,158 +0.009548,158 +0.009694,158 +0.009594,158 +0.009582,158 +0.009623,158 +0.009543,158 +0.009730,158 +0.009879,158 +0.009693,158 +0.009872,158 +0.009792,158 +0.009710,158 +0.009545,158 +0.009621,158 +0.009547,158 +0.009622,158 +0.009627,158 +0.010054,158 +0.010054,160 +0.009929,160 +0.010009,160 +0.009988,160 +0.010043,160 +0.010026,160 +0.009913,160 +0.009992,160 +0.009988,160 +0.010275,160 +0.010065,160 +0.009904,160 +0.010016,160 +0.009985,160 +0.009989,160 +0.009988,160 +0.009997,160 +0.010034,160 +0.010070,160 +0.010303,160 +0.010059,160 +0.009946,160 +0.010008,160 +0.009986,160 +0.009979,160 +0.009984,160 +0.009905,160 +0.009988,160 +0.009993,160 +0.010278,160 +0.010234,160 +0.009945,160 +0.010079,160 +0.009987,160 +0.009990,160 +0.012101,160 +0.010456,160 +0.009979,160 +0.010182,160 +0.010254,160 +0.010008,160 +0.009989,160 +0.009967,160 +0.010090,160 +0.009973,160 +0.010025,160 +0.009985,160 +0.009903,160 +0.010008,160 +0.010262,160 +0.010137,160 +0.010036,160 +0.009937,160 +0.010067,160 +0.010004,160 +0.010024,160 +0.009989,160 +0.009907,160 +0.009991,160 +0.010275,160 +0.010042,160 +0.009989,160 +0.009911,160 +0.010050,160 +0.009907,160 +0.010129,160 +0.010013,160 +0.009909,160 +0.009995,160 +0.010495,160 +0.010028,160 +0.010029,160 +0.009951,160 +0.010063,160 +0.010007,160 +0.009944,160 +0.009986,160 +0.009904,160 +0.010006,160 +0.010279,160 +0.010067,160 +0.010054,160 +0.009934,160 +0.010086,160 +0.009944,160 +0.009944,160 +0.009987,160 +0.009904,160 +0.009985,160 +0.010425,160 +0.009962,160 +0.009988,160 +0.009906,160 +0.010069,160 +0.009944,160 +0.009949,160 +0.009985,160 +0.009904,160 +0.010007,160 +0.010422,160 +0.010407,162 +0.010363,162 +0.010280,162 +0.010447,162 +0.010445,162 +0.010283,162 +0.010360,162 +0.010319,162 +0.010479,162 +0.010749,162 +0.010282,162 +0.010404,162 +0.010358,162 +0.010366,162 +0.010361,162 +0.010360,162 +0.010364,162 +0.010358,162 +0.010496,162 +0.010656,162 +0.010365,162 +0.010284,162 +0.010423,162 +0.010320,162 +0.010323,162 +0.010378,162 +0.010281,162 +0.010360,162 +0.010843,162 +0.010325,162 +0.010400,162 +0.010281,162 +0.010441,162 +0.010361,162 +0.010284,162 +0.010378,162 +0.010372,162 +0.010364,162 +0.010847,162 +0.010389,162 +0.010406,162 +0.010388,162 +0.010346,162 +0.010407,162 +0.010365,162 +0.010317,162 +0.010364,162 +0.010498,162 +0.010612,162 +0.010410,162 +0.010280,162 +0.010466,162 +0.010487,162 +0.010487,162 +0.010363,162 +0.010280,162 +0.010450,162 +0.010746,162 +0.010334,162 +0.010491,162 +0.010358,162 +0.010363,162 +0.010387,162 +0.010300,162 +0.010363,162 +0.010362,162 +0.010541,162 +0.010729,162 +0.010459,162 +0.010328,162 +0.010466,162 +0.010283,162 +0.010364,162 +0.010362,162 +0.010282,162 +0.010362,162 +0.010745,162 +0.010464,162 +0.010403,162 +0.010316,162 +0.010428,162 +0.010365,162 +0.010284,162 +0.010382,162 +0.010364,162 +0.010383,162 +0.010771,162 +0.010351,162 +0.010378,162 +0.010404,162 +0.010364,162 +0.011207,162 +0.010435,162 +0.010319,162 +0.010426,162 +0.010802,162 +0.010531,162 +0.010431,162 +0.010284,162 +0.010522,162 +0.010784,164 +0.010711,164 +0.010748,164 +0.010809,164 +0.010786,164 +0.011112,164 +0.010752,164 +0.010789,164 +0.010813,164 +0.010773,164 +0.010780,164 +0.011292,164 +0.011594,164 +0.011430,164 +0.011138,164 +0.010801,164 +0.010771,164 +0.010786,164 +0.010763,164 +0.010774,164 +0.010746,164 +0.010671,164 +0.010771,164 +0.011398,164 +0.010791,164 +0.010771,164 +0.010810,164 +0.010777,164 +0.010796,164 +0.010822,164 +0.011003,164 +0.010760,164 +0.010943,164 +0.011030,164 +0.010857,164 +0.010801,164 +0.010826,164 +0.010754,164 +0.010670,164 +0.010748,164 +0.010750,164 +0.010836,164 +0.011151,164 +0.010840,164 +0.010732,164 +0.010915,164 +0.010751,164 +0.010709,164 +0.010746,164 +0.010754,164 +0.010714,164 +0.011173,164 +0.010763,164 +0.010850,164 +0.010793,164 +0.010779,164 +0.010792,164 +0.010793,164 +0.010669,164 +0.010780,164 +0.011376,164 +0.010779,164 +0.010790,164 +0.010751,164 +0.010751,164 +0.010753,164 +0.010751,164 +0.010669,164 +0.010745,164 +0.010846,164 +0.012370,164 +0.010926,164 +0.011042,164 +0.010808,164 +0.010782,164 +0.010733,164 +0.010707,164 +0.010750,164 +0.010891,164 +0.011047,164 +0.011147,164 +0.010669,164 +0.010834,164 +0.010770,164 +0.010670,164 +0.010747,164 +0.010746,164 +0.010755,164 +0.011173,164 +0.011209,164 +0.010669,164 +0.011009,164 +0.010817,164 +0.010712,164 +0.010766,164 +0.010734,164 +0.010828,164 +0.011192,164 +0.010784,164 +0.010732,164 +0.011191,166 +0.011185,166 +0.011145,166 +0.011888,166 +0.012399,166 +0.012089,166 +0.011909,166 +0.011759,166 +0.011249,166 +0.011758,166 +0.011934,166 +0.011491,166 +0.011819,166 +0.011546,166 +0.011587,166 +0.011658,166 +0.012568,166 +0.011181,166 +0.011217,166 +0.011118,166 +0.011121,166 +0.011059,166 +0.011164,166 +0.011387,166 +0.011276,166 +0.011226,166 +0.011204,166 +0.011228,166 +0.011131,166 +0.011142,166 +0.011100,166 +0.011137,166 +0.011355,166 +0.011357,166 +0.011142,166 +0.011250,166 +0.011281,166 +0.011159,166 +0.011142,166 +0.011099,166 +0.011100,166 +0.011505,166 +0.011219,166 +0.011137,166 +0.011220,166 +0.011239,166 +0.011102,166 +0.011155,166 +0.011142,166 +0.011062,166 +0.011673,166 +0.011270,166 +0.011083,166 +0.011158,166 +0.011245,166 +0.011062,166 +0.011140,166 +0.011156,166 +0.011061,166 +0.011578,166 +0.011292,166 +0.011134,166 +0.011167,166 +0.011235,166 +0.011059,166 +0.011144,166 +0.011139,166 +0.011159,166 +0.011497,166 +0.011209,166 +0.011156,166 +0.011138,166 +0.011201,166 +0.011061,166 +0.011138,166 +0.011169,166 +0.011059,166 +0.011572,166 +0.011204,166 +0.011161,166 +0.011254,166 +0.011203,166 +0.011098,166 +0.011138,166 +0.011144,166 +0.011083,166 +0.011473,166 +0.011272,166 +0.011144,166 +0.011296,166 +0.011161,166 +0.011103,166 +0.011360,166 +0.011138,166 +0.011134,166 +0.011465,166 +0.011145,166 +0.011102,166 +0.011164,166 +0.011182,166 +0.011523,168 +0.011490,168 +0.011535,168 +0.011532,168 +0.011907,168 +0.011672,168 +0.011655,168 +0.011612,168 +0.011542,168 +0.011551,168 +0.011531,168 +0.011524,168 +0.011651,168 +0.011834,168 +0.011450,168 +0.011632,168 +0.011648,168 +0.011473,168 +0.011532,168 +0.011528,168 +0.011452,168 +0.011698,168 +0.011850,168 +0.011598,168 +0.011687,168 +0.011610,168 +0.011528,168 +0.011452,168 +0.011555,168 +0.011512,168 +0.011784,168 +0.011572,168 +0.011512,168 +0.011580,168 +0.011532,168 +0.011554,168 +0.011490,168 +0.011495,168 +0.011668,168 +0.011871,168 +0.011485,168 +0.011530,168 +0.011591,168 +0.011449,168 +0.011529,168 +0.011532,168 +0.011516,168 +0.011658,168 +0.011794,168 +0.011571,168 +0.011533,168 +0.011528,168 +0.011533,168 +0.011450,168 +0.011528,168 +0.011552,168 +0.011742,168 +0.011668,168 +0.011667,168 +0.011600,168 +0.011559,168 +0.011602,168 +0.011623,168 +0.011590,168 +0.011655,168 +0.012261,168 +0.011516,168 +0.011774,168 +0.011784,168 +0.011491,168 +0.011541,168 +0.011557,168 +0.011546,168 +0.011727,168 +0.011933,168 +0.011591,168 +0.011511,168 +0.011567,168 +0.011619,168 +0.011493,168 +0.011491,168 +0.011567,168 +0.012135,168 +0.011495,168 +0.011536,168 +0.011575,168 +0.011452,168 +0.011510,168 +0.011513,168 +0.011452,168 +0.011755,168 +0.012195,168 +0.011600,168 +0.011611,168 +0.011585,168 +0.011533,168 +0.011453,168 +0.011526,168 +0.011563,168 +0.011778,168 +0.012368,170 +0.011991,170 +0.012023,170 +0.011874,170 +0.011995,170 +0.011975,170 +0.011873,170 +0.012019,170 +0.012605,170 +0.011974,170 +0.012064,170 +0.012011,170 +0.011956,170 +0.011913,170 +0.011915,170 +0.011957,170 +0.012581,170 +0.011992,170 +0.011972,170 +0.012224,170 +0.011968,170 +0.011880,170 +0.011963,170 +0.011961,170 +0.012367,170 +0.012179,170 +0.012012,170 +0.012050,170 +0.011872,170 +0.011946,170 +0.011983,170 +0.011910,170 +0.012138,170 +0.012355,170 +0.012069,170 +0.011953,170 +0.011972,170 +0.011951,170 +0.011969,170 +0.011873,170 +0.011954,170 +0.012545,170 +0.011952,170 +0.012034,170 +0.011974,170 +0.011952,170 +0.011891,170 +0.011952,170 +0.011949,170 +0.012361,170 +0.012149,170 +0.012212,170 +0.012514,170 +0.012752,170 +0.012681,170 +0.012633,170 +0.012701,170 +0.012961,170 +0.012976,170 +0.013305,170 +0.013122,170 +0.013128,170 +0.013197,170 +0.013457,170 +0.012856,170 +0.014079,170 +0.012390,170 +0.012251,170 +0.012068,170 +0.011998,170 +0.012010,170 +0.011881,170 +0.012047,170 +0.013430,170 +0.012022,170 +0.012064,170 +0.012012,170 +0.011969,170 +0.011879,170 +0.011970,170 +0.012012,170 +0.013293,170 +0.012159,170 +0.012003,170 +0.012090,170 +0.011921,170 +0.011919,170 +0.011975,170 +0.011976,170 +0.013089,170 +0.013243,170 +0.012087,170 +0.012064,170 +0.012142,170 +0.011978,170 +0.012004,170 +0.011963,170 +0.011878,170 +0.013426,170 +0.011999,170 +0.012542,172 +0.012343,172 +0.012399,172 +0.012399,172 +0.012399,172 +0.012335,172 +0.013855,172 +0.012485,172 +0.012488,172 +0.012322,172 +0.012376,172 +0.012417,172 +0.012376,172 +0.012359,172 +0.013822,172 +0.012456,172 +0.012528,172 +0.012299,172 +0.012400,172 +0.012376,172 +0.012380,172 +0.012348,172 +0.013919,172 +0.012396,172 +0.012518,172 +0.012300,172 +0.012436,172 +0.012373,172 +0.012377,172 +0.012768,172 +0.013555,172 +0.012493,172 +0.012480,172 +0.012365,172 +0.012372,172 +0.012416,172 +0.012470,172 +0.012911,172 +0.013230,172 +0.012400,172 +0.012480,172 +0.012401,172 +0.012358,172 +0.012374,172 +0.012399,172 +0.012936,172 +0.013161,172 +0.012432,172 +0.012491,172 +0.012339,172 +0.012351,172 +0.012387,172 +0.012380,172 +0.012970,172 +0.013251,172 +0.012388,172 +0.012437,172 +0.012403,172 +0.012297,172 +0.012398,172 +0.012422,172 +0.012949,172 +0.013123,172 +0.012379,172 +0.012475,172 +0.012376,172 +0.012297,172 +0.012430,172 +0.012380,172 +0.013706,172 +0.013553,172 +0.012487,172 +0.012477,172 +0.012439,172 +0.012298,172 +0.012377,172 +0.012376,172 +0.013300,172 +0.012890,172 +0.012415,172 +0.012543,172 +0.012378,172 +0.012305,172 +0.012375,172 +0.012374,172 +0.013355,172 +0.012861,172 +0.012377,172 +0.012459,172 +0.012386,172 +0.012342,172 +0.012377,172 +0.012387,172 +0.013479,172 +0.012737,172 +0.012374,172 +0.012439,172 +0.012419,172 +0.012339,172 +0.012335,172 +0.012924,174 +0.014114,174 +0.013398,174 +0.012870,174 +0.012829,174 +0.012810,174 +0.012898,174 +0.012773,174 +0.012770,174 +0.014461,174 +0.012943,174 +0.012952,174 +0.012893,174 +0.012770,174 +0.012819,174 +0.012815,174 +0.013198,174 +0.013806,174 +0.012834,174 +0.012930,174 +0.012905,174 +0.013421,174 +0.012810,174 +0.012833,174 +0.014129,174 +0.013014,174 +0.012818,174 +0.012832,174 +0.012812,174 +0.012827,174 +0.012774,174 +0.012827,174 +0.014350,174 +0.012876,174 +0.012939,174 +0.012771,174 +0.012778,174 +0.012826,174 +0.012832,174 +0.012847,174 +0.014217,174 +0.012893,174 +0.012886,174 +0.012816,174 +0.012773,174 +0.012781,174 +0.012813,174 +0.014284,174 +0.013887,174 +0.013176,174 +0.012836,174 +0.012812,174 +0.012850,174 +0.012854,174 +0.012751,174 +0.014305,174 +0.012886,174 +0.012893,174 +0.012796,174 +0.012766,174 +0.012814,174 +0.012808,174 +0.012820,174 +0.014250,174 +0.012876,174 +0.012902,174 +0.012811,174 +0.012777,174 +0.012769,174 +0.012870,174 +0.013717,174 +0.013426,174 +0.012750,174 +0.012822,174 +0.012850,174 +0.012808,174 +0.012984,174 +0.012814,174 +0.013902,174 +0.012985,174 +0.012943,174 +0.012767,174 +0.012812,174 +0.012810,174 +0.012809,174 +0.012775,174 +0.014276,174 +0.012971,174 +0.012871,174 +0.012878,174 +0.012763,174 +0.012850,174 +0.012817,174 +0.012812,174 +0.014245,174 +0.012864,174 +0.013058,174 +0.012952,174 +0.012890,174 +0.012775,174 +0.013229,176 +0.014257,176 +0.013616,176 +0.013359,176 +0.013247,176 +0.013200,176 +0.013245,176 +0.013236,176 +0.013294,176 +0.014650,176 +0.013181,176 +0.013312,176 +0.013240,176 +0.013241,176 +0.013264,176 +0.013196,176 +0.014077,176 +0.013740,176 +0.013320,176 +0.013239,176 +0.013155,176 +0.013252,176 +0.013269,176 +0.013234,176 +0.015676,176 +0.013342,176 +0.013354,176 +0.013246,176 +0.013241,176 +0.013235,176 +0.013202,176 +0.014308,176 +0.013464,176 +0.013379,176 +0.013273,176 +0.013302,176 +0.013184,176 +0.013255,176 +0.013260,176 +0.014662,176 +0.013348,176 +0.013158,176 +0.013240,176 +0.013244,176 +0.013241,176 +0.013302,176 +0.014299,176 +0.013475,176 +0.013319,176 +0.013235,176 +0.013244,176 +0.013223,176 +0.013300,176 +0.013448,176 +0.014596,176 +0.013353,176 +0.013236,176 +0.013191,176 +0.013241,176 +0.013890,176 +0.013450,176 +0.014640,176 +0.013330,176 +0.013404,176 +0.013243,176 +0.013239,176 +0.013238,176 +0.013216,176 +0.013558,176 +0.014477,176 +0.013404,176 +0.013368,176 +0.013281,176 +0.013190,176 +0.013259,176 +0.013234,176 +0.014619,176 +0.013257,176 +0.013273,176 +0.013255,176 +0.013242,176 +0.013230,176 +0.013262,176 +0.013705,176 +0.014162,176 +0.013396,176 +0.013258,176 +0.013253,176 +0.013167,176 +0.013313,176 +0.013258,176 +0.014743,176 +0.013368,176 +0.013229,176 +0.013240,176 +0.013265,176 +0.013312,176 +0.013221,176 +0.014368,176 +0.014610,176 +0.014034,178 +0.013804,178 +0.013749,178 +0.013730,178 +0.013697,178 +0.013688,178 +0.015298,178 +0.013925,178 +0.013806,178 +0.013768,178 +0.013693,178 +0.013685,178 +0.013730,178 +0.015227,178 +0.013905,178 +0.013775,178 +0.013737,178 +0.013648,178 +0.013803,178 +0.013741,178 +0.015209,178 +0.013851,178 +0.013757,178 +0.013646,178 +0.013730,178 +0.013816,178 +0.013727,178 +0.014983,178 +0.013994,178 +0.013671,178 +0.013728,178 +0.013737,178 +0.013749,178 +0.013727,178 +0.014320,178 +0.014624,178 +0.013803,178 +0.013733,178 +0.013728,178 +0.013793,178 +0.013732,178 +0.013658,178 +0.015135,178 +0.013893,178 +0.013753,178 +0.013730,178 +0.013949,178 +0.014305,178 +0.013707,178 +0.015145,178 +0.013894,178 +0.013792,178 +0.013752,178 +0.013750,178 +0.013733,178 +0.013735,178 +0.015082,178 +0.013848,178 +0.013724,178 +0.013745,178 +0.013650,178 +0.013775,178 +0.013733,178 +0.014791,178 +0.014185,178 +0.013790,178 +0.013675,178 +0.013743,178 +0.013723,178 +0.013748,178 +0.013917,178 +0.016409,178 +0.013868,178 +0.013665,178 +0.013760,178 +0.013723,178 +0.013813,178 +0.013727,178 +0.015177,178 +0.013749,178 +0.013743,178 +0.013724,178 +0.013724,178 +0.013728,178 +0.013685,178 +0.015080,178 +0.013865,178 +0.013746,178 +0.013721,178 +0.013739,178 +0.013731,178 +0.013676,178 +0.015119,178 +0.013960,178 +0.013744,178 +0.013728,178 +0.013740,178 +0.013644,178 +0.013724,178 +0.014658,178 +0.014728,180 +0.014195,180 +0.014154,180 +0.014114,180 +0.014113,180 +0.014158,180 +0.015102,180 +0.014781,180 +0.014233,180 +0.014154,180 +0.014149,180 +0.014076,180 +0.014217,180 +0.014995,180 +0.014969,180 +0.014297,180 +0.014176,180 +0.014168,180 +0.014086,180 +0.014151,180 +0.014921,180 +0.014900,180 +0.014164,180 +0.014154,180 +0.014149,180 +0.014153,180 +0.014112,180 +0.014883,180 +0.014967,180 +0.014175,180 +0.014164,180 +0.014196,180 +0.014109,180 +0.014114,180 +0.014899,180 +0.015049,180 +0.014223,180 +0.014156,180 +0.014178,180 +0.014150,180 +0.014075,180 +0.015177,180 +0.015930,180 +0.014194,180 +0.014163,180 +0.014190,180 +0.014157,180 +0.014110,180 +0.014913,180 +0.014957,180 +0.014214,180 +0.014177,180 +0.014151,180 +0.014155,180 +0.014152,180 +0.014882,180 +0.014835,180 +0.014170,180 +0.014159,180 +0.014152,180 +0.014232,180 +0.014157,180 +0.015053,180 +0.014741,180 +0.014195,180 +0.014153,180 +0.014174,180 +0.014151,180 +0.014157,180 +0.015240,180 +0.014557,180 +0.014173,180 +0.014154,180 +0.014157,180 +0.014151,180 +0.014394,180 +0.015120,180 +0.014651,180 +0.014242,180 +0.014196,180 +0.014211,180 +0.014216,180 +0.014153,180 +0.015174,180 +0.014765,180 +0.014133,180 +0.014154,180 +0.014189,180 +0.014172,180 +0.014150,180 +0.015249,180 +0.014679,180 +0.014261,180 +0.014184,180 +0.014153,180 +0.014189,180 +0.014164,180 +0.015344,180 +0.014498,180 +0.014108,180 +0.014750,182 +0.014647,182 +0.014627,182 +0.014627,182 +0.016130,182 +0.014691,182 +0.014653,182 +0.014672,182 +0.014551,182 +0.014638,182 +0.014671,182 +0.017304,182 +0.014720,182 +0.014631,182 +0.014627,182 +0.014625,182 +0.014627,182 +0.015040,182 +0.015694,182 +0.014651,182 +0.014626,182 +0.014629,182 +0.014627,182 +0.014628,182 +0.015926,182 +0.014910,182 +0.014648,182 +0.014550,182 +0.014717,182 +0.014645,182 +0.014633,182 +0.016201,182 +0.014751,182 +0.014878,182 +0.014713,182 +0.014713,182 +0.014655,182 +0.014610,182 +0.016184,182 +0.014636,182 +0.014632,182 +0.014627,182 +0.014632,182 +0.014793,182 +0.015369,182 +0.015352,182 +0.014551,182 +0.014627,182 +0.014633,182 +0.014628,182 +0.014625,182 +0.016009,182 +0.014969,182 +0.014744,182 +0.014692,182 +0.014556,182 +0.014629,182 +0.014630,182 +0.016128,182 +0.015961,182 +0.014838,182 +0.014701,182 +0.014754,182 +0.014700,182 +0.014594,182 +0.016209,182 +0.014634,182 +0.014625,182 +0.014630,182 +0.014634,182 +0.014626,182 +0.015189,182 +0.015702,182 +0.014674,182 +0.014607,182 +0.014588,182 +0.014629,182 +0.014722,182 +0.016583,182 +0.015458,182 +0.014648,182 +0.014629,182 +0.014654,182 +0.014622,182 +0.014551,182 +0.016172,182 +0.014692,182 +0.014670,182 +0.014647,182 +0.014626,182 +0.014631,182 +0.014628,182 +0.016231,182 +0.014702,182 +0.014695,182 +0.014647,182 +0.014689,182 +0.014630,182 +0.015389,182 +0.015426,182 +0.015261,184 +0.015180,184 +0.015138,184 +0.015059,184 +0.015058,184 +0.016465,184 +0.015138,184 +0.015098,184 +0.015097,184 +0.015119,184 +0.015141,184 +0.015094,184 +0.016480,184 +0.015096,184 +0.015165,184 +0.015160,184 +0.015066,184 +0.015055,184 +0.016511,184 +0.015245,184 +0.015117,184 +0.015112,184 +0.015097,184 +0.015093,184 +0.015099,184 +0.016688,184 +0.015242,184 +0.015145,184 +0.015171,184 +0.015055,184 +0.015094,184 +0.015913,184 +0.016243,184 +0.016548,184 +0.016859,184 +0.016615,184 +0.016799,184 +0.017313,184 +0.016958,184 +0.016048,184 +0.016098,184 +0.015850,184 +0.015472,184 +0.015232,184 +0.015827,184 +0.015177,184 +0.015074,184 +0.016331,184 +0.017115,184 +0.016935,184 +0.016747,184 +0.016620,184 +0.016549,184 +0.016444,184 +0.016073,184 +0.016638,184 +0.016661,184 +0.017202,184 +0.016771,184 +0.016886,184 +0.016380,184 +0.016665,184 +0.016209,184 +0.016098,184 +0.015419,184 +0.015109,184 +0.015642,184 +0.017083,184 +0.016561,184 +0.015799,184 +0.015359,184 +0.015220,184 +0.015253,184 +0.016316,184 +0.017189,184 +0.016395,184 +0.016625,184 +0.016639,184 +0.016613,184 +0.016478,184 +0.016285,184 +0.016545,184 +0.016739,184 +0.017193,184 +0.018658,184 +0.016758,184 +0.016925,184 +0.016327,184 +0.015753,184 +0.016161,184 +0.017930,184 +0.016808,184 +0.016986,184 +0.016812,184 +0.018616,184 +0.017193,184 +0.017303,184 +0.019176,184 +0.018340,184 +0.019973,184 +0.020155,186 +0.020461,186 +0.018463,186 +0.019075,186 +0.024476,186 +0.022738,186 +0.020556,186 +0.019866,186 +0.017708,186 +0.018356,186 +0.017593,186 +0.018223,186 +0.019948,186 +0.020820,186 +0.022140,186 +0.017918,186 +0.019225,186 +0.019098,186 +0.019009,186 +0.022953,186 +0.017083,186 +0.018396,186 +0.017968,186 +0.017585,186 +0.016829,186 +0.016879,186 +0.016319,186 +0.016866,186 +0.018337,186 +0.018310,186 +0.023732,186 +0.018696,186 +0.019207,186 +0.019455,186 +0.018706,186 +0.017146,186 +0.016986,186 +0.017028,186 +0.019344,186 +0.019544,186 +0.017739,186 +0.017609,186 +0.017587,186 +0.017680,186 +0.017810,186 +0.017584,186 +0.017399,186 +0.018720,186 +0.017195,186 +0.017573,186 +0.017484,186 +0.018048,186 +0.021768,186 +0.016621,186 +0.017351,186 +0.016885,186 +0.016948,186 +0.017927,186 +0.017122,186 +0.017224,186 +0.017469,186 +0.017162,186 +0.017409,186 +0.017101,186 +0.017373,186 +0.016490,186 +0.017339,186 +0.017151,186 +0.017822,186 +0.017549,186 +0.017109,186 +0.016668,186 +0.016529,186 +0.016398,186 +0.017232,186 +0.019138,186 +0.017349,186 +0.016798,186 +0.016739,186 +0.017289,186 +0.016649,186 +0.017188,186 +0.016960,186 +0.016722,186 +0.017282,186 +0.016667,186 +0.016988,186 +0.016480,186 +0.016038,186 +0.015908,186 +0.015761,186 +0.015867,186 +0.019385,186 +0.017620,186 +0.018975,186 +0.017683,186 +0.016649,186 +0.017682,186 +0.017443,186 +0.017369,186 +0.017585,188 +0.017031,188 +0.016650,188 +0.016580,188 +0.016551,188 +0.016911,188 +0.017369,188 +0.017895,188 +0.020415,188 +0.021828,188 +0.020295,188 +0.020074,188 +0.020325,188 +0.018933,188 +0.016831,188 +0.016935,188 +0.016587,188 +0.016250,188 +0.016128,188 +0.016203,188 +0.016281,188 +0.016457,188 +0.016501,188 +0.016292,188 +0.016134,188 +0.017463,188 +0.016336,188 +0.016530,188 +0.016388,188 +0.016234,188 +0.016892,188 +0.021228,188 +0.018101,188 +0.018236,188 +0.019020,188 +0.022148,188 +0.028301,188 +0.030740,188 +0.028133,188 +0.030402,188 +0.030221,188 +0.021442,188 +0.026085,188 +0.021689,188 +0.021782,188 +0.019309,188 +0.018858,188 +0.016389,188 +0.016632,188 +0.019297,188 +0.017420,188 +0.018507,188 +0.016734,188 +0.017010,188 +0.017164,188 +0.017296,188 +0.019475,188 +0.018051,188 +0.016476,188 +0.018042,188 +0.016878,188 +0.016812,188 +0.018170,188 +0.017259,188 +0.016538,188 +0.016762,188 +0.017282,188 +0.017397,188 +0.022841,188 +0.018055,188 +0.016597,188 +0.016511,188 +0.016567,188 +0.016492,188 +0.018150,188 +0.017119,188 +0.016564,188 +0.017333,188 +0.016671,188 +0.016647,188 +0.016544,188 +0.016785,188 +0.016593,188 +0.017043,188 +0.016483,188 +0.016506,188 +0.020677,188 +0.016481,188 +0.016269,188 +0.016441,188 +0.016390,188 +0.016472,188 +0.020768,188 +0.016408,188 +0.016359,188 +0.016669,188 +0.016571,188 +0.017968,188 +0.019100,188 +0.016422,188 +0.019606,190 +0.018196,190 +0.017098,190 +0.017581,190 +0.017235,190 +0.016891,190 +0.017145,190 +0.017270,190 +0.017056,190 +0.021680,190 +0.020330,190 +0.019509,190 +0.017363,190 +0.017317,190 +0.017935,190 +0.017530,190 +0.017335,190 +0.018212,190 +0.017494,190 +0.017188,190 +0.017696,190 +0.016806,190 +0.016855,190 +0.017064,190 +0.017031,190 +0.017257,190 +0.017479,190 +0.016840,190 +0.016886,190 +0.017175,190 +0.016892,190 +0.016751,190 +0.017574,190 +0.016842,190 +0.016957,190 +0.017035,190 +0.016909,190 +0.017014,190 +0.017247,190 +0.016834,190 +0.016835,190 +0.017247,190 +0.017006,190 +0.017128,190 +0.018882,190 +0.018347,190 +0.017874,190 +0.017716,190 +0.016836,190 +0.017167,190 +0.016848,190 +0.016718,190 +0.016687,190 +0.016791,190 +0.016808,190 +0.017179,190 +0.016809,190 +0.016723,190 +0.016876,190 +0.017000,190 +0.016726,190 +0.017112,190 +0.016764,190 +0.016678,190 +0.016707,190 +0.016774,190 +0.016693,190 +0.017114,190 +0.016812,190 +0.016817,190 +0.016675,190 +0.016843,190 +0.016779,190 +0.017179,190 +0.016748,190 +0.016754,190 +0.017375,190 +0.017169,190 +0.018405,190 +0.018924,190 +0.018512,190 +0.018088,190 +0.017260,190 +0.017003,190 +0.016994,190 +0.018513,190 +0.017271,190 +0.017029,190 +0.017007,190 +0.016876,190 +0.016957,190 +0.019317,190 +0.019256,190 +0.018045,190 +0.017711,190 +0.017179,190 +0.021522,190 +0.019157,190 +0.022006,190 +0.022502,190 +0.024940,192 +0.020805,192 +0.018494,192 +0.018604,192 +0.018872,192 +0.020463,192 +0.019122,192 +0.018341,192 +0.018278,192 +0.018342,192 +0.021521,192 +0.021664,192 +0.023983,192 +0.022446,192 +0.020787,192 +0.020216,192 +0.021117,192 +0.021752,192 +0.020148,192 +0.020033,192 +0.019823,192 +0.019258,192 +0.018466,192 +0.018968,192 +0.019993,192 +0.024043,192 +0.020247,192 +0.020460,192 +0.022285,192 +0.032353,192 +0.020860,192 +0.019693,192 +0.019178,192 +0.019545,192 +0.019595,192 +0.022936,192 +0.019735,192 +0.020366,192 +0.020715,192 +0.020817,192 +0.019938,192 +0.019200,192 +0.019328,192 +0.019081,192 +0.019019,192 +0.024591,192 +0.020063,192 +0.023090,192 +0.020689,192 +0.025426,192 +0.024649,192 +0.022197,192 +0.023562,192 +0.025272,192 +0.021982,192 +0.019063,192 +0.020815,192 +0.018930,192 +0.019309,192 +0.021683,192 +0.018894,192 +0.018693,192 +0.018402,192 +0.018643,192 +0.018803,192 +0.018865,192 +0.018530,192 +0.018566,192 +0.018457,192 +0.019478,192 +0.019840,192 +0.019749,192 +0.021034,192 +0.020868,192 +0.023697,192 +0.019251,192 +0.019106,192 +0.021241,192 +0.019936,192 +0.020166,192 +0.019412,192 +0.019460,192 +0.019504,192 +0.019592,192 +0.019792,192 +0.019798,192 +0.019799,192 +0.019798,192 +0.021687,192 +0.020310,192 +0.020672,192 +0.020906,192 +0.020747,192 +0.020806,192 +0.020942,192 +0.022014,192 +0.020865,192 +0.020481,192 +0.021178,192 +0.020042,192 +0.019345,194 +0.020383,194 +0.034984,194 +0.031715,194 +0.019095,194 +0.019188,194 +0.019084,194 +0.019325,194 +0.018859,194 +0.019776,194 +0.018427,194 +0.018625,194 +0.018061,194 +0.018269,194 +0.018030,194 +0.018468,194 +0.017982,194 +0.018246,194 +0.018547,194 +0.019330,194 +0.019578,194 +0.019471,194 +0.020268,194 +0.019597,194 +0.019489,194 +0.019100,194 +0.019014,194 +0.019099,194 +0.018724,194 +0.018987,194 +0.018608,194 +0.018548,194 +0.018599,194 +0.018297,194 +0.018905,194 +0.018515,194 +0.018691,194 +0.018296,194 +0.018482,194 +0.018275,194 +0.018193,194 +0.017980,194 +0.018071,194 +0.018040,194 +0.017936,194 +0.019145,194 +0.019417,194 +0.019837,194 +0.020615,194 +0.020887,194 +0.019485,194 +0.018711,194 +0.018365,194 +0.019080,194 +0.018409,194 +0.018458,194 +0.018273,194 +0.017884,194 +0.017895,194 +0.018663,194 +0.019215,194 +0.019486,194 +0.019641,194 +0.019856,194 +0.019866,194 +0.019767,194 +0.020457,194 +0.019443,194 +0.019975,194 +0.019074,194 +0.018775,194 +0.019472,194 +0.020400,194 +0.020998,194 +0.020603,194 +0.020092,194 +0.019683,194 +0.020105,194 +0.018864,194 +0.018451,194 +0.017971,194 +0.018226,194 +0.017998,194 +0.017893,194 +0.018022,194 +0.017815,194 +0.017903,194 +0.018246,194 +0.019260,194 +0.019605,194 +0.019167,194 +0.019089,194 +0.019311,194 +0.019635,194 +0.019365,194 +0.019919,194 +0.020112,194 +0.019885,194 +0.019468,194 +0.019149,194 +0.020764,196 +0.021087,196 +0.020729,196 +0.023838,196 +0.024036,196 +0.019970,196 +0.019897,196 +0.020047,196 +0.019956,196 +0.019867,196 +0.019909,196 +0.021403,196 +0.021023,196 +0.021649,196 +0.020910,196 +0.020714,196 +0.021551,196 +0.021570,196 +0.021105,196 +0.019902,196 +0.019433,196 +0.021446,196 +0.021803,196 +0.020211,196 +0.019600,196 +0.018518,196 +0.019530,196 +0.020621,196 +0.021180,196 +0.020092,196 +0.019216,196 +0.019500,196 +0.021280,196 +0.021502,196 +0.020392,196 +0.020218,196 +0.019788,196 +0.019832,196 +0.019178,196 +0.019315,196 +0.018625,196 +0.018539,196 +0.019664,196 +0.019096,196 +0.019631,196 +0.019488,196 +0.019109,196 +0.019395,196 +0.019174,196 +0.019152,196 +0.018386,196 +0.018477,196 +0.018987,196 +0.018399,196 +0.019330,196 +0.019047,196 +0.018537,196 +0.018668,196 +0.018769,196 +0.018420,196 +0.018592,196 +0.018385,196 +0.018368,196 +0.018968,196 +0.018484,196 +0.018433,196 +0.018916,196 +0.018328,196 +0.018830,196 +0.018451,196 +0.018356,196 +0.018438,196 +0.018313,196 +0.018338,196 +0.018935,196 +0.018504,196 +0.018554,196 +0.018682,196 +0.018337,196 +0.018847,196 +0.019009,196 +0.018384,196 +0.019396,196 +0.018847,196 +0.018546,196 +0.018771,196 +0.018494,196 +0.018434,196 +0.018456,196 +0.018361,196 +0.019148,196 +0.021199,196 +0.019170,196 +0.018582,196 +0.018312,196 +0.018855,196 +0.023224,196 +0.019320,196 +0.023507,196 +0.021675,196 +0.020363,198 +0.021072,198 +0.020478,198 +0.019864,198 +0.022227,198 +0.020976,198 +0.019821,198 +0.019979,198 +0.019839,198 +0.021022,198 +0.020894,198 +0.019946,198 +0.020093,198 +0.024282,198 +0.022166,198 +0.020987,198 +0.021312,198 +0.020292,198 +0.019523,198 +0.019733,198 +0.019085,198 +0.019108,198 +0.018861,198 +0.020641,198 +0.022971,198 +0.023156,198 +0.022558,198 +0.023455,198 +0.021469,198 +0.020916,198 +0.021697,198 +0.021540,198 +0.021498,198 +0.022028,198 +0.023256,198 +0.021457,198 +0.021465,198 +0.020630,198 +0.021839,198 +0.020525,198 +0.020847,198 +0.020563,198 +0.020045,198 +0.020640,198 +0.020792,198 +0.020395,198 +0.019915,198 +0.019510,198 +0.019546,198 +0.018955,198 +0.019296,198 +0.018956,198 +0.018959,198 +0.019419,198 +0.021557,198 +0.024834,198 +0.020640,198 +0.019464,198 +0.019883,198 +0.020924,198 +0.020797,198 +0.019979,198 +0.020777,198 +0.020949,198 +0.020096,198 +0.020566,198 +0.020725,198 +0.020589,198 +0.020503,198 +0.021146,198 +0.020854,198 +0.020709,198 +0.020673,198 +0.021265,198 +0.020957,198 +0.020087,198 +0.020293,198 +0.020254,198 +0.020485,198 +0.020327,198 +0.019938,198 +0.019418,198 +0.020064,198 +0.019959,198 +0.020235,198 +0.019863,198 +0.019784,198 +0.019847,198 +0.019759,198 +0.019440,198 +0.019175,198 +0.019037,198 +0.019055,198 +0.019500,198 +0.018947,198 +0.018935,198 +0.018942,198 +0.019043,198 +0.019386,198 +0.018894,198 +0.019847,200 +0.019664,200 +0.019531,200 +0.019984,200 +0.019496,200 +0.019535,200 +0.019523,200 +0.019396,200 +0.019900,200 +0.019467,200 +0.019590,200 +0.019588,200 +0.019606,200 +0.019987,200 +0.020046,200 +0.019704,200 +0.019461,200 +0.020299,200 +0.020112,200 +0.019736,200 +0.019486,200 +0.019468,200 +0.019677,200 +0.019764,200 +0.020011,200 +0.019543,200 +0.019450,200 +0.019493,200 +0.019740,200 +0.019989,200 +0.019563,200 +0.019551,200 +0.019500,200 +0.019565,200 +0.020163,200 +0.019851,200 +0.019784,200 +0.019433,200 +0.019716,200 +0.020197,200 +0.019575,200 +0.019520,200 +0.019471,200 +0.019425,200 +0.020289,200 +0.019476,200 +0.019521,200 +0.019553,200 +0.019613,200 +0.020180,200 +0.019593,200 +0.019575,200 +0.019641,200 +0.019589,200 +0.020003,200 +0.019793,200 +0.019558,200 +0.019446,200 +0.019542,200 +0.019870,200 +0.019855,200 +0.020083,200 +0.019634,200 +0.019726,200 +0.020650,200 +0.019880,200 +0.019689,200 +0.020130,200 +0.019559,200 +0.019814,200 +0.019751,200 +0.019683,200 +0.019536,200 +0.019511,200 +0.019739,200 +0.019761,200 +0.019844,200 +0.019614,200 +0.019510,200 +0.019615,200 +0.019933,200 +0.019595,200 +0.019627,200 +0.019514,200 +0.019771,200 +0.019989,200 +0.019759,200 +0.019605,200 +0.019446,200 +0.019555,200 +0.020018,200 +0.019672,200 +0.019454,200 +0.019554,200 +0.019475,200 +0.019982,200 +0.019757,200 +0.019448,200 +0.019456,200 +0.019556,200 +0.020752,202 +0.020315,202 +0.020130,202 +0.020352,202 +0.020185,202 +0.020527,202 +0.020467,202 +0.020032,202 +0.020118,202 +0.020047,202 +0.020468,202 +0.020382,202 +0.020043,202 +0.020195,202 +0.020701,202 +0.022772,202 +0.020800,202 +0.020752,202 +0.020241,202 +0.020193,202 +0.020553,202 +0.021345,202 +0.021025,202 +0.021084,202 +0.021334,202 +0.021501,202 +0.021238,202 +0.020361,202 +0.020826,202 +0.020559,202 +0.021365,202 +0.021705,202 +0.021215,202 +0.020839,202 +0.021010,202 +0.024230,202 +0.020649,202 +0.020775,202 +0.020427,202 +0.021548,202 +0.020331,202 +0.020407,202 +0.020270,202 +0.020106,202 +0.020695,202 +0.022353,202 +0.020113,202 +0.020133,202 +0.020351,202 +0.020511,202 +0.020268,202 +0.020175,202 +0.020279,202 +0.020470,202 +0.020585,202 +0.020178,202 +0.020050,202 +0.021290,202 +0.020567,202 +0.020655,202 +0.020220,202 +0.020202,202 +0.020527,202 +0.022670,202 +0.021468,202 +0.020876,202 +0.022385,202 +0.032710,202 +0.039798,202 +0.023425,202 +0.021605,202 +0.023522,202 +0.021182,202 +0.020169,202 +0.020112,202 +0.020041,202 +0.021666,202 +0.020232,202 +0.020173,202 +0.021271,202 +0.022316,202 +0.022846,202 +0.021547,202 +0.023117,202 +0.022271,202 +0.023128,202 +0.024963,202 +0.022957,202 +0.025744,202 +0.023609,202 +0.021734,202 +0.021805,202 +0.021457,202 +0.021720,202 +0.024516,202 +0.022754,202 +0.023032,202 +0.021576,202 +0.022953,202 +0.020970,202 +0.021015,204 +0.020775,204 +0.020687,204 +0.025122,204 +0.020993,204 +0.020820,204 +0.020792,204 +0.020859,204 +0.030238,204 +0.025164,204 +0.026316,204 +0.023593,204 +0.025047,204 +0.023127,204 +0.022618,204 +0.022424,204 +0.022037,204 +0.022084,204 +0.021993,204 +0.022581,204 +0.021904,204 +0.021925,204 +0.022160,204 +0.022226,204 +0.022588,204 +0.028373,204 +0.022144,204 +0.023337,204 +0.023259,204 +0.022549,204 +0.023086,204 +0.023397,204 +0.022853,204 +0.028375,204 +0.023074,204 +0.022656,204 +0.022478,204 +0.022516,204 +0.025986,204 +0.020992,204 +0.020852,204 +0.020867,204 +0.025466,204 +0.021012,204 +0.020711,204 +0.020913,204 +0.021363,204 +0.027080,204 +0.022212,204 +0.021433,204 +0.020768,204 +0.025439,204 +0.021289,204 +0.023418,204 +0.026657,204 +0.022670,204 +0.023941,204 +0.023481,204 +0.025152,204 +0.022343,204 +0.023359,204 +0.023745,204 +0.023200,204 +0.022828,204 +0.023002,204 +0.022384,204 +0.022177,204 +0.022080,204 +0.021990,204 +0.022732,204 +0.022659,204 +0.023318,204 +0.022884,204 +0.022393,204 +0.023143,204 +0.023760,204 +0.024075,204 +0.022287,204 +0.022691,204 +0.021653,204 +0.021537,204 +0.020961,204 +0.022480,204 +0.020901,204 +0.022064,204 +0.024598,204 +0.028897,204 +0.024398,204 +0.022677,204 +0.022657,204 +0.022089,204 +0.021633,204 +0.022691,204 +0.024345,204 +0.022917,204 +0.024167,204 +0.022165,204 +0.022049,204 +0.022787,204 +0.024235,204 +0.023591,206 +0.021978,206 +0.021865,206 +0.021844,206 +0.022636,206 +0.022349,206 +0.021367,206 +0.021330,206 +0.022050,206 +0.021592,206 +0.021232,206 +0.021594,206 +0.022438,206 +0.022745,206 +0.022449,206 +0.021736,206 +0.021858,206 +0.022040,206 +0.021889,206 +0.021391,206 +0.021359,206 +0.021393,206 +0.021920,206 +0.021935,206 +0.022188,206 +0.021793,206 +0.021650,206 +0.022413,206 +0.021509,206 +0.021635,206 +0.022036,206 +0.023080,206 +0.021413,206 +0.021489,206 +0.021287,206 +0.021372,206 +0.022243,206 +0.022011,206 +0.021568,206 +0.022526,206 +0.022047,206 +0.021898,206 +0.021383,206 +0.021404,206 +0.021395,206 +0.021860,206 +0.021563,206 +0.021460,206 +0.021246,206 +0.021360,206 +0.022058,206 +0.021339,206 +0.022831,206 +0.021602,206 +0.021552,206 +0.021860,206 +0.021494,206 +0.021493,206 +0.021341,206 +0.022150,206 +0.023089,206 +0.023404,206 +0.023811,206 +0.023137,206 +0.023687,206 +0.023525,206 +0.022122,206 +0.021608,206 +0.022198,206 +0.021359,206 +0.022185,206 +0.021756,206 +0.021619,206 +0.021804,206 +0.021404,206 +0.021511,206 +0.021431,206 +0.022140,206 +0.021525,206 +0.021277,206 +0.021323,206 +0.021513,206 +0.022128,206 +0.021489,206 +0.023350,206 +0.021501,206 +0.022080,206 +0.021529,206 +0.021403,206 +0.021514,206 +0.021426,206 +0.022244,206 +0.021401,206 +0.021319,206 +0.022172,206 +0.022706,206 +0.022246,206 +0.021965,206 +0.021504,206 +0.022424,206 +0.023821,208 +0.023756,208 +0.022642,208 +0.025208,208 +0.023727,208 +0.022863,208 +0.022806,208 +0.022508,208 +0.022684,208 +0.022997,208 +0.023056,208 +0.023113,208 +0.022604,208 +0.023785,208 +0.029033,208 +0.024733,208 +0.024317,208 +0.024554,208 +0.024225,208 +0.025887,208 +0.024642,208 +0.025190,208 +0.024142,208 +0.024546,208 +0.022975,208 +0.023746,208 +0.023763,208 +0.026540,208 +0.024444,208 +0.023780,208 +0.023109,208 +0.022683,208 +0.022263,208 +0.021896,208 +0.022531,208 +0.025044,208 +0.023229,208 +0.022732,208 +0.023278,208 +0.022880,208 +0.024107,208 +0.024268,208 +0.024868,208 +0.025449,208 +0.024925,208 +0.024397,208 +0.025436,208 +0.025071,208 +0.025322,208 +0.024356,208 +0.026775,208 +0.024093,208 +0.026201,208 +0.025142,208 +0.027131,208 +0.024924,208 +0.025702,208 +0.027040,208 +0.024313,208 +0.024575,208 +0.024335,208 +0.024293,208 +0.023861,208 +0.023234,208 +0.022936,208 +0.022000,208 +0.022155,208 +0.023588,208 +0.024183,208 +0.022588,208 +0.021907,208 +0.022326,208 +0.022018,208 +0.021848,208 +0.021839,208 +0.022088,208 +0.022409,208 +0.021985,208 +0.021948,208 +0.021927,208 +0.022259,208 +0.021915,208 +0.022055,208 +0.021779,208 +0.021774,208 +0.022601,208 +0.022210,208 +0.021924,208 +0.022733,208 +0.023556,208 +0.025291,208 +0.024384,208 +0.024610,208 +0.028181,208 +0.024314,208 +0.024542,208 +0.024557,208 +0.023488,208 +0.023457,208 +0.023533,208 +0.024409,210 +0.024628,210 +0.023856,210 +0.023852,210 +0.023106,210 +0.023128,210 +0.023243,210 +0.023334,210 +0.022987,210 +0.022623,210 +0.022790,210 +0.022955,210 +0.022740,210 +0.022705,210 +0.022813,210 +0.022882,210 +0.023087,210 +0.022539,210 +0.022487,210 +0.023094,210 +0.022589,210 +0.022518,210 +0.022693,210 +0.022863,210 +0.022825,210 +0.022861,210 +0.022547,210 +0.022669,210 +0.022950,210 +0.022901,210 +0.023057,210 +0.022649,210 +0.023103,210 +0.022778,210 +0.022605,210 +0.023652,210 +0.024703,210 +0.025658,210 +0.024492,210 +0.023719,210 +0.024246,210 +0.024166,210 +0.024462,210 +0.023157,210 +0.023018,210 +0.024428,210 +0.026391,210 +0.024282,210 +0.023907,210 +0.025583,210 +0.023684,210 +0.023131,210 +0.022876,210 +0.024564,210 +0.022791,210 +0.022825,210 +0.022587,210 +0.024037,210 +0.023186,210 +0.022641,210 +0.022504,210 +0.022791,210 +0.024149,210 +0.022694,210 +0.022492,210 +0.022470,210 +0.024329,210 +0.023516,210 +0.022771,210 +0.022512,210 +0.023819,210 +0.023292,210 +0.022586,210 +0.022538,210 +0.022760,210 +0.023383,210 +0.023399,210 +0.022960,210 +0.022517,210 +0.023320,210 +0.022742,210 +0.022517,210 +0.022731,210 +0.022745,210 +0.023166,210 +0.023166,210 +0.022732,210 +0.023988,210 +0.024082,210 +0.024657,210 +0.024366,210 +0.027884,210 +0.024597,210 +0.025377,210 +0.023830,210 +0.023895,210 +0.024427,210 +0.023678,210 +0.025564,210 +0.024984,210 +0.028780,212 +0.029890,212 +0.027592,212 +0.026942,212 +0.030883,212 +0.027178,212 +0.028512,212 +0.039651,212 +0.028242,212 +0.028991,212 +0.026668,212 +0.027360,212 +0.026401,212 +0.029501,212 +0.026908,212 +0.027813,212 +0.027291,212 +0.026234,212 +0.027539,212 +0.028791,212 +0.027450,212 +0.025350,212 +0.023689,212 +0.023496,212 +0.023258,212 +0.023522,212 +0.024155,212 +0.024813,212 +0.026071,212 +0.027582,212 +0.025773,212 +0.024817,212 +0.023433,212 +0.023553,212 +0.023926,212 +0.024485,212 +0.024293,212 +0.024646,212 +0.029259,212 +0.025543,212 +0.024065,212 +0.024499,212 +0.030856,212 +0.027562,212 +0.024638,212 +0.023682,212 +0.023831,212 +0.023276,212 +0.023219,212 +0.023363,212 +0.023826,212 +0.023578,212 +0.023316,212 +0.023402,212 +0.023999,212 +0.023216,212 +0.023572,212 +0.023125,212 +0.023700,212 +0.025048,212 +0.024970,212 +0.024854,212 +0.024401,212 +0.025642,212 +0.025771,212 +0.025708,212 +0.024839,212 +0.025416,212 +0.023692,212 +0.023449,212 +0.024185,212 +0.024160,212 +0.023241,212 +0.025328,212 +0.023427,212 +0.024180,212 +0.023727,212 +0.023739,212 +0.023470,212 +0.023785,212 +0.023785,212 +0.026845,212 +0.026689,212 +0.032715,212 +0.027248,212 +0.026124,212 +0.025759,212 +0.025625,212 +0.024113,212 +0.023480,212 +0.023333,212 +0.023605,212 +0.023243,212 +0.023336,212 +0.023319,212 +0.023747,212 +0.023551,212 +0.023361,212 +0.024556,212 +0.024892,212 +0.026700,214 +0.025213,214 +0.026438,214 +0.025136,214 +0.026425,214 +0.025937,214 +0.025493,214 +0.024801,214 +0.024645,214 +0.025036,214 +0.024143,214 +0.024138,214 +0.024073,214 +0.023911,214 +0.024143,214 +0.024270,214 +0.024084,214 +0.024074,214 +0.023962,214 +0.024107,214 +0.024537,214 +0.024517,214 +0.024748,214 +0.024388,214 +0.024160,214 +0.024152,214 +0.023880,214 +0.024127,214 +0.024769,214 +0.024106,214 +0.023967,214 +0.024425,214 +0.025422,214 +0.024347,214 +0.024800,214 +0.023930,214 +0.024677,214 +0.023916,214 +0.024202,214 +0.023872,214 +0.024607,214 +0.023927,214 +0.023970,214 +0.024261,214 +0.025395,214 +0.024604,214 +0.024098,214 +0.024544,214 +0.024544,214 +0.024166,214 +0.023802,214 +0.023982,214 +0.024028,214 +0.024306,214 +0.024041,214 +0.024064,214 +0.024016,214 +0.024493,214 +0.024140,214 +0.023797,214 +0.023974,214 +0.024329,214 +0.023998,214 +0.023922,214 +0.023908,214 +0.024607,214 +0.023883,214 +0.024193,214 +0.024173,214 +0.024611,214 +0.023901,214 +0.023930,214 +0.023932,214 +0.024221,214 +0.024181,214 +0.023771,214 +0.024193,214 +0.023987,214 +0.024391,214 +0.023819,214 +0.023993,214 +0.023855,214 +0.024511,214 +0.023991,214 +0.023807,214 +0.024126,214 +0.024321,214 +0.024102,214 +0.023873,214 +0.023921,214 +0.024535,214 +0.024155,214 +0.023932,214 +0.024392,214 +0.024515,214 +0.023947,214 +0.024139,214 +0.023944,214 +0.027535,214 +0.025248,214 +0.025484,216 +0.025123,216 +0.030448,216 +0.025789,216 +0.024894,216 +0.025904,216 +0.026197,216 +0.024432,216 +0.024402,216 +0.024708,216 +0.026282,216 +0.024615,216 +0.024535,216 +0.024753,216 +0.026081,216 +0.024561,216 +0.024475,216 +0.024744,216 +0.025945,216 +0.024761,216 +0.024542,216 +0.024724,216 +0.025159,216 +0.024840,216 +0.024601,216 +0.024741,216 +0.025042,216 +0.024965,216 +0.024499,216 +0.024812,216 +0.024926,216 +0.024801,216 +0.024435,216 +0.024676,216 +0.024981,216 +0.025004,216 +0.024671,216 +0.024859,216 +0.025062,216 +0.024994,216 +0.024513,216 +0.024685,216 +0.024627,216 +0.025029,216 +0.024553,216 +0.024694,216 +0.024752,216 +0.024954,216 +0.024574,216 +0.024582,216 +0.024523,216 +0.025109,216 +0.024530,216 +0.024503,216 +0.024665,216 +0.024862,216 +0.024782,216 +0.024510,216 +0.024871,216 +0.024840,216 +0.024585,216 +0.024626,216 +0.024589,216 +0.025097,216 +0.024512,216 +0.024515,216 +0.024539,216 +0.025020,216 +0.024724,216 +0.025950,216 +0.025361,216 +0.024966,216 +0.024595,216 +0.024620,216 +0.024548,216 +0.024962,216 +0.024853,216 +0.024712,216 +0.025908,216 +0.024977,216 +0.024504,216 +0.024641,216 +0.024624,216 +0.024878,216 +0.024699,216 +0.024645,216 +0.024614,216 +0.024994,216 +0.024638,216 +0.024640,216 +0.024676,216 +0.024891,216 +0.024802,216 +0.024641,216 +0.024596,216 +0.025361,216 +0.024752,216 +0.024759,216 +0.024553,216 +0.025133,216 +0.026054,218 +0.025362,218 +0.025420,218 +0.025677,218 +0.025630,218 +0.025347,218 +0.025488,218 +0.025886,218 +0.025560,218 +0.025564,218 +0.025548,218 +0.025869,218 +0.025400,218 +0.025229,218 +0.025425,218 +0.025760,218 +0.025523,218 +0.025417,218 +0.025613,218 +0.025950,218 +0.025742,218 +0.026214,218 +0.025615,218 +0.025978,218 +0.025597,218 +0.025436,218 +0.025336,218 +0.025929,218 +0.025384,218 +0.025450,218 +0.025279,218 +0.025758,218 +0.026162,218 +0.026038,218 +0.025452,218 +0.025823,218 +0.025876,218 +0.025534,218 +0.025492,218 +0.025908,218 +0.025268,218 +0.025463,218 +0.025701,218 +0.025900,218 +0.025401,218 +0.025399,218 +0.025506,218 +0.026239,218 +0.025726,218 +0.025523,218 +0.025512,218 +0.025693,218 +0.025337,218 +0.025391,218 +0.025715,218 +0.025980,218 +0.025722,218 +0.025406,218 +0.025888,218 +0.025402,218 +0.025444,218 +0.025225,218 +0.025808,218 +0.025480,218 +0.025621,218 +0.025296,218 +0.025849,218 +0.025335,218 +0.025513,218 +0.025507,218 +0.025734,218 +0.025532,218 +0.025320,218 +0.025351,218 +0.026005,218 +0.025512,218 +0.025464,218 +0.025527,218 +0.025952,218 +0.025491,218 +0.025561,218 +0.025331,218 +0.026120,218 +0.025413,218 +0.025770,218 +0.025433,218 +0.026001,218 +0.025613,218 +0.030177,218 +0.025411,218 +0.025951,218 +0.025443,218 +0.025476,218 +0.025370,218 +0.025936,218 +0.025675,218 +0.025550,218 +0.025630,218 +0.025618,218 +0.025579,218 +0.026034,220 +0.026495,220 +0.026471,220 +0.026135,220 +0.026024,220 +0.026502,220 +0.026192,220 +0.026208,220 +0.025793,220 +0.026485,220 +0.026102,220 +0.026000,220 +0.025925,220 +0.026730,220 +0.026285,220 +0.026114,220 +0.026022,220 +0.026625,220 +0.026283,220 +0.025947,220 +0.026193,220 +0.026647,220 +0.026127,220 +0.026263,220 +0.026584,220 +0.026220,220 +0.026227,220 +0.025974,220 +0.026622,220 +0.026000,220 +0.026058,220 +0.025875,220 +0.026576,220 +0.026332,220 +0.026333,220 +0.026040,220 +0.026581,220 +0.026081,220 +0.025933,220 +0.025890,220 +0.026702,220 +0.026128,220 +0.026023,220 +0.026261,220 +0.026445,220 +0.026108,220 +0.025919,220 +0.026601,220 +0.026105,220 +0.026200,220 +0.025909,220 +0.026559,220 +0.026029,220 +0.026357,220 +0.025926,220 +0.026565,220 +0.026243,220 +0.026013,220 +0.026061,220 +0.026618,220 +0.026076,220 +0.026005,220 +0.026074,220 +0.026654,220 +0.027963,220 +0.026178,220 +0.026506,220 +0.026037,220 +0.026183,220 +0.025942,220 +0.026730,220 +0.026153,220 +0.026348,220 +0.025951,220 +0.026421,220 +0.026054,220 +0.026047,220 +0.025945,220 +0.026649,220 +0.026028,220 +0.026105,220 +0.025931,220 +0.026659,220 +0.026037,220 +0.025900,220 +0.026170,220 +0.026410,220 +0.027071,220 +0.029181,220 +0.029791,220 +0.032931,220 +0.029965,220 +0.028955,220 +0.028804,220 +0.028369,220 +0.033877,220 +0.035271,220 +0.029037,220 +0.030304,220 +0.028764,220 +0.032144,222 +0.030095,222 +0.029826,222 +0.030025,222 +0.030439,222 +0.029537,222 +0.030335,222 +0.030394,222 +0.031119,222 +0.030428,222 +0.029719,222 +0.030357,222 +0.030121,222 +0.030463,222 +0.030936,222 +0.029935,222 +0.030507,222 +0.030769,222 +0.030753,222 +0.031559,222 +0.030556,222 +0.028491,222 +0.038898,222 +0.031032,222 +0.032999,222 +0.030822,222 +0.031671,222 +0.027785,222 +0.028481,222 +0.029536,222 +0.028762,222 +0.029051,222 +0.028534,222 +0.028510,222 +0.028585,222 +0.028222,222 +0.027511,222 +0.026921,222 +0.027167,222 +0.028879,222 +0.029678,222 +0.029246,222 +0.028604,222 +0.027927,222 +0.027112,222 +0.026937,222 +0.027582,222 +0.027922,222 +0.028084,222 +0.027279,222 +0.032112,222 +0.028924,222 +0.028764,222 +0.028468,222 +0.028902,222 +0.029415,222 +0.028632,222 +0.028597,222 +0.028101,222 +0.027938,222 +0.027737,222 +0.027592,222 +0.027508,222 +0.026710,222 +0.027587,222 +0.027275,222 +0.026938,222 +0.026820,222 +0.027447,222 +0.026860,222 +0.027257,222 +0.027210,222 +0.027288,222 +0.026897,222 +0.026723,222 +0.027392,222 +0.027271,222 +0.026700,222 +0.027218,222 +0.027228,222 +0.026802,222 +0.026738,222 +0.026919,222 +0.027479,222 +0.026767,222 +0.027356,222 +0.028218,222 +0.027190,222 +0.026627,222 +0.026783,222 +0.029107,222 +0.027437,222 +0.027101,222 +0.027245,222 +0.027957,222 +0.027147,222 +0.026625,222 +0.027619,222 +0.026972,222 +0.026861,222 +0.030481,224 +0.031907,224 +0.030276,224 +0.030199,224 +0.030781,224 +0.030660,224 +0.029803,224 +0.029641,224 +0.030029,224 +0.030143,224 +0.030204,224 +0.029160,224 +0.028092,224 +0.027552,224 +0.028139,224 +0.027974,224 +0.027323,224 +0.027517,224 +0.028085,224 +0.030571,224 +0.030403,224 +0.029997,224 +0.028308,224 +0.027460,224 +0.028766,224 +0.029718,224 +0.028819,224 +0.029245,224 +0.031629,224 +0.032029,224 +0.030914,224 +0.030517,224 +0.030474,224 +0.030768,224 +0.031882,224 +0.031387,224 +0.030420,224 +0.031337,224 +0.030044,224 +0.034327,224 +0.030854,224 +0.030328,224 +0.033406,224 +0.031817,224 +0.030631,224 +0.032101,224 +0.033730,224 +0.029826,224 +0.031530,224 +0.031753,224 +0.033048,224 +0.032152,224 +0.030505,224 +0.029881,224 +0.031639,224 +0.029774,224 +0.028924,224 +0.028632,224 +0.027792,224 +0.029400,224 +0.030336,224 +0.030603,224 +0.028470,224 +0.028010,224 +0.027968,224 +0.027848,224 +0.034007,224 +0.034008,224 +0.032426,224 +0.031746,224 +0.038141,224 +0.032608,224 +0.031625,224 +0.034657,224 +0.038820,224 +0.033090,224 +0.033139,224 +0.031559,224 +0.032271,224 +0.030568,224 +0.032382,224 +0.030899,224 +0.030876,224 +0.031431,224 +0.032091,224 +0.030831,224 +0.033164,224 +0.031260,224 +0.032525,224 +0.030558,224 +0.031484,224 +0.032766,224 +0.040871,224 +0.034256,224 +0.029736,224 +0.030002,224 +0.030190,224 +0.031873,224 +0.035653,224 +0.030355,224 +0.038359,226 +0.032737,226 +0.032086,226 +0.031910,226 +0.033470,226 +0.035968,226 +0.035538,226 +0.031602,226 +0.031934,226 +0.033544,226 +0.031603,226 +0.032140,226 +0.030537,226 +0.029187,226 +0.033465,226 +0.032267,226 +0.028616,226 +0.029906,226 +0.030404,226 +0.031123,226 +0.030498,226 +0.029185,226 +0.029922,226 +0.029873,226 +0.029993,226 +0.029503,226 +0.029013,226 +0.029772,226 +0.029598,226 +0.029569,226 +0.029438,226 +0.029786,226 +0.029251,226 +0.029219,226 +0.029285,226 +0.028921,226 +0.029585,226 +0.029455,226 +0.030155,226 +0.037745,226 +0.048594,226 +0.035934,226 +0.029589,226 +0.030131,226 +0.031797,226 +0.032539,226 +0.037528,226 +0.030358,226 +0.030639,226 +0.033117,226 +0.030044,226 +0.032242,226 +0.055458,226 +0.031261,226 +0.030087,226 +0.030046,226 +0.030232,226 +0.029933,226 +0.033404,226 +0.031345,226 +0.029815,226 +0.034788,226 +0.030248,226 +0.031458,226 +0.030393,226 +0.029576,226 +0.034623,226 +0.031584,226 +0.030099,226 +0.032214,226 +0.038271,226 +0.053570,226 +0.032201,226 +0.037901,226 +0.032488,226 +0.040133,226 +0.047461,226 +0.054163,226 +0.034901,226 +0.029900,226 +0.029762,226 +0.033021,226 +0.033003,226 +0.038823,226 +0.037308,226 +0.032131,226 +0.034172,226 +0.033802,226 +0.030919,226 +0.031852,226 +0.033025,226 +0.031556,226 +0.032073,226 +0.033406,226 +0.033584,226 +0.032928,226 +0.038199,226 +0.033780,226 +0.038584,226 +0.055719,226 +0.058413,228 +0.035285,228 +0.035209,228 +0.037280,228 +0.033502,228 +0.032071,228 +0.035548,228 +0.034351,228 +0.036300,228 +0.033368,228 +0.032850,228 +0.034856,228 +0.031111,228 +0.031256,228 +0.032246,228 +0.032399,228 +0.030678,228 +0.032127,228 +0.034021,228 +0.033264,228 +0.035448,228 +0.033460,228 +0.032239,228 +0.034237,228 +0.033503,228 +0.035946,228 +0.038068,228 +0.037110,228 +0.032372,228 +0.034622,228 +0.043915,228 +0.038023,228 +0.032146,228 +0.033678,228 +0.035175,228 +0.039960,228 +0.038647,228 +0.032987,228 +0.034119,228 +0.031473,228 +0.034447,228 +0.037187,228 +0.034195,228 +0.053888,228 +0.057387,228 +0.041434,228 +0.035605,228 +0.037209,228 +0.038886,228 +0.038520,228 +0.037813,228 +0.038613,228 +0.037488,228 +0.035828,228 +0.055271,228 +0.044974,228 +0.036878,228 +0.033910,228 +0.040586,228 +0.034270,228 +0.035660,228 +0.037039,228 +0.035461,228 +0.033405,228 +0.034598,228 +0.033075,228 +0.031569,228 +0.029700,228 +0.028999,228 +0.028899,228 +0.030214,228 +0.029377,228 +0.029040,228 +0.028972,228 +0.030507,228 +0.030097,228 +0.029211,228 +0.031429,228 +0.031037,228 +0.030696,228 +0.032641,228 +0.030338,228 +0.030568,228 +0.035138,228 +0.033369,228 +0.033579,228 +0.032370,228 +0.033078,228 +0.033028,228 +0.036455,228 +0.031926,228 +0.037841,228 +0.043416,228 +0.034424,228 +0.035560,228 +0.035623,228 +0.033878,228 +0.034861,228 +0.040343,228 +0.031714,228 +0.031521,230 +0.032262,230 +0.031759,230 +0.031238,230 +0.040024,230 +0.030795,230 +0.030423,230 +0.037331,230 +0.034220,230 +0.038911,230 +0.033386,230 +0.030560,230 +0.032715,230 +0.032480,230 +0.032481,230 +0.032610,230 +0.031889,230 +0.029772,230 +0.031411,230 +0.036283,230 +0.035074,230 +0.031736,230 +0.032945,230 +0.033298,230 +0.035190,230 +0.035525,230 +0.033094,230 +0.030818,230 +0.030266,230 +0.030043,230 +0.033915,230 +0.033520,230 +0.043449,230 +0.031992,230 +0.032614,230 +0.030324,230 +0.029697,230 +0.031615,230 +0.029970,230 +0.029960,230 +0.030578,230 +0.030815,230 +0.029851,230 +0.029909,230 +0.031756,230 +0.030288,230 +0.029887,230 +0.031984,230 +0.030395,230 +0.030012,230 +0.031443,230 +0.030140,230 +0.029813,230 +0.029760,230 +0.030528,230 +0.031063,230 +0.030089,230 +0.030302,230 +0.031332,230 +0.030670,230 +0.030580,230 +0.030771,230 +0.029953,230 +0.029818,230 +0.030290,230 +0.029702,230 +0.029878,230 +0.030488,230 +0.029758,230 +0.029761,230 +0.030089,230 +0.029880,230 +0.029779,230 +0.029914,230 +0.030102,230 +0.030568,230 +0.029937,230 +0.040401,230 +0.031918,230 +0.033614,230 +0.033388,230 +0.031643,230 +0.033828,230 +0.033263,230 +0.032154,230 +0.037540,230 +0.031902,230 +0.031859,230 +0.031949,230 +0.032026,230 +0.033004,230 +0.033935,230 +0.032172,230 +0.030865,230 +0.034507,230 +0.031688,230 +0.030815,230 +0.031229,230 +0.032014,230 +0.031126,230 +0.032550,232 +0.031897,232 +0.031908,232 +0.035073,232 +0.038418,232 +0.041864,232 +0.035232,232 +0.033638,232 +0.037859,232 +0.036304,232 +0.041679,232 +0.037868,232 +0.035952,232 +0.034724,232 +0.035198,232 +0.037757,232 +0.048921,232 +0.045694,232 +0.034858,232 +0.034677,232 +0.037713,232 +0.035391,232 +0.034319,232 +0.035481,232 +0.031987,232 +0.032051,232 +0.036022,232 +0.032238,232 +0.032866,232 +0.036448,232 +0.037238,232 +0.036668,232 +0.034088,232 +0.036922,232 +0.035981,232 +0.035254,232 +0.040008,232 +0.036387,232 +0.036067,232 +0.035025,232 +0.040029,232 +0.035266,232 +0.035036,232 +0.033987,232 +0.033387,232 +0.033578,232 +0.035668,232 +0.033234,232 +0.032961,232 +0.044879,232 +0.034288,232 +0.036545,232 +0.037218,232 +0.060757,232 +0.052725,232 +0.059088,232 +0.046550,232 +0.035530,232 +0.037320,232 +0.035810,232 +0.037426,232 +0.038875,232 +0.039483,232 +0.036936,232 +0.039523,232 +0.035185,232 +0.036760,232 +0.039975,232 +0.033352,232 +0.034196,232 +0.038098,232 +0.035772,232 +0.034154,232 +0.046065,232 +0.036488,232 +0.036674,232 +0.032738,232 +0.040295,232 +0.034094,232 +0.032441,232 +0.034736,232 +0.039548,232 +0.043287,232 +0.035976,232 +0.034000,232 +0.039252,232 +0.036005,232 +0.035834,232 +0.038083,232 +0.042782,232 +0.034514,232 +0.036371,232 +0.037417,232 +0.036355,232 +0.035273,232 +0.034276,232 +0.034102,232 +0.034029,232 +0.032980,232 +0.033573,232 +0.038926,234 +0.040618,234 +0.040820,234 +0.037968,234 +0.038272,234 +0.042271,234 +0.049123,234 +0.034518,234 +0.038881,234 +0.036649,234 +0.034415,234 +0.036345,234 +0.042409,234 +0.046327,234 +0.040199,234 +0.035942,234 +0.033875,234 +0.034114,234 +0.032950,234 +0.034286,234 +0.033797,234 +0.033200,234 +0.034005,234 +0.034584,234 +0.033112,234 +0.035728,234 +0.034922,234 +0.034962,234 +0.033979,234 +0.037586,234 +0.032872,234 +0.032678,234 +0.032931,234 +0.031773,234 +0.031569,234 +0.032165,234 +0.031644,234 +0.031421,234 +0.031764,234 +0.032788,234 +0.031787,234 +0.032033,234 +0.032698,234 +0.034101,234 +0.032329,234 +0.031548,234 +0.031429,234 +0.031976,234 +0.031711,234 +0.031761,234 +0.031984,234 +0.032145,234 +0.032423,234 +0.031948,234 +0.032846,234 +0.032110,234 +0.031985,234 +0.032124,234 +0.032101,234 +0.032569,234 +0.031868,234 +0.031619,234 +0.031396,234 +0.031854,234 +0.031510,234 +0.031874,234 +0.032488,234 +0.031960,234 +0.032351,234 +0.032967,234 +0.031426,234 +0.031421,234 +0.032175,234 +0.032020,234 +0.031694,234 +0.031361,234 +0.032057,234 +0.031503,234 +0.031530,234 +0.031835,234 +0.031568,234 +0.032580,234 +0.033096,234 +0.031693,234 +0.031557,234 +0.031821,234 +0.031663,234 +0.031552,234 +0.031997,234 +0.031551,234 +0.032328,234 +0.038241,234 +0.033073,234 +0.034025,234 +0.041936,234 +0.034898,234 +0.034670,234 +0.033454,234 +0.032831,234 +0.032554,234 +0.034014,236 +0.042267,236 +0.033598,236 +0.037150,236 +0.037716,236 +0.042123,236 +0.035850,236 +0.033674,236 +0.034933,236 +0.046021,236 +0.036961,236 +0.034046,236 +0.034640,236 +0.038851,236 +0.038601,236 +0.037612,236 +0.038283,236 +0.050662,236 +0.042437,236 +0.035757,236 +0.042565,236 +0.042066,236 +0.036041,236 +0.045430,236 +0.046189,236 +0.035335,236 +0.035933,236 +0.037539,236 +0.035753,236 +0.038120,236 +0.038759,236 +0.035861,236 +0.037570,236 +0.037263,236 +0.037237,236 +0.034930,236 +0.036549,236 +0.038395,236 +0.035150,236 +0.034880,236 +0.056546,236 +0.065572,236 +0.064669,236 +0.043473,236 +0.038197,236 +0.036195,236 +0.037004,236 +0.037704,236 +0.039867,236 +0.034735,236 +0.035096,236 +0.036566,236 +0.036038,236 +0.035488,236 +0.036002,236 +0.034937,236 +0.037259,236 +0.037143,236 +0.038535,236 +0.037414,236 +0.037420,236 +0.035069,236 +0.044932,236 +0.042434,236 +0.038816,236 +0.037132,236 +0.039159,236 +0.043116,236 +0.053508,236 +0.036529,236 +0.042496,236 +0.041511,236 +0.042414,236 +0.036079,236 +0.035603,236 +0.038234,236 +0.036367,236 +0.035904,236 +0.043415,236 +0.038683,236 +0.049272,236 +0.037985,236 +0.040943,236 +0.036566,236 +0.036520,236 +0.036361,236 +0.040316,236 +0.038872,236 +0.046996,236 +0.038305,236 +0.037079,236 +0.037051,236 +0.036403,236 +0.052353,236 +0.065731,236 +0.038483,236 +0.039731,236 +0.040667,236 +0.039422,236 +0.036323,236 +0.039984,238 +0.039154,238 +0.038000,238 +0.040795,238 +0.040740,238 +0.037750,238 +0.039052,238 +0.037504,238 +0.039023,238 +0.039670,238 +0.039332,238 +0.038281,238 +0.037550,238 +0.039648,238 +0.042368,238 +0.040971,238 +0.046427,238 +0.041052,238 +0.038373,238 +0.040200,238 +0.043690,238 +0.037832,238 +0.038493,238 +0.038403,238 +0.037142,238 +0.034706,238 +0.033901,238 +0.040440,238 +0.035300,238 +0.041074,238 +0.037595,238 +0.035440,238 +0.037362,238 +0.035476,238 +0.035796,238 +0.037895,238 +0.038695,238 +0.037677,238 +0.041286,238 +0.037201,238 +0.033769,238 +0.036268,238 +0.035800,238 +0.036867,238 +0.035524,238 +0.036707,238 +0.033865,238 +0.034250,238 +0.033525,238 +0.034638,238 +0.034202,238 +0.034417,238 +0.036239,238 +0.035166,238 +0.033821,238 +0.033657,238 +0.033593,238 +0.034345,238 +0.033903,238 +0.033662,238 +0.034174,238 +0.034770,238 +0.033359,238 +0.033261,238 +0.033956,238 +0.033516,238 +0.034037,238 +0.033512,238 +0.035305,238 +0.043315,238 +0.036623,238 +0.036925,238 +0.035807,238 +0.035129,238 +0.035297,238 +0.035685,238 +0.034809,238 +0.062845,238 +0.063883,238 +0.037364,238 +0.034707,238 +0.036881,238 +0.036212,238 +0.034828,238 +0.039247,238 +0.037213,238 +0.035516,238 +0.039169,238 +0.034531,238 +0.034429,238 +0.058864,238 +0.034223,238 +0.036844,238 +0.034868,238 +0.039806,238 +0.039903,238 +0.036842,238 +0.045442,238 +0.061311,238 +0.068015,238 +0.061888,240 +0.037788,240 +0.038708,240 +0.040065,240 +0.037985,240 +0.038610,240 +0.038260,240 +0.035348,240 +0.043080,240 +0.065015,240 +0.065295,240 +0.047075,240 +0.039273,240 +0.039100,240 +0.041221,240 +0.036884,240 +0.037328,240 +0.038838,240 +0.035996,240 +0.035691,240 +0.038985,240 +0.040828,240 +0.063071,240 +0.040215,240 +0.040135,240 +0.044682,240 +0.058434,240 +0.035911,240 +0.035433,240 +0.036398,240 +0.038814,240 +0.039300,240 +0.040816,240 +0.039196,240 +0.039069,240 +0.036121,240 +0.037252,240 +0.040057,240 +0.037747,240 +0.049648,240 +0.044225,240 +0.037219,240 +0.043359,240 +0.039678,240 +0.044457,240 +0.043541,240 +0.037499,240 +0.036685,240 +0.035518,240 +0.036836,240 +0.036822,240 +0.038609,240 +0.042677,240 +0.042368,240 +0.041357,240 +0.036577,240 +0.037395,240 +0.044514,240 +0.041369,240 +0.040472,240 +0.043148,240 +0.035156,240 +0.036309,240 +0.037413,240 +0.041998,240 +0.039106,240 +0.037416,240 +0.049919,240 +0.058601,240 +0.063010,240 +0.039447,240 +0.041990,240 +0.036290,240 +0.035762,240 +0.036162,240 +0.036034,240 +0.038136,240 +0.035628,240 +0.037692,240 +0.037752,240 +0.041216,240 +0.043586,240 +0.036112,240 +0.038512,240 +0.037177,240 +0.035050,240 +0.034959,240 +0.035005,240 +0.034586,240 +0.040625,240 +0.036259,240 +0.035390,240 +0.047543,240 +0.046283,240 +0.035670,240 +0.037121,240 +0.036174,240 +0.036019,240 +0.035681,240 +0.035161,240 +0.037298,242 +0.036379,242 +0.037063,242 +0.039403,242 +0.035977,242 +0.035764,242 +0.038621,242 +0.040435,242 +0.040444,242 +0.046900,242 +0.044130,242 +0.043335,242 +0.041598,242 +0.043373,242 +0.051978,242 +0.047757,242 +0.043976,242 +0.044748,242 +0.044415,242 +0.045642,242 +0.043595,242 +0.040760,242 +0.037238,242 +0.037202,242 +0.039095,242 +0.037753,242 +0.044098,242 +0.043148,242 +0.037186,242 +0.037201,242 +0.037794,242 +0.037017,242 +0.046732,242 +0.042538,242 +0.040082,242 +0.037564,242 +0.036788,242 +0.039120,242 +0.037258,242 +0.039025,242 +0.038419,242 +0.037153,242 +0.039335,242 +0.036763,242 +0.037089,242 +0.038095,242 +0.036415,242 +0.035928,242 +0.037595,242 +0.035858,242 +0.035469,242 +0.035986,242 +0.035906,242 +0.036469,242 +0.036442,242 +0.036042,242 +0.036749,242 +0.036919,242 +0.036366,242 +0.042866,242 +0.036113,242 +0.037040,242 +0.039419,242 +0.037763,242 +0.036457,242 +0.035895,242 +0.036282,242 +0.037048,242 +0.035670,242 +0.036967,242 +0.036571,242 +0.035999,242 +0.038157,242 +0.036348,242 +0.036195,242 +0.037875,242 +0.038158,242 +0.037128,242 +0.037198,242 +0.036315,242 +0.039334,242 +0.040416,242 +0.040462,242 +0.040766,242 +0.036621,242 +0.041799,242 +0.041783,242 +0.041681,242 +0.039947,242 +0.045828,242 +0.051787,242 +0.055497,242 +0.062481,242 +0.054816,242 +0.051234,242 +0.053183,242 +0.049677,242 +0.043943,242 +0.049858,242 +0.048604,242 +0.042604,244 +0.037067,244 +0.037008,244 +0.038071,244 +0.037895,244 +0.037857,244 +0.039293,244 +0.038633,244 +0.038398,244 +0.037568,244 +0.043805,244 +0.037950,244 +0.037571,244 +0.038194,244 +0.040907,244 +0.049489,244 +0.045770,244 +0.041992,244 +0.049068,244 +0.042707,244 +0.038987,244 +0.040554,244 +0.045714,244 +0.046163,244 +0.045404,244 +0.039588,244 +0.038019,244 +0.039299,244 +0.044092,244 +0.039754,244 +0.037165,244 +0.037098,244 +0.039174,244 +0.043341,244 +0.038992,244 +0.037748,244 +0.047128,244 +0.046255,244 +0.042033,244 +0.043816,244 +0.040439,244 +0.046624,244 +0.047540,244 +0.054191,244 +0.051626,244 +0.045808,244 +0.042352,244 +0.045372,244 +0.038918,244 +0.038240,244 +0.038005,244 +0.037630,244 +0.042605,244 +0.039113,244 +0.038081,244 +0.040873,244 +0.039740,244 +0.039959,244 +0.043360,244 +0.041199,244 +0.039120,244 +0.037091,244 +0.042271,244 +0.042701,244 +0.045315,244 +0.049741,244 +0.039499,244 +0.039563,244 +0.057227,244 +0.044174,244 +0.044178,244 +0.040710,244 +0.040150,244 +0.041164,244 +0.039595,244 +0.038822,244 +0.037958,244 +0.045212,244 +0.041920,244 +0.041130,244 +0.042547,244 +0.046054,244 +0.041133,244 +0.037234,244 +0.038638,244 +0.042100,244 +0.040171,244 +0.041663,244 +0.040491,244 +0.043518,244 +0.044038,244 +0.038680,244 +0.042164,244 +0.061726,244 +0.074289,244 +0.042699,244 +0.042803,244 +0.049122,244 +0.070119,244 +0.049622,244 +0.038539,246 +0.038196,246 +0.039307,246 +0.037428,246 +0.038324,246 +0.052023,246 +0.039487,246 +0.037586,246 +0.039020,246 +0.039549,246 +0.037492,246 +0.040484,246 +0.039250,246 +0.046656,246 +0.038669,246 +0.039248,246 +0.040040,246 +0.037132,246 +0.038674,246 +0.038312,246 +0.037191,246 +0.039565,246 +0.060067,246 +0.053942,246 +0.044020,246 +0.055706,246 +0.040239,246 +0.041632,246 +0.046325,246 +0.046631,246 +0.050694,246 +0.042951,246 +0.042646,246 +0.042530,246 +0.048909,246 +0.040221,246 +0.044465,246 +0.048841,246 +0.049324,246 +0.043825,246 +0.042679,246 +0.042340,246 +0.042111,246 +0.045769,246 +0.054803,246 +0.048428,246 +0.043964,246 +0.052360,246 +0.041956,246 +0.042329,246 +0.043834,246 +0.047139,246 +0.060399,246 +0.052413,246 +0.042464,246 +0.042927,246 +0.049934,246 +0.041210,246 +0.043826,246 +0.045054,246 +0.048279,246 +0.041517,246 +0.039144,246 +0.053363,246 +0.039289,246 +0.040568,246 +0.039130,246 +0.041380,246 +0.039996,246 +0.038805,246 +0.039796,246 +0.037353,246 +0.048057,246 +0.042571,246 +0.041057,246 +0.042104,246 +0.043330,246 +0.049639,246 +0.041997,246 +0.040691,246 +0.042721,246 +0.048252,246 +0.039384,246 +0.038983,246 +0.040735,246 +0.039003,246 +0.038468,246 +0.043975,246 +0.039244,246 +0.039227,246 +0.038976,246 +0.038386,246 +0.042636,246 +0.038402,246 +0.038908,246 +0.038447,246 +0.038969,246 +0.043644,246 +0.038643,246 +0.039654,246 +0.040417,248 +0.039043,248 +0.044185,248 +0.040981,248 +0.041167,248 +0.039010,248 +0.046503,248 +0.039729,248 +0.038554,248 +0.044928,248 +0.038168,248 +0.041322,248 +0.041021,248 +0.037554,248 +0.045301,248 +0.039310,248 +0.044383,248 +0.038072,248 +0.037636,248 +0.045089,248 +0.037994,248 +0.045009,248 +0.037771,248 +0.037889,248 +0.044825,248 +0.038956,248 +0.046335,248 +0.038490,248 +0.039092,248 +0.044719,248 +0.038244,248 +0.038259,248 +0.040093,248 +0.059074,248 +0.069364,248 +0.072384,248 +0.070536,248 +0.070802,248 +0.043605,248 +0.043621,248 +0.048433,248 +0.050848,248 +0.045514,248 +0.043148,248 +0.051421,248 +0.042470,248 +0.041860,248 +0.044064,248 +0.042480,248 +0.039761,248 +0.042519,248 +0.046595,248 +0.043080,248 +0.041553,248 +0.040925,248 +0.039039,248 +0.041334,248 +0.041843,248 +0.043456,248 +0.052848,248 +0.054206,248 +0.043880,248 +0.039692,248 +0.049379,248 +0.044408,248 +0.044133,248 +0.042658,248 +0.040781,248 +0.039622,248 +0.040741,248 +0.040740,248 +0.040613,248 +0.042183,248 +0.047676,248 +0.045665,248 +0.040499,248 +0.039285,248 +0.040557,248 +0.040458,248 +0.039474,248 +0.041121,248 +0.041969,248 +0.048307,248 +0.043854,248 +0.046862,248 +0.039862,248 +0.044932,248 +0.040158,248 +0.044907,248 +0.039039,248 +0.038666,248 +0.040718,248 +0.039401,248 +0.041912,248 +0.039699,248 +0.038408,248 +0.039801,248 +0.037801,248 +0.038018,248 +0.041077,248 +0.041118,250 +0.041625,250 +0.042281,250 +0.041250,250 +0.047224,250 +0.052398,250 +0.042484,250 +0.041450,250 +0.044243,250 +0.043093,250 +0.043305,250 +0.044385,250 +0.040806,250 +0.042173,250 +0.043244,250 +0.043859,250 +0.041508,250 +0.040480,250 +0.041561,250 +0.052677,250 +0.049975,250 +0.043095,250 +0.042289,250 +0.040271,250 +0.042032,250 +0.041356,250 +0.040589,250 +0.042898,250 +0.040365,250 +0.042170,250 +0.041341,250 +0.047620,250 +0.040095,250 +0.042915,250 +0.042191,250 +0.040765,250 +0.041442,250 +0.040396,250 +0.038723,250 +0.039274,250 +0.038511,250 +0.039335,250 +0.039447,250 +0.038701,250 +0.041427,250 +0.039387,250 +0.041807,250 +0.039079,250 +0.038644,250 +0.039729,250 +0.038817,250 +0.039518,250 +0.039032,250 +0.038899,250 +0.041545,250 +0.040623,250 +0.038601,250 +0.039554,250 +0.038782,250 +0.038914,250 +0.038213,250 +0.038458,250 +0.038830,250 +0.038276,250 +0.038921,250 +0.038286,250 +0.038049,250 +0.039573,250 +0.038401,250 +0.038713,250 +0.038589,250 +0.038117,250 +0.038831,250 +0.038402,250 +0.038166,250 +0.038875,250 +0.038836,250 +0.039089,250 +0.038327,250 +0.038419,250 +0.039411,250 +0.042661,250 +0.041217,250 +0.039954,250 +0.040938,250 +0.040428,250 +0.040414,250 +0.046576,250 +0.040224,250 +0.041112,250 +0.045884,250 +0.039604,250 +0.040516,250 +0.039564,250 +0.040219,250 +0.040064,250 +0.039664,250 +0.047404,250 +0.040092,250 +0.047241,250 +0.041014,252 +0.041330,252 +0.044109,252 +0.041699,252 +0.041691,252 +0.043507,252 +0.049178,252 +0.039971,252 +0.039065,252 +0.047117,252 +0.039674,252 +0.048511,252 +0.040083,252 +0.040037,252 +0.039856,252 +0.040304,252 +0.043659,252 +0.040051,252 +0.039996,252 +0.039877,252 +0.041357,252 +0.041120,252 +0.040048,252 +0.040099,252 +0.039636,252 +0.039485,252 +0.040500,252 +0.039753,252 +0.040429,252 +0.039844,252 +0.039803,252 +0.040322,252 +0.041272,252 +0.040620,252 +0.039722,252 +0.039304,252 +0.040193,252 +0.039097,252 +0.039661,252 +0.039098,252 +0.038839,252 +0.040025,252 +0.039618,252 +0.040018,252 +0.039926,252 +0.039517,252 +0.040126,252 +0.040258,252 +0.040113,252 +0.040086,252 +0.039453,252 +0.041034,252 +0.039821,252 +0.040005,252 +0.039831,252 +0.039674,252 +0.040629,252 +0.041473,252 +0.039830,252 +0.040176,252 +0.039588,252 +0.040798,252 +0.039369,252 +0.039816,252 +0.040228,252 +0.039705,252 +0.040574,252 +0.039849,252 +0.043661,252 +0.039510,252 +0.039278,252 +0.040141,252 +0.039366,252 +0.039836,252 +0.039810,252 +0.039245,252 +0.040290,252 +0.039499,252 +0.039695,252 +0.040437,252 +0.040627,252 +0.040927,252 +0.041921,252 +0.040642,252 +0.039550,252 +0.039489,252 +0.040235,252 +0.039898,252 +0.039762,252 +0.040119,252 +0.040233,252 +0.040398,252 +0.039181,252 +0.043033,252 +0.044545,252 +0.044985,252 +0.047034,252 +0.044280,252 +0.054477,252 +0.050319,252 +0.057066,254 +0.045915,254 +0.053807,254 +0.045821,254 +0.046224,254 +0.053504,254 +0.046008,254 +0.042736,254 +0.042936,254 +0.042031,254 +0.049899,254 +0.045839,254 +0.043794,254 +0.045294,254 +0.042477,254 +0.042991,254 +0.042728,254 +0.050819,254 +0.042482,254 +0.048271,254 +0.040985,254 +0.040710,254 +0.047932,254 +0.040411,254 +0.048790,254 +0.040995,254 +0.048399,254 +0.041008,254 +0.046948,254 +0.043205,254 +0.041398,254 +0.049819,254 +0.064929,254 +0.056505,254 +0.043840,254 +0.045254,254 +0.046367,254 +0.048988,254 +0.048867,254 +0.047641,254 +0.046717,254 +0.041652,254 +0.040698,254 +0.041314,254 +0.041291,254 +0.041492,254 +0.041668,254 +0.041032,254 +0.043226,254 +0.040972,254 +0.041882,254 +0.042040,254 +0.041288,254 +0.043481,254 +0.041075,254 +0.042863,254 +0.042624,254 +0.041805,254 +0.045990,254 +0.042427,254 +0.047742,254 +0.042355,254 +0.045689,254 +0.046819,254 +0.047558,254 +0.045499,254 +0.044920,254 +0.042057,254 +0.041470,254 +0.042317,254 +0.041304,254 +0.042961,254 +0.041028,254 +0.042244,254 +0.041813,254 +0.043338,254 +0.043398,254 +0.041723,254 +0.042069,254 +0.042506,254 +0.040893,254 +0.041919,254 +0.041103,254 +0.041800,254 +0.041996,254 +0.041740,254 +0.042997,254 +0.040920,254 +0.041795,254 +0.041676,254 +0.041098,254 +0.041497,254 +0.041171,254 +0.042121,254 +0.041001,254 +0.041654,254 +0.045172,254 +0.040708,254 +0.041422,254 +0.040343,254 +0.046370,256 +0.045655,256 +0.048878,256 +0.045398,256 +0.045694,256 +0.046966,256 +0.045426,256 +0.045866,256 +0.045093,256 +0.046127,256 +0.045129,256 +0.046048,256 +0.045077,256 +0.048681,256 +0.045522,256 +0.052923,256 +0.048435,256 +0.046260,256 +0.045517,256 +0.046115,256 +0.046228,256 +0.045122,256 +0.046320,256 +0.046687,256 +0.046604,256 +0.045214,256 +0.046405,256 +0.045484,256 +0.046130,256 +0.045156,256 +0.046180,256 +0.045839,256 +0.045490,256 +0.046040,256 +0.045252,256 +0.046244,256 +0.045412,256 +0.046311,256 +0.045113,256 +0.049488,256 +0.045643,256 +0.046900,256 +0.046661,256 +0.045409,256 +0.046062,256 +0.045338,256 +0.045944,256 +0.045376,256 +0.046158,256 +0.045406,256 +0.046151,256 +0.045319,256 +0.045680,256 +0.045820,256 +0.045328,256 +0.045860,256 +0.045192,256 +0.046020,256 +0.045257,256 +0.046302,256 +0.045438,256 +0.058704,256 +0.047125,256 +0.050324,256 +0.045177,256 +0.046064,256 +0.045252,256 +0.045498,256 +0.045675,256 +0.045127,256 +0.046056,256 +0.045348,256 +0.046808,256 +0.045555,256 +0.045877,256 +0.045550,256 +0.046480,256 +0.045690,256 +0.045546,256 +0.045840,256 +0.045534,256 +0.052565,256 +0.045433,256 +0.046270,256 +0.045094,256 +0.045598,256 +0.045110,256 +0.045658,256 +0.045319,256 +0.045527,256 +0.045396,256 +0.045103,256 +0.045891,256 +0.045382,256 +0.046379,256 +0.045006,256 +0.045845,256 +0.045230,256 +0.045804,256 +0.045221,256 +0.043128,258 +0.043097,258 +0.042982,258 +0.043606,258 +0.042851,258 +0.044028,258 +0.042502,258 +0.043378,258 +0.043095,258 +0.042678,258 +0.043282,258 +0.042649,258 +0.043546,258 +0.042667,258 +0.042888,258 +0.043258,258 +0.042892,258 +0.043451,258 +0.042961,258 +0.043597,258 +0.042769,258 +0.043045,258 +0.043404,258 +0.042599,258 +0.044687,258 +0.042961,258 +0.046317,258 +0.042790,258 +0.043971,258 +0.043444,258 +0.042786,258 +0.044754,258 +0.042692,258 +0.044956,258 +0.042697,258 +0.045201,258 +0.043495,258 +0.043298,258 +0.047522,258 +0.047937,258 +0.047038,258 +0.042625,258 +0.045165,258 +0.042676,258 +0.045141,258 +0.043566,258 +0.046159,258 +0.049445,258 +0.051943,258 +0.048570,258 +0.050922,258 +0.077064,258 +0.054108,258 +0.075734,258 +0.049988,258 +0.055326,258 +0.054183,258 +0.052520,258 +0.050749,258 +0.049838,258 +0.050774,258 +0.048713,258 +0.046663,258 +0.051461,258 +0.050249,258 +0.050005,258 +0.056744,258 +0.050853,258 +0.048940,258 +0.049486,258 +0.049413,258 +0.048170,258 +0.043561,258 +0.043528,258 +0.046977,258 +0.047641,258 +0.045539,258 +0.046903,258 +0.049043,258 +0.051012,258 +0.050541,258 +0.051858,258 +0.050450,258 +0.043314,258 +0.045638,258 +0.051711,258 +0.048072,258 +0.049489,258 +0.049104,258 +0.046936,258 +0.045119,258 +0.044753,258 +0.044203,258 +0.044305,258 +0.046464,258 +0.047061,258 +0.045169,258 +0.045110,258 +0.047880,258 +0.046840,258 +0.050664,260 +0.047291,260 +0.050600,260 +0.045224,260 +0.044480,260 +0.046777,260 +0.047652,260 +0.048565,260 +0.048601,260 +0.047835,260 +0.054151,260 +0.043818,260 +0.051183,260 +0.044731,260 +0.052353,260 +0.044937,260 +0.045090,260 +0.044738,260 +0.044539,260 +0.044189,260 +0.044068,260 +0.044165,260 +0.044131,260 +0.044706,260 +0.043923,260 +0.044485,260 +0.044039,260 +0.044352,260 +0.043917,260 +0.044257,260 +0.044521,260 +0.044229,260 +0.044743,260 +0.044407,260 +0.045388,260 +0.046720,260 +0.046403,260 +0.044388,260 +0.047111,260 +0.048361,260 +0.049818,260 +0.050172,260 +0.049104,260 +0.051559,260 +0.049807,260 +0.053649,260 +0.051756,260 +0.051425,260 +0.049529,260 +0.050346,260 +0.049346,260 +0.048547,260 +0.048216,260 +0.049552,260 +0.049367,260 +0.046374,260 +0.048519,260 +0.047924,260 +0.052343,260 +0.054300,260 +0.046514,260 +0.047875,260 +0.047481,260 +0.048849,260 +0.046673,260 +0.046245,260 +0.044684,260 +0.048325,260 +0.048049,260 +0.050329,260 +0.047061,260 +0.048243,260 +0.050512,260 +0.052190,260 +0.048308,260 +0.049647,260 +0.047268,260 +0.048502,260 +0.044475,260 +0.045791,260 +0.044151,260 +0.045445,260 +0.049574,260 +0.048230,260 +0.049027,260 +0.054493,260 +0.053909,260 +0.050246,260 +0.050147,260 +0.047211,260 +0.047581,260 +0.044123,260 +0.049601,260 +0.049980,260 +0.058061,260 +0.060819,260 +0.065946,260 +0.056675,260 +0.071167,260 +0.054238,260 +0.068391,262 +0.054044,262 +0.063854,262 +0.055572,262 +0.055039,262 +0.053090,262 +0.059861,262 +0.075603,262 +0.060356,262 +0.053670,262 +0.053980,262 +0.057140,262 +0.060211,262 +0.057499,262 +0.052951,262 +0.051282,262 +0.051657,262 +0.048438,262 +0.050060,262 +0.050079,262 +0.056088,262 +0.050441,262 +0.054786,262 +0.054944,262 +0.061158,262 +0.063592,262 +0.049756,262 +0.049989,262 +0.047498,262 +0.048026,262 +0.048181,262 +0.051458,262 +0.053053,262 +0.052789,262 +0.054084,262 +0.058270,262 +0.048062,262 +0.056312,262 +0.048521,262 +0.061651,262 +0.056249,262 +0.055687,262 +0.052286,262 +0.055558,262 +0.053551,262 +0.052897,262 +0.055583,262 +0.052118,262 +0.055595,262 +0.052332,262 +0.052024,262 +0.050782,262 +0.050073,262 +0.047154,262 +0.050550,262 +0.046832,262 +0.051025,262 +0.051053,262 +0.054520,262 +0.051870,262 +0.050002,262 +0.046938,262 +0.049972,262 +0.046934,262 +0.049755,262 +0.049122,262 +0.054521,262 +0.053756,262 +0.052077,262 +0.049274,262 +0.049231,262 +0.047972,262 +0.048660,262 +0.049238,262 +0.053002,262 +0.050456,262 +0.051622,262 +0.050363,262 +0.050675,262 +0.057281,262 +0.056032,262 +0.057048,262 +0.051817,262 +0.049484,262 +0.048476,262 +0.048065,262 +0.057571,262 +0.053732,262 +0.050675,262 +0.048509,262 +0.049214,262 +0.047276,262 +0.053407,262 +0.056771,262 +0.063283,262 +0.055163,262 +0.054900,262 +0.054134,262 +0.054612,262 +0.053658,262 +0.056285,264 +0.052211,264 +0.050864,264 +0.049217,264 +0.050019,264 +0.050148,264 +0.050645,264 +0.050201,264 +0.049772,264 +0.049309,264 +0.047067,264 +0.049003,264 +0.047070,264 +0.047391,264 +0.046381,264 +0.047166,264 +0.048396,264 +0.047551,264 +0.046881,264 +0.047159,264 +0.047023,264 +0.047268,264 +0.046398,264 +0.046534,264 +0.046563,264 +0.046307,264 +0.047036,264 +0.046239,264 +0.046973,264 +0.046144,264 +0.047086,264 +0.046353,264 +0.047711,264 +0.046246,264 +0.047048,264 +0.046189,264 +0.048609,264 +0.046199,264 +0.046267,264 +0.047407,264 +0.046089,264 +0.047786,264 +0.046747,264 +0.046999,264 +0.046237,264 +0.046987,264 +0.046402,264 +0.048332,264 +0.047240,264 +0.047567,264 +0.047951,264 +0.048270,264 +0.046454,264 +0.048006,264 +0.046843,264 +0.046841,264 +0.047899,264 +0.046480,264 +0.048260,264 +0.046080,264 +0.048094,264 +0.046167,264 +0.048128,264 +0.051792,264 +0.050430,264 +0.049137,264 +0.048897,264 +0.048034,264 +0.047286,264 +0.046188,264 +0.046870,264 +0.046286,264 +0.046630,264 +0.046781,264 +0.046262,264 +0.049960,264 +0.051342,264 +0.049265,264 +0.046303,264 +0.047130,264 +0.046226,264 +0.047704,264 +0.046374,264 +0.046911,264 +0.046082,264 +0.047771,264 +0.046475,264 +0.049328,264 +0.046435,264 +0.046622,264 +0.046266,264 +0.046550,264 +0.048710,264 +0.049719,264 +0.048527,264 +0.048581,264 +0.050060,264 +0.049059,264 +0.047369,264 +0.046636,264 +0.051725,266 +0.051314,266 +0.053410,266 +0.055430,266 +0.054625,266 +0.053391,266 +0.051943,266 +0.051466,266 +0.050024,266 +0.050617,266 +0.049899,266 +0.050297,266 +0.050409,266 +0.050722,266 +0.050274,266 +0.050730,266 +0.054686,266 +0.053915,266 +0.051247,266 +0.051398,266 +0.050113,266 +0.050549,266 +0.054031,266 +0.051283,266 +0.049816,266 +0.050561,266 +0.050195,266 +0.050661,266 +0.049893,266 +0.050586,266 +0.050073,266 +0.050903,266 +0.050330,266 +0.050627,266 +0.049771,266 +0.050922,266 +0.051920,266 +0.053144,266 +0.053605,266 +0.053413,266 +0.052102,266 +0.052975,266 +0.052856,266 +0.054334,266 +0.053598,266 +0.052921,266 +0.052794,266 +0.052685,266 +0.052804,266 +0.051450,266 +0.051631,266 +0.050223,266 +0.050900,266 +0.058479,266 +0.056501,266 +0.055018,266 +0.054116,266 +0.052089,266 +0.052082,266 +0.050745,266 +0.051203,266 +0.050035,266 +0.050797,266 +0.050062,266 +0.051296,266 +0.052480,266 +0.050936,266 +0.057681,266 +0.058276,266 +0.055856,266 +0.053685,266 +0.053777,266 +0.053911,266 +0.052941,266 +0.051741,266 +0.050494,266 +0.055502,266 +0.059932,266 +0.054018,266 +0.052270,266 +0.050435,266 +0.077285,266 +0.054011,266 +0.050785,266 +0.054649,266 +0.052420,266 +0.052819,266 +0.054659,266 +0.054409,266 +0.054260,266 +0.053533,266 +0.053754,266 +0.052733,266 +0.052416,266 +0.051040,266 +0.052033,266 +0.052009,266 +0.052529,266 +0.052487,266 +0.052117,266 +0.052258,268 +0.053511,268 +0.064842,268 +0.059756,268 +0.059964,268 +0.056388,268 +0.060106,268 +0.053551,268 +0.053074,268 +0.052905,268 +0.059101,268 +0.052455,268 +0.053274,268 +0.054025,268 +0.062822,268 +0.056024,268 +0.055818,268 +0.053038,268 +0.052923,268 +0.052858,268 +0.052785,268 +0.052192,268 +0.050187,268 +0.050496,268 +0.052006,268 +0.052511,268 +0.050390,268 +0.050760,268 +0.050301,268 +0.050783,268 +0.050071,268 +0.050577,268 +0.050098,268 +0.050878,268 +0.050046,268 +0.050771,268 +0.050167,268 +0.051274,268 +0.051997,268 +0.051412,268 +0.050190,268 +0.050241,268 +0.051350,268 +0.052092,268 +0.050312,268 +0.050354,268 +0.050081,268 +0.050403,268 +0.050523,268 +0.052009,268 +0.050330,268 +0.050170,268 +0.050514,268 +0.050418,268 +0.050490,268 +0.050214,268 +0.050398,268 +0.050309,268 +0.050384,268 +0.050148,268 +0.050418,268 +0.050590,268 +0.054156,268 +0.053955,268 +0.054889,268 +0.061761,268 +0.066656,268 +0.053520,268 +0.051113,268 +0.050269,268 +0.050530,268 +0.051181,268 +0.050927,268 +0.050556,268 +0.050343,268 +0.050250,268 +0.050333,268 +0.050440,268 +0.050843,268 +0.050310,268 +0.050533,268 +0.050466,268 +0.050440,268 +0.050083,268 +0.050723,268 +0.050275,268 +0.050505,268 +0.050215,268 +0.050782,268 +0.050139,268 +0.050525,268 +0.050406,268 +0.050330,268 +0.050213,268 +0.050382,268 +0.051692,268 +0.051835,268 +0.051324,268 +0.052542,268 +0.050617,268 +0.053960,270 +0.054397,270 +0.053719,270 +0.054373,270 +0.053741,270 +0.054123,270 +0.054112,270 +0.054448,270 +0.053833,270 +0.054301,270 +0.054003,270 +0.054069,270 +0.054124,270 +0.053797,270 +0.054256,270 +0.054018,270 +0.054296,270 +0.053865,270 +0.055765,270 +0.053850,270 +0.054618,270 +0.053893,270 +0.055188,270 +0.058444,270 +0.057940,270 +0.056482,270 +0.058558,270 +0.056220,270 +0.055996,270 +0.058367,270 +0.056417,270 +0.058341,270 +0.062754,270 +0.056253,270 +0.061714,270 +0.057928,270 +0.056349,270 +0.058408,270 +0.058224,270 +0.057903,270 +0.057873,270 +0.059330,270 +0.060017,270 +0.058020,270 +0.057583,270 +0.056950,270 +0.056838,270 +0.057761,270 +0.057302,270 +0.057690,270 +0.059148,270 +0.057890,270 +0.057142,270 +0.057580,270 +0.057715,270 +0.058074,270 +0.057601,270 +0.058007,270 +0.057046,270 +0.056160,270 +0.056786,270 +0.065296,270 +0.060188,270 +0.070213,270 +0.060761,270 +0.060641,270 +0.056608,270 +0.054322,270 +0.056702,270 +0.068307,270 +0.061488,270 +0.059540,270 +0.059322,270 +0.062787,270 +0.056925,270 +0.062799,270 +0.058443,270 +0.057363,270 +0.057748,270 +0.060106,270 +0.064343,270 +0.061347,270 +0.062039,270 +0.063974,270 +0.064517,270 +0.060165,270 +0.062633,270 +0.059059,270 +0.056930,270 +0.054548,270 +0.061077,270 +0.053595,270 +0.059761,270 +0.053469,270 +0.059381,270 +0.059112,270 +0.053274,270 +0.059535,270 +0.053350,270 +0.058998,270 +0.051533,272 +0.056155,272 +0.056381,272 +0.050555,272 +0.056389,272 +0.050467,272 +0.056186,272 +0.050446,272 +0.056900,272 +0.052880,272 +0.056857,272 +0.050859,272 +0.056792,272 +0.050541,272 +0.056909,272 +0.054983,272 +0.051940,272 +0.056142,272 +0.050491,272 +0.057792,272 +0.058770,272 +0.056321,272 +0.057960,272 +0.056229,272 +0.058982,272 +0.056232,272 +0.056269,272 +0.056030,272 +0.057696,272 +0.054746,272 +0.053061,272 +0.051260,272 +0.051097,272 +0.050458,272 +0.050925,272 +0.051690,272 +0.051156,272 +0.051179,272 +0.052154,272 +0.050605,272 +0.051061,272 +0.050549,272 +0.051130,272 +0.051958,272 +0.053018,272 +0.053542,272 +0.051333,272 +0.054512,272 +0.055631,272 +0.056081,272 +0.056137,272 +0.056946,272 +0.055434,272 +0.060452,272 +0.052961,272 +0.055519,272 +0.055727,272 +0.056935,272 +0.052991,272 +0.050753,272 +0.051385,272 +0.050604,272 +0.052218,272 +0.052902,272 +0.053580,272 +0.051193,272 +0.052471,272 +0.050534,272 +0.052734,272 +0.050638,272 +0.052118,272 +0.050569,272 +0.052254,272 +0.050403,272 +0.052877,272 +0.050546,272 +0.051199,272 +0.050424,272 +0.051033,272 +0.050499,272 +0.050719,272 +0.050657,272 +0.051270,272 +0.050571,272 +0.051184,272 +0.050471,272 +0.051083,272 +0.050534,272 +0.051226,272 +0.050497,272 +0.050930,272 +0.050515,272 +0.050652,272 +0.050458,272 +0.050849,272 +0.050960,272 +0.050717,272 +0.050660,272 +0.050604,272 +0.050627,272 +0.055355,274 +0.055286,274 +0.055058,274 +0.077759,274 +0.062612,274 +0.084260,274 +0.104903,274 +0.106103,274 +0.077543,274 +0.085944,274 +0.080646,274 +0.056136,274 +0.056251,274 +0.056378,274 +0.056039,274 +0.056316,274 +0.056571,274 +0.068323,274 +0.065931,274 +0.059785,274 +0.058998,274 +0.056701,274 +0.061016,274 +0.062724,274 +0.056139,274 +0.057446,274 +0.057002,274 +0.059934,274 +0.060444,274 +0.060331,274 +0.070187,274 +0.102343,274 +0.101983,274 +0.085944,274 +0.057725,274 +0.060507,274 +0.078247,274 +0.073117,274 +0.066163,274 +0.060576,274 +0.059118,274 +0.064332,274 +0.068698,274 +0.063827,274 +0.068858,274 +0.062736,274 +0.068263,274 +0.061657,274 +0.059037,274 +0.062543,274 +0.062379,274 +0.065076,274 +0.061394,274 +0.065859,274 +0.059628,274 +0.060438,274 +0.058751,274 +0.060736,274 +0.056983,274 +0.059483,274 +0.058811,274 +0.060062,274 +0.059005,274 +0.058105,274 +0.059569,274 +0.061596,274 +0.067420,274 +0.065639,274 +0.065058,274 +0.064804,274 +0.064150,274 +0.061249,274 +0.060533,274 +0.060707,274 +0.060454,274 +0.063287,274 +0.059066,274 +0.058902,274 +0.062817,274 +0.057138,274 +0.058739,274 +0.056870,274 +0.060131,274 +0.058255,274 +0.057846,274 +0.056016,274 +0.059232,274 +0.059195,274 +0.058514,274 +0.066063,274 +0.068293,274 +0.066232,274 +0.064580,274 +0.059091,274 +0.060501,274 +0.060111,274 +0.060989,274 +0.059421,274 +0.065569,274 +0.061068,274 +0.060733,276 +0.055370,276 +0.077650,276 +0.057427,276 +0.057217,276 +0.057550,276 +0.057177,276 +0.056801,276 +0.062281,276 +0.056746,276 +0.061197,276 +0.057997,276 +0.058909,276 +0.058194,276 +0.059997,276 +0.058988,276 +0.058429,276 +0.064624,276 +0.057617,276 +0.060444,276 +0.060571,276 +0.058261,276 +0.060075,276 +0.059849,276 +0.060039,276 +0.057928,276 +0.058232,276 +0.060680,276 +0.062127,276 +0.060752,276 +0.062138,276 +0.058386,276 +0.058208,276 +0.057690,276 +0.055231,276 +0.055463,276 +0.056137,276 +0.066303,276 +0.060803,276 +0.061295,276 +0.060621,276 +0.061494,276 +0.065527,276 +0.065753,276 +0.069152,276 +0.060415,276 +0.060932,276 +0.060823,276 +0.060634,276 +0.068160,276 +0.071643,276 +0.067290,276 +0.066832,276 +0.066297,276 +0.069288,276 +0.066156,276 +0.061526,276 +0.059984,276 +0.065361,276 +0.059491,276 +0.056447,276 +0.059148,276 +0.059728,276 +0.057638,276 +0.060436,276 +0.074956,276 +0.064729,276 +0.071866,276 +0.078464,276 +0.065329,276 +0.082083,276 +0.060430,276 +0.061510,276 +0.069063,276 +0.064846,276 +0.058104,276 +0.056249,276 +0.059217,276 +0.063967,276 +0.062880,276 +0.055427,276 +0.061798,276 +0.057072,276 +0.065297,276 +0.064682,276 +0.062539,276 +0.060433,276 +0.061693,276 +0.064777,276 +0.062460,276 +0.061834,276 +0.057039,276 +0.063286,276 +0.058734,276 +0.062493,276 +0.061756,276 +0.059587,276 +0.058489,276 +0.058649,276 +0.055728,276 +0.058655,278 +0.058376,278 +0.057495,278 +0.058710,278 +0.058263,278 +0.066848,278 +0.065266,278 +0.058434,278 +0.066578,278 +0.066915,278 +0.069207,278 +0.070718,278 +0.063471,278 +0.061312,278 +0.059197,278 +0.059363,278 +0.058063,278 +0.058907,278 +0.060127,278 +0.058821,278 +0.058679,278 +0.058371,278 +0.060246,278 +0.062742,278 +0.058916,278 +0.059371,278 +0.059822,278 +0.060244,278 +0.062157,278 +0.063462,278 +0.066566,278 +0.068093,278 +0.071604,278 +0.073728,278 +0.069347,278 +0.070758,278 +0.070580,278 +0.062849,278 +0.065264,278 +0.058941,278 +0.058012,278 +0.063789,278 +0.066193,278 +0.072972,278 +0.069772,278 +0.065957,278 +0.070013,278 +0.067595,278 +0.073879,278 +0.063638,278 +0.067512,278 +0.068782,278 +0.070986,278 +0.076221,278 +0.074177,278 +0.066303,278 +0.062857,278 +0.063683,278 +0.061570,278 +0.062001,278 +0.060927,278 +0.062514,278 +0.059205,278 +0.058478,278 +0.059849,278 +0.063694,278 +0.065171,278 +0.072492,278 +0.065300,278 +0.064288,278 +0.064443,278 +0.063192,278 +0.060911,278 +0.063925,278 +0.059304,278 +0.059943,278 +0.059610,278 +0.057801,278 +0.059888,278 +0.058579,278 +0.059326,278 +0.059327,278 +0.058302,278 +0.063137,278 +0.061572,278 +0.060818,278 +0.059413,278 +0.057830,278 +0.063835,278 +0.057556,278 +0.064423,278 +0.063405,278 +0.058073,278 +0.072706,278 +0.068393,278 +0.068173,278 +0.067488,278 +0.064341,278 +0.065489,278 +0.061618,278 +0.063219,280 +0.060395,280 +0.061169,280 +0.060930,280 +0.057626,280 +0.055814,280 +0.056872,280 +0.056238,280 +0.057810,280 +0.056633,280 +0.056554,280 +0.057295,280 +0.056093,280 +0.056544,280 +0.056032,280 +0.056596,280 +0.056284,280 +0.055857,280 +0.056353,280 +0.055744,280 +0.056309,280 +0.055758,280 +0.056570,280 +0.056137,280 +0.056888,280 +0.056344,280 +0.055935,280 +0.056404,280 +0.055796,280 +0.056614,280 +0.055893,280 +0.056381,280 +0.056788,280 +0.056024,280 +0.056255,280 +0.056147,280 +0.056318,280 +0.055886,280 +0.056246,280 +0.055850,280 +0.056286,280 +0.056400,280 +0.055959,280 +0.056493,280 +0.055887,280 +0.056421,280 +0.056425,280 +0.069027,280 +0.063965,280 +0.062629,280 +0.063214,280 +0.066614,280 +0.061499,280 +0.061985,280 +0.063162,280 +0.065707,280 +0.060343,280 +0.060719,280 +0.063382,280 +0.060085,280 +0.063920,280 +0.062268,280 +0.060334,280 +0.057546,280 +0.066008,280 +0.056917,280 +0.059449,280 +0.061266,280 +0.061639,280 +0.061490,280 +0.061053,280 +0.062394,280 +0.061806,280 +0.066203,280 +0.065063,280 +0.068803,280 +0.073897,280 +0.071415,280 +0.061651,280 +0.062140,280 +0.068908,280 +0.069307,280 +0.067386,280 +0.062752,280 +0.069230,280 +0.070114,280 +0.064809,280 +0.060479,280 +0.061138,280 +0.063538,280 +0.061519,280 +0.058772,280 +0.059980,280 +0.061173,280 +0.061562,280 +0.058449,280 +0.059663,280 +0.071151,280 +0.060882,280 +0.066724,280 +0.072016,282 +0.074860,282 +0.070270,282 +0.073070,282 +0.069344,282 +0.076691,282 +0.086220,282 +0.078314,282 +0.068736,282 +0.066885,282 +0.068434,282 +0.066834,282 +0.066249,282 +0.072824,282 +0.075319,282 +0.071495,282 +0.069390,282 +0.068081,282 +0.067893,282 +0.068946,282 +0.067668,282 +0.068085,282 +0.067531,282 +0.069401,282 +0.076482,282 +0.074109,282 +0.068777,282 +0.070797,282 +0.071662,282 +0.070121,282 +0.097231,282 +0.079167,282 +0.069282,282 +0.069333,282 +0.073691,282 +0.068289,282 +0.072362,282 +0.068569,282 +0.068555,282 +0.069764,282 +0.072091,282 +0.065155,282 +0.064922,282 +0.070280,282 +0.064525,282 +0.066633,282 +0.062893,282 +0.064499,282 +0.062042,282 +0.061602,282 +0.061429,282 +0.061333,282 +0.061341,282 +0.060931,282 +0.061759,282 +0.061270,282 +0.060762,282 +0.061671,282 +0.060706,282 +0.061936,282 +0.065297,282 +0.061463,282 +0.062186,282 +0.061000,282 +0.061329,282 +0.061405,282 +0.062654,282 +0.064562,282 +0.064346,282 +0.064517,282 +0.062018,282 +0.062551,282 +0.063137,282 +0.061378,282 +0.061309,282 +0.061441,282 +0.062240,282 +0.063585,282 +0.070333,282 +0.064389,282 +0.062171,282 +0.065352,282 +0.066117,282 +0.067361,282 +0.064329,282 +0.061419,282 +0.061788,282 +0.061899,282 +0.060952,282 +0.062098,282 +0.064113,282 +0.064734,282 +0.065608,282 +0.062708,282 +0.062502,282 +0.061444,282 +0.062500,282 +0.063233,282 +0.062965,282 +0.062939,282 +0.061046,284 +0.060496,284 +0.060836,284 +0.062635,284 +0.061098,284 +0.062422,284 +0.060454,284 +0.061306,284 +0.060970,284 +0.059322,284 +0.060996,284 +0.059282,284 +0.062343,284 +0.061150,284 +0.059339,284 +0.062270,284 +0.059404,284 +0.060982,284 +0.061201,284 +0.059487,284 +0.061295,284 +0.059402,284 +0.061040,284 +0.061154,284 +0.059433,284 +0.061046,284 +0.059347,284 +0.061015,284 +0.062313,284 +0.060296,284 +0.061069,284 +0.059390,284 +0.061376,284 +0.061045,284 +0.059254,284 +0.061072,284 +0.059390,284 +0.061039,284 +0.060863,284 +0.060137,284 +0.061132,284 +0.059248,284 +0.061549,284 +0.061096,284 +0.059492,284 +0.062208,284 +0.059378,284 +0.064014,284 +0.061461,284 +0.059358,284 +0.062296,284 +0.074642,284 +0.071049,284 +0.066325,284 +0.069245,284 +0.068743,284 +0.070516,284 +0.071255,284 +0.067085,284 +0.065974,284 +0.066825,284 +0.067573,284 +0.068968,284 +0.064459,284 +0.061483,284 +0.075049,284 +0.065255,284 +0.077691,284 +0.090725,284 +0.067188,284 +0.065421,284 +0.070782,284 +0.066749,284 +0.067901,284 +0.065804,284 +0.064306,284 +0.061525,284 +0.060358,284 +0.062015,284 +0.060604,284 +0.060064,284 +0.061275,284 +0.059862,284 +0.061431,284 +0.062032,284 +0.061327,284 +0.061746,284 +0.059494,284 +0.060965,284 +0.060872,284 +0.059400,284 +0.062127,284 +0.059301,284 +0.061337,284 +0.061756,284 +0.059648,284 +0.060987,284 +0.059261,284 +0.061118,284 +0.061140,284 +0.063425,286 +0.064737,286 +0.064355,286 +0.063657,286 +0.064667,286 +0.063042,286 +0.064707,286 +0.065789,286 +0.063100,286 +0.065326,286 +0.066364,286 +0.063675,286 +0.064873,286 +0.064375,286 +0.063434,286 +0.063620,286 +0.063581,286 +0.064280,286 +0.063903,286 +0.063200,286 +0.063643,286 +0.063740,286 +0.063307,286 +0.063884,286 +0.063368,286 +0.063508,286 +0.063826,286 +0.063174,286 +0.063968,286 +0.064779,286 +0.063249,286 +0.065129,286 +0.065503,286 +0.066801,286 +0.065673,286 +0.066431,286 +0.066196,286 +0.065085,286 +0.064430,286 +0.064809,286 +0.063816,286 +0.063359,286 +0.063642,286 +0.063762,286 +0.063233,286 +0.063836,286 +0.063836,286 +0.063249,286 +0.064058,286 +0.063400,286 +0.063894,286 +0.063750,286 +0.063127,286 +0.063740,286 +0.064056,286 +0.063366,286 +0.063874,286 +0.063578,286 +0.063819,286 +0.063598,286 +0.063287,286 +0.063787,286 +0.063828,286 +0.063347,286 +0.064371,286 +0.063440,286 +0.063083,286 +0.063631,286 +0.063373,286 +0.063355,286 +0.063701,286 +0.063124,286 +0.063970,286 +0.063441,286 +0.062995,286 +0.063621,286 +0.063674,286 +0.065323,286 +0.064494,286 +0.067087,286 +0.064575,286 +0.064647,286 +0.063564,286 +0.064806,286 +0.064180,286 +0.063215,286 +0.063833,286 +0.063644,286 +0.063111,286 +0.063867,286 +0.063236,286 +0.063614,286 +0.063930,286 +0.062981,286 +0.063888,286 +0.063725,286 +0.063463,286 +0.063839,286 +0.063619,286 +0.063223,286 +0.064376,288 +0.063707,288 +0.064364,288 +0.064462,288 +0.066459,288 +0.064684,288 +0.065017,288 +0.063947,288 +0.064447,288 +0.064137,288 +0.063646,288 +0.065175,288 +0.070360,288 +0.071598,288 +0.071383,288 +0.070829,288 +0.069477,288 +0.069394,288 +0.068970,288 +0.069672,288 +0.069716,288 +0.071996,288 +0.074610,288 +0.068118,288 +0.065774,288 +0.069773,288 +0.074340,288 +0.070091,288 +0.070158,288 +0.068244,288 +0.067423,288 +0.068650,288 +0.069801,288 +0.070965,288 +0.071539,288 +0.071692,288 +0.070481,288 +0.078654,288 +0.072991,288 +0.067273,288 +0.064580,288 +0.065642,288 +0.067566,288 +0.066009,288 +0.066068,288 +0.068610,288 +0.069114,288 +0.068622,288 +0.065788,288 +0.064485,288 +0.065000,288 +0.066887,288 +0.074228,288 +0.069965,288 +0.077213,288 +0.066733,288 +0.071594,288 +0.069941,288 +0.064325,288 +0.070085,288 +0.065749,288 +0.065430,288 +0.083415,288 +0.071016,288 +0.076565,288 +0.072772,288 +0.069500,288 +0.069351,288 +0.066924,288 +0.066275,288 +0.064787,288 +0.066885,288 +0.064586,288 +0.064665,288 +0.067937,288 +0.069406,288 +0.079028,288 +0.082235,288 +0.071772,288 +0.065477,288 +0.068255,288 +0.070726,288 +0.070777,288 +0.070487,288 +0.066012,288 +0.067938,288 +0.068077,288 +0.073226,288 +0.066543,288 +0.066800,288 +0.065631,288 +0.085718,288 +0.089092,288 +0.087413,288 +0.070510,288 +0.066891,288 +0.066570,288 +0.064278,288 +0.064291,288 +0.066164,288 +0.066856,290 +0.066542,290 +0.066700,290 +0.066331,290 +0.066329,290 +0.066563,290 +0.066186,290 +0.066713,290 +0.066740,290 +0.066146,290 +0.066181,290 +0.066832,290 +0.066045,290 +0.066206,290 +0.066781,290 +0.066178,290 +0.066023,290 +0.066379,290 +0.074327,290 +0.067359,290 +0.066890,290 +0.066038,290 +0.066210,290 +0.066857,290 +0.065996,290 +0.066408,290 +0.066721,290 +0.066083,290 +0.066572,290 +0.066601,290 +0.065704,290 +0.066854,290 +0.066663,290 +0.065723,290 +0.066815,290 +0.066464,290 +0.065716,290 +0.066601,290 +0.066705,290 +0.065860,290 +0.066663,290 +0.066405,290 +0.065973,290 +0.066908,290 +0.066657,290 +0.065943,290 +0.066938,290 +0.066389,290 +0.065999,290 +0.066745,290 +0.066303,290 +0.066258,290 +0.067397,290 +0.066411,290 +0.066299,290 +0.066642,290 +0.066156,290 +0.074817,290 +0.070316,290 +0.068684,290 +0.066628,290 +0.067040,290 +0.066562,290 +0.066173,290 +0.067013,290 +0.066810,290 +0.065973,290 +0.066960,290 +0.066530,290 +0.066101,290 +0.066809,290 +0.066522,290 +0.066021,290 +0.066746,290 +0.066434,290 +0.066097,290 +0.066708,290 +0.066651,290 +0.066335,290 +0.066961,290 +0.066217,290 +0.066568,290 +0.066737,290 +0.065997,290 +0.067041,290 +0.067766,290 +0.065829,290 +0.066719,290 +0.066944,290 +0.065817,290 +0.066878,290 +0.066380,290 +0.066074,290 +0.067010,290 +0.067114,290 +0.065857,290 +0.066773,290 +0.066490,290 +0.065858,290 +0.066554,290 +0.066309,292 +0.065868,292 +0.066050,292 +0.066186,292 +0.067014,292 +0.070358,292 +0.066037,292 +0.066376,292 +0.066464,292 +0.065910,292 +0.067182,292 +0.066370,292 +0.066138,292 +0.066665,292 +0.072453,292 +0.065768,292 +0.065263,292 +0.067144,292 +0.065889,292 +0.065232,292 +0.065898,292 +0.065375,292 +0.065452,292 +0.065864,292 +0.065250,292 +0.065853,292 +0.065723,292 +0.064962,292 +0.066235,292 +0.065645,292 +0.065551,292 +0.066315,292 +0.066393,292 +0.066390,292 +0.066038,292 +0.065460,292 +0.066657,292 +0.066426,292 +0.065633,292 +0.067215,292 +0.066436,292 +0.065902,292 +0.065923,292 +0.066517,292 +0.065837,292 +0.065519,292 +0.066377,292 +0.065731,292 +0.065825,292 +0.066306,292 +0.065418,292 +0.065969,292 +0.066479,292 +0.065072,292 +0.066340,292 +0.065952,292 +0.065452,292 +0.066103,292 +0.066080,292 +0.065526,292 +0.066222,292 +0.065902,292 +0.065540,292 +0.066321,292 +0.065830,292 +0.065732,292 +0.067067,292 +0.066852,292 +0.065767,292 +0.066326,292 +0.066414,292 +0.065622,292 +0.066265,292 +0.066090,292 +0.065993,292 +0.066376,292 +0.065403,292 +0.066079,292 +0.066214,292 +0.065233,292 +0.066158,292 +0.066097,292 +0.065168,292 +0.066237,292 +0.065953,292 +0.065484,292 +0.066720,292 +0.072731,292 +0.076935,292 +0.080018,292 +0.082379,292 +0.080917,292 +0.074605,292 +0.068439,292 +0.069450,292 +0.068890,292 +0.068080,292 +0.068419,292 +0.068819,292 +0.069171,292 +0.076822,294 +0.076086,294 +0.078940,294 +0.074760,294 +0.074426,294 +0.073137,294 +0.072081,294 +0.070823,294 +0.072792,294 +0.072130,294 +0.072409,294 +0.072391,294 +0.072992,294 +0.079275,294 +0.086944,294 +0.083957,294 +0.076999,294 +0.076847,294 +0.078900,294 +0.071525,294 +0.071786,294 +0.072034,294 +0.072026,294 +0.074384,294 +0.074108,294 +0.071156,294 +0.070194,294 +0.070710,294 +0.070922,294 +0.070716,294 +0.070229,294 +0.070987,294 +0.070825,294 +0.069836,294 +0.071088,294 +0.070921,294 +0.070434,294 +0.070411,294 +0.071038,294 +0.070787,294 +0.070330,294 +0.071036,294 +0.070979,294 +0.070156,294 +0.070996,294 +0.070858,294 +0.070398,294 +0.070803,294 +0.071150,294 +0.070646,294 +0.071168,294 +0.071539,294 +0.070709,294 +0.069758,294 +0.071038,294 +0.071165,294 +0.070349,294 +0.073770,294 +0.070953,294 +0.072926,294 +0.069917,294 +0.071281,294 +0.071955,294 +0.071535,294 +0.077098,294 +0.074606,294 +0.074303,294 +0.071320,294 +0.070532,294 +0.070896,294 +0.070341,294 +0.069827,294 +0.070714,294 +0.070326,294 +0.072954,294 +0.074486,294 +0.073188,294 +0.070619,294 +0.070657,294 +0.070815,294 +0.071126,294 +0.074661,294 +0.073268,294 +0.076067,294 +0.083637,294 +0.074073,294 +0.082686,294 +0.077119,294 +0.075453,294 +0.076002,294 +0.071392,294 +0.072592,294 +0.074008,294 +0.069877,294 +0.071344,294 +0.070870,294 +0.071150,294 +0.071804,294 +0.071079,294 +0.071553,294 +0.066974,296 +0.068582,296 +0.068594,296 +0.067236,296 +0.068186,296 +0.068300,296 +0.066251,296 +0.068456,296 +0.068182,296 +0.067526,296 +0.068491,296 +0.069412,296 +0.066596,296 +0.068758,296 +0.068368,296 +0.066651,296 +0.068386,296 +0.068434,296 +0.066997,296 +0.068163,296 +0.068334,296 +0.067285,296 +0.071464,296 +0.072527,296 +0.069374,296 +0.066762,296 +0.069384,296 +0.068125,296 +0.066689,296 +0.072023,296 +0.074263,296 +0.066657,296 +0.068572,296 +0.068314,296 +0.066261,296 +0.068553,296 +0.067026,296 +0.066611,296 +0.067615,296 +0.067246,296 +0.066506,296 +0.067668,296 +0.067284,296 +0.066467,296 +0.067471,296 +0.067280,296 +0.067456,296 +0.068320,296 +0.068635,296 +0.066139,296 +0.068106,296 +0.068149,296 +0.066075,296 +0.068784,296 +0.068268,296 +0.066233,296 +0.069456,296 +0.067947,296 +0.066422,296 +0.067812,296 +0.068153,296 +0.066867,296 +0.067462,296 +0.068132,296 +0.067164,296 +0.067326,296 +0.068220,296 +0.067258,296 +0.067231,296 +0.068053,296 +0.068183,296 +0.067775,296 +0.068161,296 +0.067675,296 +0.067005,296 +0.068616,296 +0.067729,296 +0.066907,296 +0.068243,296 +0.067927,296 +0.066670,296 +0.068298,296 +0.067857,296 +0.067380,296 +0.068326,296 +0.068842,296 +0.067039,296 +0.068302,296 +0.068213,296 +0.066634,296 +0.068386,296 +0.067673,296 +0.066894,296 +0.068327,296 +0.066926,296 +0.066740,296 +0.067472,296 +0.066996,296 +0.066620,296 +0.067563,296 +0.074082,298 +0.072820,298 +0.073513,298 +0.073754,298 +0.074084,298 +0.073198,298 +0.073715,298 +0.073480,298 +0.073005,298 +0.073204,298 +0.073714,298 +0.073746,298 +0.072662,298 +0.073693,298 +0.073421,298 +0.073221,298 +0.072732,298 +0.073666,298 +0.073410,298 +0.072768,298 +0.073171,298 +0.073607,298 +0.072946,298 +0.072686,298 +0.073423,298 +0.073634,298 +0.074629,298 +0.072765,298 +0.073651,298 +0.073395,298 +0.072872,298 +0.073192,298 +0.073592,298 +0.073454,298 +0.072587,298 +0.073284,298 +0.073709,298 +0.073488,298 +0.072771,298 +0.073605,298 +0.073534,298 +0.073027,298 +0.073515,298 +0.073689,298 +0.073708,298 +0.072601,298 +0.073632,298 +0.073809,298 +0.073004,298 +0.073058,298 +0.073719,298 +0.073876,298 +0.073224,298 +0.073554,298 +0.073837,298 +0.073483,298 +0.073045,298 +0.073656,298 +0.073569,298 +0.073026,298 +0.075732,298 +0.079497,298 +0.077026,298 +0.076725,298 +0.075296,298 +0.074288,298 +0.075321,298 +0.077556,298 +0.077182,298 +0.080477,298 +0.079437,298 +0.079661,298 +0.079812,298 +0.075677,298 +0.074235,298 +0.073422,298 +0.073126,298 +0.072768,298 +0.073769,298 +0.074062,298 +0.073833,298 +0.074786,298 +0.074297,298 +0.073377,298 +0.072905,298 +0.076307,298 +0.078593,298 +0.074184,298 +0.073057,298 +0.073524,298 +0.073492,298 +0.073582,298 +0.072937,298 +0.073603,298 +0.073564,298 +0.072902,298 +0.073522,298 +0.079887,298 +0.083117,298 +0.075722,298 diff --git a/buch/papers/multiplikation/code/meas/test/blas.txt b/buch/papers/multiplikation/code/meas/test/blas.txt new file mode 100644 index 0000000..7b0a9d1 --- /dev/null +++ b/buch/papers/multiplikation/code/meas/test/blas.txt @@ -0,0 +1,14900 @@ +0.000001,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000000,6 +0.000001,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000001,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000010,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000000,8 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000010,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000010,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000010,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000010,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000001,10 +0.000002,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000001,12 +0.000003,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000013,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000002,14 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000003,16 +0.000005,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000006,18 +0.000007,18 +0.000007,18 +0.000007,18 +0.000006,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000013,18 +0.000004,18 +0.000013,18 +0.000004,18 +0.000013,18 +0.000004,18 +0.000013,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000013,18 +0.000004,18 +0.000013,18 +0.000004,18 +0.000014,18 +0.000004,18 +0.000014,18 +0.000004,18 +0.000014,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000004,18 +0.000007,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000005,20 +0.000008,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000011,22 +0.000012,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000016,22 +0.000007,22 +0.000016,22 +0.000007,22 +0.000016,22 +0.000016,22 +0.000016,22 +0.000007,22 +0.000016,22 +0.000016,22 +0.000016,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000016,22 +0.000007,22 +0.000016,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000006,22 +0.000010,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000010,24 +0.000018,24 +0.000018,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000008,24 +0.000013,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000020,26 +0.000011,26 +0.000020,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000020,26 +0.000020,26 +0.000021,26 +0.000031,26 +0.000011,26 +0.000019,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000020,26 +0.000020,26 +0.000020,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000010,26 +0.000015,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000022,28 +0.000022,28 +0.000021,28 +0.000022,28 +0.000021,28 +0.000023,28 +0.000022,28 +0.000023,28 +0.000022,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000024,28 +0.000024,28 +0.000025,28 +0.000035,28 +0.000048,28 +0.000055,28 +0.000045,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000026,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000023,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000020,28 +0.000025,28 +0.000025,28 +0.000025,28 +0.000024,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000013,28 +0.000025,28 +0.000032,30 +0.000031,30 +0.000030,30 +0.000031,30 +0.000030,30 +0.000030,30 +0.000073,30 +0.000030,30 +0.000030,30 +0.000031,30 +0.000017,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000019,30 +0.000030,30 +0.000030,30 +0.000030,30 +0.000030,30 +0.000030,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000026,30 +0.000029,30 +0.000040,30 +0.000041,30 +0.000041,30 +0.000040,30 +0.000038,30 +0.000042,30 +0.000023,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000027,30 +0.000030,30 +0.000030,30 +0.000040,30 +0.000040,30 +0.000031,30 +0.000028,30 +0.000028,30 +0.000024,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000015,30 +0.000021,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000021,32 +0.000025,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000028,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000029,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000028,32 +0.000039,32 +0.000043,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000022,32 +0.000028,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000040,32 +0.000038,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000019,32 +0.000043,32 +0.000047,32 +0.000031,32 +0.000047,34 +0.000039,34 +0.000035,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000022,34 +0.000027,34 +0.000050,34 +0.000023,34 +0.000023,34 +0.000023,34 +0.000023,34 +0.000023,34 +0.000033,34 +0.000023,34 +0.000042,36 +0.000028,36 +0.000037,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000037,36 +0.000036,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000043,36 +0.000050,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000027,36 +0.000037,36 +0.000036,36 +0.000037,36 +0.000059,36 +0.000049,36 +0.000027,36 +0.000037,36 +0.000057,36 +0.000048,36 +0.000046,36 +0.000047,36 +0.000027,36 +0.000046,36 +0.000027,36 +0.000027,36 +0.000035,38 +0.000036,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000051,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000042,38 +0.000041,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000051,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000031,38 +0.000044,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000086,40 +0.000090,40 +0.000051,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000058,40 +0.000062,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000042,40 +0.000053,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000059,42 +0.000077,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000068,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000068,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000064,42 +0.000058,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000048,42 +0.000058,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000078,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000078,44 +0.000095,44 +0.000073,44 +0.000096,44 +0.000097,44 +0.000085,44 +0.000064,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000065,44 +0.000064,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000075,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000054,44 +0.000068,46 +0.000062,46 +0.000078,46 +0.000083,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000085,46 +0.000072,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000081,46 +0.000133,46 +0.000080,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000097,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000061,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000062,46 +0.000073,48 +0.000069,48 +0.000108,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000090,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000089,48 +0.000069,48 +0.000069,48 +0.000095,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000088,48 +0.000079,48 +0.000099,48 +0.000141,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000091,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000069,48 +0.000085,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000092,50 +0.000138,50 +0.000097,50 +0.000151,50 +0.000117,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000098,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000099,50 +0.000077,50 +0.000078,50 +0.000078,50 +0.000078,50 +0.000117,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000150,50 +0.000111,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000078,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000100,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000077,50 +0.000089,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000131,52 +0.000106,52 +0.000147,52 +0.000130,52 +0.000105,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000123,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000106,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000110,52 +0.000128,52 +0.000153,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000110,52 +0.000095,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000086,52 +0.000099,54 +0.000116,54 +0.000161,54 +0.000169,54 +0.000144,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000153,54 +0.000096,54 +0.000096,54 +0.000115,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000114,54 +0.000115,54 +0.000170,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000106,54 +0.000196,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000131,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000139,54 +0.000096,54 +0.000130,54 +0.000096,54 +0.000096,54 +0.000120,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000096,54 +0.000110,56 +0.000125,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000133,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000136,56 +0.000159,56 +0.000159,56 +0.000143,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000126,56 +0.000106,56 +0.000106,56 +0.000125,56 +0.000106,56 +0.000130,56 +0.000135,56 +0.000183,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000172,56 +0.000149,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000106,56 +0.000119,56 +0.000115,56 +0.000123,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000129,58 +0.000127,58 +0.000117,58 +0.000117,58 +0.000156,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000136,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000136,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000152,58 +0.000138,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000117,58 +0.000134,58 +0.000153,60 +0.000178,60 +0.000226,60 +0.000188,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000148,60 +0.000128,60 +0.000128,60 +0.000149,60 +0.000142,60 +0.000132,60 +0.000132,60 +0.000157,60 +0.000190,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000153,60 +0.000132,60 +0.000161,60 +0.000132,60 +0.000132,60 +0.000132,60 +0.000142,60 +0.000180,60 +0.000141,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000212,60 +0.000390,60 +0.000275,60 +0.000261,60 +0.000269,60 +0.000234,60 +0.000272,60 +0.000241,60 +0.000238,60 +0.000326,60 +0.000245,60 +0.000182,60 +0.000150,60 +0.000167,60 +0.000153,60 +0.000138,60 +0.000128,60 +0.000159,60 +0.000249,60 +0.000157,60 +0.000128,60 +0.000164,60 +0.000165,60 +0.000128,60 +0.000128,60 +0.000230,60 +0.000176,60 +0.000244,60 +0.000238,60 +0.000162,60 +0.000128,60 +0.000128,60 +0.000170,60 +0.000148,60 +0.000129,60 +0.000142,60 +0.000128,60 +0.000128,60 +0.000128,60 +0.000180,60 +0.000212,60 +0.000189,60 +0.000191,60 +0.000161,60 +0.000143,60 +0.000166,60 +0.000135,60 +0.000135,60 +0.000135,60 +0.000135,60 +0.000135,60 +0.000135,60 +0.000135,60 +0.000142,60 +0.000169,60 +0.000128,60 +0.000128,60 +0.000144,62 +0.000141,62 +0.000141,62 +0.000188,62 +0.000215,62 +0.000213,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000161,62 +0.000141,62 +0.000161,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000167,62 +0.000145,62 +0.000184,62 +0.000145,62 +0.000223,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000165,62 +0.000165,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000178,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000165,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000178,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000145,62 +0.000150,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000141,62 +0.000156,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000198,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000248,64 +0.000255,64 +0.000163,64 +0.000154,64 +0.000154,64 +0.000174,64 +0.000154,64 +0.000174,64 +0.000153,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000190,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000195,64 +0.000192,64 +0.000154,64 +0.000164,64 +0.000216,64 +0.000164,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000168,64 +0.000173,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000173,64 +0.000173,64 +0.000154,64 +0.000154,64 +0.000173,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000173,64 +0.000189,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000173,64 +0.000174,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000154,64 +0.000172,66 +0.000169,66 +0.000169,66 +0.000194,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000240,66 +0.000283,66 +0.000188,66 +0.000169,66 +0.000169,66 +0.000188,66 +0.000169,66 +0.000189,66 +0.000169,66 +0.000196,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000179,66 +0.000227,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000191,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000179,66 +0.000198,66 +0.000169,66 +0.000169,66 +0.000189,66 +0.000207,66 +0.000169,66 +0.000169,66 +0.000188,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000191,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000169,66 +0.000186,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000198,68 +0.000307,68 +0.000251,68 +0.000183,68 +0.000183,68 +0.000209,68 +0.000223,68 +0.000345,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000303,68 +0.000331,68 +0.000331,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000255,68 +0.000283,68 +0.000183,68 +0.000201,68 +0.000203,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000215,68 +0.000223,68 +0.000183,68 +0.000203,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000203,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000355,68 +0.000196,68 +0.000183,68 +0.000221,68 +0.000183,68 +0.000256,68 +0.000184,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000183,68 +0.000246,68 +0.000312,68 +0.000193,68 +0.000183,68 +0.000183,68 +0.000203,68 +0.000203,68 +0.000218,70 +0.000355,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000237,70 +0.000342,70 +0.000334,70 +0.000339,70 +0.000351,70 +0.000373,70 +0.000355,70 +0.000281,70 +0.000363,70 +0.000341,70 +0.000323,70 +0.000200,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000233,70 +0.000348,70 +0.000199,70 +0.000242,70 +0.000199,70 +0.000199,70 +0.000238,70 +0.000199,70 +0.000210,70 +0.000208,70 +0.000199,70 +0.000199,70 +0.000219,70 +0.000199,70 +0.000378,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000326,70 +0.000209,70 +0.000199,70 +0.000239,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000200,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000341,70 +0.000229,70 +0.000199,70 +0.000291,70 +0.000325,70 +0.000303,70 +0.000199,70 +0.000214,70 +0.000210,70 +0.000210,70 +0.000210,70 +0.000210,70 +0.000214,70 +0.000205,70 +0.000205,70 +0.000210,70 +0.000199,70 +0.000375,70 +0.000347,70 +0.000410,70 +0.000361,70 +0.000362,70 +0.000371,70 +0.000203,70 +0.000199,70 +0.000199,70 +0.000199,70 +0.000382,70 +0.000200,70 +0.000210,70 +0.000345,70 +0.000490,70 +0.000247,70 +0.000255,70 +0.000199,70 +0.000199,70 +0.000359,70 +0.000230,70 +0.000281,70 +0.000210,70 +0.000251,70 +0.000311,72 +0.000259,72 +0.000226,72 +0.000215,72 +0.000235,72 +0.000215,72 +0.000235,72 +0.000367,72 +0.000451,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000250,72 +0.000215,72 +0.000215,72 +0.000393,72 +0.000215,72 +0.000215,72 +0.000293,72 +0.000309,72 +0.000215,72 +0.000304,72 +0.000325,72 +0.000221,72 +0.000221,72 +0.000221,72 +0.000374,72 +0.000227,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000244,72 +0.000356,72 +0.000545,72 +0.000385,72 +0.000391,72 +0.000216,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000420,72 +0.000388,72 +0.000393,72 +0.000223,72 +0.000215,72 +0.000233,72 +0.000270,72 +0.000348,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000254,72 +0.000220,72 +0.000390,72 +0.000215,72 +0.000215,72 +0.000257,72 +0.000308,72 +0.000215,72 +0.000235,72 +0.000301,72 +0.000279,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000215,72 +0.000230,72 +0.000351,72 +0.000215,72 +0.000257,72 +0.000314,72 +0.000254,72 +0.000215,72 +0.000215,72 +0.000281,72 +0.000317,72 +0.000390,72 +0.000292,72 +0.000227,72 +0.000234,72 +0.000221,72 +0.000247,72 +0.000250,72 +0.000227,72 +0.000215,72 +0.000344,74 +0.000473,74 +0.000451,74 +0.000574,74 +0.000248,74 +0.000357,74 +0.000234,74 +0.000233,74 +0.000233,74 +0.000350,74 +0.000234,74 +0.000233,74 +0.000312,74 +0.000311,74 +0.000233,74 +0.000233,74 +0.000314,74 +0.000265,74 +0.000233,74 +0.000234,74 +0.000346,74 +0.000273,74 +0.000234,74 +0.000287,74 +0.000351,74 +0.000234,74 +0.000293,74 +0.000363,74 +0.000233,74 +0.000233,74 +0.000239,74 +0.000348,74 +0.000234,74 +0.000234,74 +0.000302,74 +0.000282,74 +0.000234,74 +0.000234,74 +0.000338,74 +0.000243,74 +0.000233,74 +0.000260,74 +0.000344,74 +0.000234,74 +0.000233,74 +0.000238,74 +0.000346,74 +0.000233,74 +0.000233,74 +0.000299,74 +0.000465,74 +0.000260,74 +0.000274,74 +0.000246,74 +0.000246,74 +0.000287,74 +0.000351,74 +0.000233,74 +0.000233,74 +0.000233,74 +0.000460,74 +0.000435,74 +0.000513,74 +0.000318,74 +0.000234,74 +0.000354,74 +0.000234,74 +0.000233,74 +0.000299,74 +0.000326,74 +0.000233,74 +0.000233,74 +0.000316,74 +0.000256,74 +0.000233,74 +0.000234,74 +0.000351,74 +0.000234,74 +0.000233,74 +0.000234,74 +0.000376,74 +0.000233,74 +0.000253,74 +0.000364,74 +0.000276,74 +0.000234,74 +0.000234,74 +0.000362,74 +0.000234,74 +0.000233,74 +0.000238,74 +0.000346,74 +0.000233,74 +0.000233,74 +0.000313,74 +0.000270,74 +0.000233,74 +0.000269,74 +0.000347,74 +0.000233,74 +0.000260,76 +0.000270,76 +0.000352,76 +0.000252,76 +0.000251,76 +0.000368,76 +0.000251,76 +0.000286,76 +0.000487,76 +0.000252,76 +0.000315,76 +0.000396,76 +0.000262,76 +0.000251,76 +0.000269,76 +0.000351,76 +0.000251,76 +0.000251,76 +0.000444,76 +0.000423,76 +0.000509,76 +0.000443,76 +0.000575,76 +0.000445,76 +0.000520,76 +0.000373,76 +0.000252,76 +0.000372,76 +0.000251,76 +0.000251,76 +0.000279,76 +0.000341,76 +0.000251,76 +0.000312,76 +0.000423,76 +0.000252,76 +0.000251,76 +0.000366,76 +0.000252,76 +0.000251,76 +0.000256,76 +0.000356,76 +0.000252,76 +0.000251,76 +0.000361,76 +0.000251,76 +0.000251,76 +0.000316,76 +0.000334,76 +0.000252,76 +0.000251,76 +0.000362,76 +0.000252,76 +0.000251,76 +0.000268,76 +0.000343,76 +0.000252,76 +0.000251,76 +0.000360,76 +0.000346,76 +0.000320,76 +0.000341,76 +0.000279,76 +0.000296,76 +0.000336,76 +0.000273,76 +0.000251,76 +0.000251,76 +0.000470,76 +0.000439,76 +0.000464,76 +0.000459,76 +0.000586,76 +0.000261,76 +0.000258,76 +0.000345,76 +0.000258,76 +0.000258,76 +0.000283,76 +0.000318,76 +0.000258,76 +0.000258,76 +0.000258,76 +0.000258,76 +0.000258,76 +0.000295,76 +0.000420,76 +0.000291,76 +0.000251,76 +0.000284,76 +0.000251,76 +0.000251,76 +0.000276,76 +0.000405,76 +0.000251,76 +0.000251,76 +0.000251,76 +0.000251,76 +0.000251,76 +0.000287,76 +0.000432,78 +0.000271,78 +0.000271,78 +0.000406,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000420,78 +0.000271,78 +0.000313,78 +0.000500,78 +0.000325,78 +0.000278,78 +0.000298,78 +0.000308,78 +0.000271,78 +0.000427,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000382,78 +0.000539,78 +0.000500,78 +0.000324,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000400,78 +0.000311,78 +0.000305,78 +0.000360,78 +0.000283,78 +0.000292,78 +0.000281,78 +0.000313,78 +0.000316,78 +0.000280,78 +0.000294,78 +0.000292,78 +0.000295,78 +0.000284,78 +0.000282,78 +0.000271,78 +0.000320,78 +0.000271,78 +0.000347,78 +0.000315,78 +0.000271,78 +0.000271,78 +0.000308,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000306,78 +0.000271,78 +0.000271,78 +0.000341,78 +0.000384,78 +0.000271,78 +0.000291,78 +0.000291,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000391,78 +0.000474,78 +0.000490,78 +0.000437,78 +0.000272,78 +0.000271,78 +0.000271,78 +0.000282,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000309,78 +0.000272,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000271,78 +0.000310,78 +0.000271,78 +0.000315,78 +0.000293,80 +0.000310,80 +0.000290,80 +0.000290,80 +0.000323,80 +0.000290,80 +0.000291,80 +0.000290,80 +0.000291,80 +0.000290,80 +0.000290,80 +0.000291,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000330,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000474,80 +0.000291,80 +0.000310,80 +0.000311,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000328,80 +0.000290,80 +0.000290,80 +0.000450,80 +0.000537,80 +0.000440,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000332,80 +0.000291,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000330,80 +0.000290,80 +0.000313,80 +0.000290,80 +0.000314,80 +0.000290,80 +0.000290,80 +0.000291,80 +0.000291,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000301,80 +0.000333,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000310,80 +0.000454,80 +0.000291,80 +0.000448,80 +0.000310,80 +0.000335,80 +0.000291,80 +0.000290,80 +0.000291,80 +0.000291,80 +0.000337,80 +0.000592,80 +0.000518,80 +0.000362,80 +0.000290,80 +0.000290,80 +0.000290,80 +0.000317,80 +0.000291,80 +0.000290,80 +0.000290,80 +0.000291,80 +0.000291,80 +0.000290,80 +0.000324,82 +0.000313,82 +0.000313,82 +0.000473,82 +0.000313,82 +0.000366,82 +0.000313,82 +0.000352,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000469,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000353,82 +0.000464,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000472,82 +0.000333,82 +0.000323,82 +0.000526,82 +0.000313,82 +0.000312,82 +0.000312,82 +0.000476,82 +0.000555,82 +0.000576,82 +0.000616,82 +0.000313,82 +0.000356,82 +0.000313,82 +0.000386,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000393,82 +0.000392,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000343,82 +0.000332,82 +0.000336,82 +0.000313,82 +0.000503,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000352,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000468,82 +0.000313,82 +0.000313,82 +0.000424,82 +0.000313,82 +0.000314,82 +0.000421,82 +0.000461,82 +0.000313,82 +0.000332,82 +0.000354,82 +0.000313,82 +0.000313,82 +0.000313,82 +0.000484,82 +0.000571,82 +0.000426,82 +0.000313,82 +0.000353,82 +0.000476,82 +0.000312,82 +0.000367,82 +0.000362,82 +0.000312,82 +0.000312,82 +0.000312,82 +0.000312,82 +0.000353,82 +0.000410,82 +0.000312,82 +0.000348,82 +0.000314,82 +0.000352,82 +0.000454,82 +0.000326,82 +0.000377,84 +0.000335,84 +0.000336,84 +0.000340,84 +0.000470,84 +0.000336,84 +0.000376,84 +0.000335,84 +0.000336,84 +0.000492,84 +0.000336,84 +0.000336,84 +0.000336,84 +0.000336,84 +0.000359,84 +0.000449,84 +0.000375,84 +0.000438,84 +0.000415,84 +0.000430,84 +0.000406,84 +0.000336,84 +0.000335,84 +0.000336,84 +0.000343,84 +0.000608,84 +0.000601,84 +0.000591,84 +0.000681,84 +0.000572,84 +0.000592,84 +0.000335,84 +0.000335,84 +0.000335,84 +0.000389,84 +0.000549,84 +0.000385,84 +0.000390,84 +0.000335,84 +0.000375,84 +0.000360,84 +0.000399,84 +0.000399,84 +0.000348,84 +0.000383,84 +0.000377,84 +0.000349,84 +0.000488,84 +0.000384,84 +0.000335,84 +0.000442,84 +0.000337,84 +0.000336,84 +0.000336,84 +0.000336,84 +0.000451,84 +0.000413,84 +0.000463,84 +0.000488,84 +0.000388,84 +0.000385,84 +0.000336,84 +0.000335,84 +0.000624,84 +0.000716,84 +0.000602,84 +0.000619,84 +0.000336,84 +0.000479,84 +0.000336,84 +0.000336,84 +0.000335,84 +0.000336,84 +0.000445,84 +0.000424,84 +0.000336,84 +0.000446,84 +0.000336,84 +0.000373,84 +0.000336,84 +0.000356,84 +0.000335,84 +0.000372,84 +0.000336,84 +0.000522,84 +0.000336,84 +0.000341,84 +0.000438,84 +0.000336,84 +0.000444,84 +0.000336,84 +0.000336,84 +0.000336,84 +0.000335,84 +0.000375,84 +0.000489,84 +0.000336,84 +0.000335,84 +0.000359,84 +0.000494,84 +0.000477,86 +0.000420,86 +0.000358,86 +0.000358,86 +0.000406,86 +0.000458,86 +0.000697,86 +0.000648,86 +0.000407,86 +0.000369,86 +0.000358,86 +0.000499,86 +0.000358,86 +0.000526,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000395,86 +0.000379,86 +0.000358,86 +0.000434,86 +0.000358,86 +0.000358,86 +0.000489,86 +0.000388,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000387,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000532,86 +0.000368,86 +0.000378,86 +0.000379,86 +0.000393,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000472,86 +0.000666,86 +0.000555,86 +0.000358,86 +0.000358,86 +0.000391,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000393,86 +0.000407,86 +0.000358,86 +0.000392,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000384,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000401,86 +0.000502,86 +0.000358,86 +0.000434,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000610,86 +0.000596,86 +0.000358,86 +0.000444,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000358,86 +0.000393,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000452,88 +0.000402,88 +0.000382,88 +0.000416,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000381,88 +0.000412,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000434,88 +0.000480,88 +0.000382,88 +0.000421,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000426,88 +0.000730,88 +0.000542,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000417,88 +0.000382,88 +0.000416,88 +0.000382,88 +0.000402,88 +0.000382,88 +0.000415,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000431,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000381,88 +0.000382,88 +0.000382,88 +0.000381,88 +0.000382,88 +0.000456,88 +0.000544,88 +0.000403,88 +0.000414,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000381,88 +0.000442,88 +0.000729,88 +0.000707,88 +0.000537,88 +0.000382,88 +0.000382,88 +0.000381,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000628,88 +0.000746,88 +0.000518,88 +0.000409,88 +0.000569,88 +0.000488,88 +0.000509,88 +0.000535,88 +0.000407,88 +0.000392,88 +0.000466,88 +0.000425,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000382,88 +0.000458,90 +0.000408,90 +0.000408,90 +0.000590,90 +0.000408,90 +0.000488,90 +0.000408,90 +0.000428,90 +0.000408,90 +0.000447,90 +0.000408,90 +0.000447,90 +0.000510,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000450,90 +0.000408,90 +0.000409,90 +0.000408,90 +0.000408,90 +0.000448,90 +0.000428,90 +0.000408,90 +0.000444,90 +0.000446,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000446,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000582,90 +0.000417,90 +0.000428,90 +0.000428,90 +0.000408,90 +0.000440,90 +0.000408,90 +0.000408,90 +0.000438,90 +0.000569,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000444,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000442,90 +0.000418,90 +0.000420,90 +0.000475,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000446,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000534,90 +0.000467,90 +0.000427,90 +0.000429,90 +0.000440,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000418,90 +0.000500,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000441,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000408,90 +0.000445,92 +0.000435,92 +0.000466,92 +0.000452,92 +0.000476,92 +0.000467,92 +0.000435,92 +0.000435,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000470,92 +0.000444,92 +0.000435,92 +0.000434,92 +0.000435,92 +0.000463,92 +0.000532,92 +0.000593,92 +0.000465,92 +0.000486,92 +0.000435,92 +0.000435,92 +0.000435,92 +0.000435,92 +0.000484,92 +0.000526,92 +0.000434,92 +0.000434,92 +0.000457,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000435,92 +0.000435,92 +0.000434,92 +0.000537,92 +0.000475,92 +0.000434,92 +0.000503,92 +0.000435,92 +0.000435,92 +0.000434,92 +0.000434,92 +0.000465,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000579,92 +0.000434,92 +0.000474,92 +0.000434,92 +0.000435,92 +0.000434,92 +0.000434,92 +0.000435,92 +0.000537,92 +0.000470,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000454,92 +0.000434,92 +0.000470,92 +0.000434,92 +0.000468,92 +0.000478,92 +0.000435,92 +0.000466,92 +0.000434,92 +0.000454,92 +0.000434,92 +0.000473,92 +0.000446,92 +0.000451,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000482,92 +0.000619,92 +0.000445,92 +0.000463,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000434,92 +0.000484,94 +0.000565,94 +0.000493,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000507,94 +0.000740,94 +0.000755,94 +0.000503,94 +0.000684,94 +0.000541,94 +0.000739,94 +0.000463,94 +0.000472,94 +0.000596,94 +0.000465,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000496,94 +0.000463,94 +0.000580,94 +0.000588,94 +0.000511,94 +0.000507,94 +0.000462,94 +0.000482,94 +0.000495,94 +0.000502,94 +0.000566,94 +0.000463,94 +0.000478,94 +0.000475,94 +0.000477,94 +0.000462,94 +0.000487,94 +0.000463,94 +0.000462,94 +0.000462,94 +0.000463,94 +0.000530,94 +0.000508,94 +0.000463,94 +0.000538,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000463,94 +0.000496,94 +0.000475,94 +0.000478,94 +0.000526,94 +0.000581,94 +0.000483,94 +0.000487,94 +0.000462,94 +0.000494,94 +0.000463,94 +0.000463,94 +0.000565,94 +0.000606,94 +0.000495,94 +0.000463,94 +0.000563,94 +0.000500,94 +0.000657,94 +0.000624,94 +0.000506,94 +0.000488,94 +0.000515,94 +0.000580,94 +0.000657,94 +0.000534,94 +0.000529,94 +0.000533,94 +0.000540,94 +0.000562,94 +0.000494,94 +0.000537,94 +0.000565,94 +0.000878,94 +0.000931,94 +0.000894,94 +0.000959,94 +0.000763,94 +0.000537,94 +0.000584,94 +0.000978,94 +0.001019,94 +0.001073,94 +0.000778,94 +0.000477,94 +0.000535,96 +0.000582,96 +0.000641,96 +0.000605,96 +0.000597,96 +0.000584,96 +0.000516,96 +0.000534,96 +0.000892,96 +0.000842,96 +0.000522,96 +0.000502,96 +0.000502,96 +0.000609,96 +0.000636,96 +0.000555,96 +0.000502,96 +0.000502,96 +0.000502,96 +0.000502,96 +0.000514,96 +0.000489,96 +0.000504,96 +0.000564,96 +0.000502,96 +0.000707,96 +0.000916,96 +0.000739,96 +0.000601,96 +0.000697,96 +0.000612,96 +0.000552,96 +0.000490,96 +0.000489,96 +0.000489,96 +0.000489,96 +0.000530,96 +0.000490,96 +0.000490,96 +0.000490,96 +0.000490,96 +0.000490,96 +0.000489,96 +0.000560,96 +0.000598,96 +0.000510,96 +0.000529,96 +0.000489,96 +0.000490,96 +0.000490,96 +0.000498,96 +0.000504,96 +0.000568,96 +0.000502,96 +0.000509,96 +0.000977,96 +0.000834,96 +0.000513,96 +0.000615,96 +0.000572,96 +0.000549,96 +0.000577,96 +0.000508,96 +0.000490,96 +0.000490,96 +0.000527,96 +0.000489,96 +0.000498,96 +0.000502,96 +0.000510,96 +0.000490,96 +0.000489,96 +0.000490,96 +0.000549,96 +0.000661,96 +0.000490,96 +0.000534,96 +0.000490,96 +0.000490,96 +0.000490,96 +0.000498,96 +0.000546,96 +0.000549,96 +0.000550,96 +0.000503,96 +0.000772,96 +0.000877,96 +0.000647,96 +0.000529,96 +0.001050,96 +0.000608,96 +0.000727,96 +0.000565,96 +0.000638,96 +0.000607,96 +0.000500,96 +0.000668,96 +0.000520,96 +0.000490,96 +0.000490,96 +0.000576,98 +0.000523,98 +0.000704,98 +0.000562,98 +0.000563,98 +0.000523,98 +0.000523,98 +0.000564,98 +0.000581,98 +0.000601,98 +0.000634,98 +0.000532,98 +0.000543,98 +0.000626,98 +0.000597,98 +0.000598,98 +0.000631,98 +0.000684,98 +0.000586,98 +0.000643,98 +0.000603,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000555,98 +0.000523,98 +0.000523,98 +0.000663,98 +0.000564,98 +0.000582,98 +0.000538,98 +0.000563,98 +0.000523,98 +0.000563,98 +0.000601,98 +0.000588,98 +0.000581,98 +0.000543,98 +0.000586,98 +0.000556,98 +0.000582,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000725,98 +0.000686,98 +0.000551,98 +0.000551,98 +0.000562,98 +0.000550,98 +0.000536,98 +0.000536,98 +0.000567,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000533,98 +0.000722,98 +0.000543,98 +0.000594,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000562,98 +0.000543,98 +0.000605,98 +0.000593,98 +0.000553,98 +0.000562,98 +0.000701,98 +0.000523,98 +0.000763,98 +0.000631,98 +0.000759,98 +0.000582,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000565,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000523,98 +0.000702,98 +0.000568,98 +0.000563,98 +0.000523,98 +0.000523,98 +0.000552,98 +0.000552,98 +0.000722,98 +0.000579,98 +0.000602,98 +0.000600,100 +0.000567,100 +0.000610,100 +0.000552,100 +0.000695,100 +0.000765,100 +0.000756,100 +0.000605,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000591,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000663,100 +0.000571,100 +0.000591,100 +0.000552,100 +0.000552,100 +0.000592,100 +0.000620,100 +0.000613,100 +0.000572,100 +0.000716,100 +0.000567,100 +0.000675,100 +0.000552,100 +0.000552,100 +0.000766,100 +0.000738,100 +0.000699,100 +0.000611,100 +0.000552,100 +0.000552,100 +0.000598,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000643,100 +0.000704,100 +0.000612,100 +0.000552,100 +0.000552,100 +0.000552,100 +0.000591,100 +0.000704,100 +0.000632,100 +0.000552,100 +0.000711,100 +0.000567,100 +0.000650,100 +0.000635,100 +0.000670,100 +0.001211,100 +0.000648,100 +0.000753,100 +0.000768,100 +0.000696,100 +0.000578,100 +0.000625,100 +0.000567,100 +0.000567,100 +0.000603,100 +0.000567,100 +0.000627,100 +0.000567,100 +0.000593,100 +0.000567,100 +0.000567,100 +0.000594,100 +0.000573,100 +0.000749,100 +0.000572,100 +0.000587,100 +0.000678,100 +0.000579,100 +0.000580,100 +0.000552,100 +0.000642,100 +0.000743,100 +0.000706,100 +0.000611,100 +0.000592,100 +0.000553,100 +0.000552,100 +0.000552,100 +0.000553,100 +0.000552,100 +0.000553,100 +0.000595,100 +0.000553,100 +0.000553,100 +0.000752,100 +0.000619,102 +0.000624,102 +0.000599,102 +0.000604,102 +0.000623,102 +0.000663,102 +0.000725,102 +0.000620,102 +0.000668,102 +0.000805,102 +0.000604,102 +0.000584,102 +0.000627,102 +0.000769,102 +0.000735,102 +0.000616,102 +0.000610,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000622,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000741,102 +0.000642,102 +0.000647,102 +0.000604,102 +0.000584,102 +0.000623,102 +0.000662,102 +0.000776,102 +0.000644,102 +0.000625,102 +0.000584,102 +0.000585,102 +0.000584,102 +0.000584,102 +0.000739,102 +0.000766,102 +0.000677,102 +0.000624,102 +0.000585,102 +0.000584,102 +0.000584,102 +0.000620,102 +0.000585,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000606,102 +0.000776,102 +0.000668,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000624,102 +0.000783,102 +0.000739,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000660,102 +0.000688,102 +0.000643,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000618,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000584,102 +0.000674,102 +0.000626,102 +0.000731,102 +0.000665,102 +0.000584,102 +0.000623,102 +0.000663,102 +0.000700,102 +0.000696,102 +0.000584,102 +0.000584,102 +0.000585,102 +0.000595,102 +0.000630,102 +0.000584,102 +0.000623,102 +0.000604,102 +0.000623,102 +0.000585,102 +0.000584,102 +0.000627,102 +0.000584,102 +0.000631,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000663,104 +0.000839,104 +0.000650,104 +0.000641,104 +0.000617,104 +0.000617,104 +0.000691,104 +0.000753,104 +0.000980,104 +0.000890,104 +0.000617,104 +0.000650,104 +0.000626,104 +0.000617,104 +0.001098,104 +0.000670,104 +0.000933,104 +0.000782,104 +0.000709,104 +0.000728,104 +0.000733,104 +0.000617,104 +0.000644,104 +0.000617,104 +0.000784,104 +0.000660,104 +0.000646,104 +0.000617,104 +0.000648,104 +0.000784,104 +0.000789,104 +0.000865,104 +0.000654,104 +0.000633,104 +0.000655,104 +0.000617,104 +0.000618,104 +0.000638,104 +0.000656,104 +0.000617,104 +0.000698,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000653,104 +0.000617,104 +0.000617,104 +0.000808,104 +0.000636,104 +0.000657,104 +0.000654,104 +0.000617,104 +0.000794,104 +0.000804,104 +0.000651,104 +0.000640,104 +0.000643,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000656,104 +0.000681,104 +0.000656,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000642,104 +0.000617,104 +0.000617,104 +0.000680,104 +0.000785,104 +0.000661,104 +0.000648,104 +0.000617,104 +0.000656,104 +0.000754,104 +0.000617,104 +0.000617,104 +0.000644,104 +0.000617,104 +0.000633,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000685,104 +0.000637,104 +0.000656,104 +0.000617,104 +0.000617,104 +0.000617,104 +0.000630,104 +0.000679,106 +0.000652,106 +0.000652,106 +0.000651,106 +0.000836,106 +0.000702,106 +0.000674,106 +0.000691,106 +0.000803,106 +0.000652,106 +0.000652,106 +0.000696,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000681,106 +0.000691,106 +0.000671,106 +0.000690,106 +0.000651,106 +0.000653,106 +0.000679,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000744,106 +0.000651,106 +0.000652,106 +0.000651,106 +0.000652,106 +0.000652,106 +0.000656,106 +0.000654,106 +0.000652,106 +0.000651,106 +0.000652,106 +0.000652,106 +0.000654,106 +0.000652,106 +0.000691,106 +0.000652,106 +0.000691,106 +0.000651,106 +0.000656,106 +0.000652,106 +0.000651,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000654,106 +0.000711,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000656,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000656,106 +0.000654,106 +0.000652,106 +0.000652,106 +0.001086,106 +0.000704,106 +0.000987,106 +0.000778,106 +0.000766,106 +0.000692,106 +0.000831,106 +0.000699,106 +0.000692,106 +0.000752,106 +0.000652,106 +0.000651,106 +0.000652,106 +0.000652,106 +0.000685,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000652,106 +0.000690,106 +0.000652,106 +0.000652,106 +0.000651,106 +0.000691,106 +0.000652,106 +0.000696,106 +0.000652,106 +0.000652,106 +0.000651,106 +0.000652,106 +0.000652,106 +0.000730,108 +0.000690,108 +0.000752,108 +0.000689,108 +0.000689,108 +0.000726,108 +0.000690,108 +0.000689,108 +0.000690,108 +0.000690,108 +0.000769,108 +0.000729,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000728,108 +0.000711,108 +0.000728,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000694,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000753,108 +0.000709,108 +0.000715,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000696,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000700,108 +0.000721,108 +0.000728,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000694,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000752,108 +0.000692,108 +0.000690,108 +0.000690,108 +0.000689,108 +0.000690,108 +0.000689,108 +0.000694,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000690,108 +0.000689,108 +0.000731,108 +0.000690,108 +0.000729,108 +0.000690,108 +0.000690,108 +0.000694,108 +0.000689,108 +0.000689,108 +0.000690,108 +0.000689,108 +0.000690,108 +0.000711,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000693,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000691,108 +0.000721,108 +0.000698,108 +0.000728,108 +0.000689,108 +0.000694,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000689,108 +0.000691,108 +0.000689,108 +0.000689,108 +0.000739,110 +0.000726,110 +0.000726,110 +0.000731,110 +0.000726,110 +0.000785,110 +0.000726,110 +0.000726,110 +0.000729,110 +0.000727,110 +0.000726,110 +0.000765,110 +0.000726,110 +0.000767,110 +0.000882,110 +0.000767,110 +0.000752,110 +0.000763,110 +0.000796,110 +0.000783,110 +0.000819,110 +0.000881,110 +0.000726,110 +0.000726,110 +0.000764,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000761,110 +0.000780,110 +0.000726,110 +0.000748,110 +0.000757,110 +0.000757,110 +0.000772,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000764,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000772,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000729,110 +0.000788,110 +0.000890,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000769,110 +0.000754,110 +0.000767,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000749,110 +0.000726,110 +0.000728,110 +0.000737,110 +0.000922,110 +0.000800,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000749,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000766,110 +0.000746,110 +0.000765,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000763,110 +0.000729,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000765,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000749,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000726,110 +0.000751,110 +0.000817,112 +0.000763,112 +0.000803,112 +0.000764,112 +0.000766,112 +0.000763,112 +0.000764,112 +0.000763,112 +0.000763,112 +0.000809,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000765,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000768,112 +0.000763,112 +0.000802,112 +0.000802,112 +0.000763,112 +0.000766,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000767,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000767,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000767,112 +0.000763,112 +0.000802,112 +0.000763,112 +0.000895,112 +0.000818,112 +0.000801,112 +0.000821,112 +0.000797,112 +0.000868,112 +0.000816,112 +0.000763,112 +0.000783,112 +0.000763,112 +0.000763,112 +0.000786,112 +0.000764,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000788,112 +0.000764,112 +0.000763,112 +0.000802,112 +0.000763,112 +0.000825,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000857,112 +0.000764,112 +0.000764,112 +0.000763,112 +0.000763,112 +0.000788,112 +0.000764,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000801,112 +0.000822,112 +0.000946,112 +0.000824,112 +0.000814,112 +0.000841,112 +0.000804,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000800,112 +0.000763,112 +0.000763,112 +0.000837,112 +0.000916,112 +0.000820,112 +0.000763,112 +0.000763,112 +0.000763,112 +0.000827,114 +0.000849,114 +0.000812,114 +0.000811,114 +0.000812,114 +0.000811,114 +0.000885,114 +0.000831,114 +0.000851,114 +0.000812,114 +0.000812,114 +0.000850,114 +0.000812,114 +0.000812,114 +0.000812,114 +0.000812,114 +0.000836,114 +0.000812,114 +0.000812,114 +0.000812,114 +0.000812,114 +0.000847,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000874,114 +0.000811,114 +0.000851,114 +0.000812,114 +0.000839,114 +0.000811,114 +0.000812,114 +0.000811,114 +0.000811,114 +0.000834,114 +0.000812,114 +0.000811,114 +0.000811,114 +0.000862,114 +0.000836,114 +0.000812,114 +0.000812,114 +0.000812,114 +0.000812,114 +0.000839,114 +0.000812,114 +0.000851,114 +0.000851,114 +0.000812,114 +0.000837,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000839,114 +0.000812,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000816,114 +0.000812,114 +0.000812,114 +0.000811,114 +0.000864,114 +0.000812,114 +0.000812,114 +0.000850,114 +0.000812,114 +0.000858,114 +0.000978,114 +0.000837,114 +0.000856,114 +0.000860,114 +0.000867,114 +0.000872,114 +0.000832,114 +0.000812,114 +0.000812,114 +0.000847,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000835,114 +0.000811,114 +0.000812,114 +0.000811,114 +0.000851,114 +0.000876,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000845,114 +0.000814,114 +0.000811,114 +0.000811,114 +0.000811,114 +0.000816,114 +0.000811,114 +0.000870,116 +0.000850,116 +0.000850,116 +0.000932,116 +0.000851,116 +0.000850,116 +0.000850,116 +0.000925,116 +0.000890,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000852,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000854,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000931,116 +0.000851,116 +0.000851,116 +0.000850,116 +0.000850,116 +0.000920,116 +0.000850,116 +0.000889,116 +0.000850,116 +0.000850,116 +0.000873,116 +0.000851,116 +0.000850,116 +0.000851,116 +0.000855,116 +0.000851,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000853,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000855,116 +0.000890,116 +0.000889,116 +0.000850,116 +0.000852,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000854,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000852,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000855,116 +0.000850,116 +0.000890,116 +0.000850,116 +0.000889,116 +0.000853,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000856,116 +0.000851,116 +0.000850,116 +0.000865,116 +0.000855,116 +0.000851,116 +0.000850,116 +0.000851,116 +0.000850,116 +0.000857,116 +0.000850,116 +0.000870,116 +0.000875,116 +0.000889,116 +0.000852,116 +0.000897,116 +0.000883,116 +0.000907,116 +0.000925,116 +0.000870,116 +0.000907,116 +0.000859,116 +0.000850,116 +0.000873,116 +0.000850,116 +0.000850,116 +0.000850,116 +0.000932,118 +0.000889,118 +0.000890,118 +0.000928,118 +0.000889,118 +0.000951,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000925,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000891,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000919,118 +0.000971,118 +0.000889,118 +0.000889,118 +0.000950,118 +0.000928,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000894,118 +0.000889,118 +0.000890,118 +0.000889,118 +0.000891,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000894,118 +0.000889,118 +0.000890,118 +0.000889,118 +0.000951,118 +0.000889,118 +0.000929,118 +0.000889,118 +0.000889,118 +0.000893,118 +0.000889,118 +0.000913,118 +0.000889,118 +0.000897,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000897,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000895,118 +0.000928,118 +0.000889,118 +0.000928,118 +0.000895,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000895,118 +0.000889,118 +0.000889,118 +0.000906,118 +0.000898,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000900,118 +0.000889,118 +0.000928,118 +0.000928,118 +0.000891,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000893,118 +0.000889,118 +0.000888,118 +0.000889,118 +0.000891,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000889,118 +0.000894,118 +0.000889,118 +0.000933,118 +0.000889,118 +0.000930,118 +0.000889,118 +0.000995,120 +0.000992,120 +0.001008,120 +0.000973,120 +0.000965,120 +0.001004,120 +0.000957,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000964,120 +0.000935,120 +0.000937,120 +0.000974,120 +0.001011,120 +0.000935,120 +0.000937,120 +0.000935,120 +0.000958,120 +0.000935,120 +0.000936,120 +0.000935,120 +0.000940,120 +0.000936,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000973,120 +0.001014,120 +0.000936,120 +0.000975,120 +0.000969,120 +0.000974,120 +0.000936,120 +0.000935,120 +0.000969,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000940,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000958,120 +0.000935,120 +0.000935,120 +0.000965,120 +0.000935,120 +0.001004,120 +0.000975,120 +0.000935,120 +0.000935,120 +0.000997,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000941,120 +0.000935,120 +0.000937,120 +0.000935,120 +0.000937,120 +0.000935,120 +0.000937,120 +0.000935,120 +0.000935,120 +0.000937,120 +0.000974,120 +0.000974,120 +0.000935,120 +0.000940,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000937,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000940,120 +0.000935,120 +0.000935,120 +0.000935,120 +0.000934,120 +0.000937,120 +0.000974,120 +0.000935,120 +0.000974,120 +0.000940,120 +0.000935,120 +0.000961,120 +0.000936,120 +0.000941,120 +0.000938,120 +0.000935,120 +0.000938,120 +0.000941,120 +0.000936,120 +0.000936,120 +0.000995,120 +0.000941,120 +0.001005,122 +0.000983,122 +0.001022,122 +0.001049,122 +0.000983,122 +0.000983,122 +0.001040,122 +0.001136,122 +0.001051,122 +0.001031,122 +0.001070,122 +0.001012,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.001006,122 +0.000983,122 +0.000984,122 +0.001022,122 +0.001019,122 +0.001012,122 +0.000983,122 +0.000983,122 +0.001006,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000988,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.001006,122 +0.001090,122 +0.001003,122 +0.000983,122 +0.001051,122 +0.001022,122 +0.000983,122 +0.000983,122 +0.000985,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000985,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000988,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000985,122 +0.001027,122 +0.001022,122 +0.000983,122 +0.000987,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000985,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000987,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000985,122 +0.000983,122 +0.001022,122 +0.001022,122 +0.000988,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000990,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.001009,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000986,122 +0.001022,122 +0.000983,122 +0.001022,122 +0.000989,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000985,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.000985,122 +0.000983,122 +0.000983,122 +0.000983,122 +0.001059,124 +0.001033,124 +0.001073,124 +0.001073,124 +0.001036,124 +0.001033,124 +0.001033,124 +0.001158,124 +0.001078,124 +0.001099,124 +0.001071,124 +0.001124,124 +0.001057,124 +0.001033,124 +0.001033,124 +0.001057,124 +0.001034,124 +0.001034,124 +0.001072,124 +0.001098,124 +0.001034,124 +0.001034,124 +0.001057,124 +0.001034,124 +0.001034,124 +0.001034,124 +0.001038,124 +0.001034,124 +0.001034,124 +0.001034,124 +0.001068,124 +0.001092,124 +0.001033,124 +0.001033,124 +0.001109,124 +0.001073,124 +0.001033,124 +0.001033,124 +0.001036,124 +0.001033,124 +0.001033,124 +0.001033,124 +0.001038,124 +0.001033,124 +0.001033,124 +0.001036,124 +0.001034,124 +0.001033,124 +0.001033,124 +0.001038,124 +0.001072,124 +0.001072,124 +0.001034,124 +0.001036,124 +0.001034,124 +0.001034,124 +0.001034,124 +0.001038,124 +0.001034,124 +0.001034,124 +0.001034,124 +0.001036,124 +0.001033,124 +0.001034,124 +0.001034,124 +0.001038,124 +0.001073,124 +0.001073,124 +0.001036,124 +0.001034,124 +0.001034,124 +0.001034,124 +0.001061,124 +0.001033,124 +0.001033,124 +0.001033,124 +0.001036,124 +0.001033,124 +0.001033,124 +0.001033,124 +0.001059,124 +0.001033,124 +0.001073,124 +0.001072,124 +0.001067,124 +0.001033,124 +0.001033,124 +0.001033,124 +0.001038,124 +0.001033,124 +0.001033,124 +0.001036,124 +0.001033,124 +0.001033,124 +0.001033,124 +0.001038,124 +0.001033,124 +0.001033,124 +0.001073,124 +0.001075,124 +0.001105,126 +0.001084,126 +0.001175,126 +0.001258,126 +0.001130,126 +0.001150,126 +0.001208,126 +0.001215,126 +0.001107,126 +0.001083,126 +0.001121,126 +0.001168,126 +0.001122,126 +0.001185,126 +0.001123,126 +0.001111,126 +0.001149,126 +0.001120,126 +0.001168,126 +0.001139,126 +0.001147,126 +0.001169,126 +0.001084,126 +0.001149,126 +0.001201,126 +0.001249,126 +0.001189,126 +0.001217,126 +0.001123,126 +0.001168,126 +0.001228,126 +0.001204,126 +0.001151,126 +0.001149,126 +0.001206,126 +0.001173,126 +0.001381,126 +0.001185,126 +0.001208,126 +0.001172,126 +0.001250,126 +0.001249,126 +0.001187,126 +0.001148,126 +0.001207,126 +0.001239,126 +0.001200,126 +0.001223,126 +0.001148,126 +0.001199,126 +0.001234,126 +0.001242,126 +0.001171,126 +0.001173,126 +0.001230,126 +0.001272,126 +0.001191,126 +0.001209,126 +0.001169,126 +0.001210,126 +0.001245,126 +0.001253,126 +0.001148,126 +0.001197,126 +0.001235,126 +0.001149,126 +0.001150,126 +0.001207,126 +0.001209,126 +0.001245,126 +0.001266,126 +0.001189,126 +0.001210,126 +0.001300,126 +0.001375,126 +0.001252,126 +0.001221,126 +0.001355,126 +0.001453,126 +0.001288,126 +0.001281,126 +0.001253,126 +0.001228,126 +0.001283,126 +0.001296,126 +0.001215,126 +0.001245,126 +0.001442,126 +0.001202,126 +0.001205,126 +0.001170,126 +0.001228,126 +0.001194,126 +0.001167,126 +0.001169,126 +0.001238,126 +0.001135,126 +0.001112,126 +0.001131,126 +0.001218,126 +0.001382,128 +0.001331,128 +0.001270,128 +0.001313,128 +0.001256,128 +0.001326,128 +0.001293,128 +0.001140,128 +0.001395,128 +0.001199,128 +0.001249,128 +0.001276,128 +0.001238,128 +0.001316,128 +0.001350,128 +0.001339,128 +0.001203,128 +0.001262,128 +0.001302,128 +0.001210,128 +0.001162,128 +0.001297,128 +0.001271,128 +0.001223,128 +0.001257,128 +0.001159,128 +0.001138,128 +0.001228,128 +0.001189,128 +0.001330,128 +0.001185,128 +0.001196,128 +0.001140,128 +0.001139,128 +0.001293,128 +0.001178,128 +0.001178,128 +0.001178,128 +0.001139,128 +0.001138,128 +0.001139,128 +0.001262,128 +0.001179,128 +0.001139,128 +0.001172,128 +0.001140,128 +0.001139,128 +0.001139,128 +0.001178,128 +0.001179,128 +0.001158,128 +0.001211,128 +0.001139,128 +0.001139,128 +0.001139,128 +0.001175,128 +0.001139,128 +0.001140,128 +0.001161,128 +0.001139,128 +0.001139,128 +0.001138,128 +0.001183,128 +0.001139,128 +0.001178,128 +0.001173,128 +0.001139,128 +0.001240,128 +0.001419,128 +0.001814,128 +0.001751,128 +0.001291,128 +0.001630,128 +0.001826,128 +0.001257,128 +0.001138,128 +0.001217,128 +0.001177,128 +0.001138,128 +0.001137,128 +0.001177,128 +0.001278,128 +0.001591,128 +0.001900,128 +0.001170,128 +0.001295,128 +0.001161,128 +0.001207,128 +0.001140,128 +0.001270,128 +0.001356,128 +0.001140,128 +0.001186,128 +0.001140,128 +0.001188,128 +0.001189,128 +0.001161,128 +0.001139,128 +0.001160,128 +0.001239,128 +0.001271,130 +0.001282,130 +0.001341,130 +0.001218,130 +0.001237,130 +0.001244,130 +0.001288,130 +0.001208,130 +0.001301,130 +0.001274,130 +0.001237,130 +0.001239,130 +0.001224,130 +0.001258,130 +0.001198,130 +0.001244,130 +0.001263,130 +0.001237,130 +0.001243,130 +0.001323,130 +0.001227,130 +0.001264,130 +0.001210,130 +0.001232,130 +0.001414,130 +0.001217,130 +0.001218,130 +0.001241,130 +0.001198,130 +0.001239,130 +0.001235,130 +0.001243,130 +0.001323,130 +0.001197,130 +0.001231,130 +0.001198,130 +0.001264,130 +0.001457,130 +0.001198,130 +0.001198,130 +0.001387,130 +0.001198,130 +0.001232,130 +0.001277,130 +0.001321,130 +0.001276,130 +0.001322,130 +0.001198,130 +0.001198,130 +0.001263,130 +0.001405,130 +0.001230,130 +0.001230,130 +0.001298,130 +0.001347,130 +0.001305,130 +0.001444,130 +0.001218,130 +0.001217,130 +0.001365,130 +0.001294,130 +0.001370,130 +0.001236,130 +0.001350,130 +0.001473,130 +0.001258,130 +0.001375,130 +0.001332,130 +0.001422,130 +0.001261,130 +0.001310,130 +0.001338,130 +0.001298,130 +0.001352,130 +0.001393,130 +0.001251,130 +0.001344,130 +0.001407,130 +0.001295,130 +0.001275,130 +0.001400,130 +0.001198,130 +0.001439,130 +0.001305,130 +0.001198,130 +0.001288,130 +0.001342,130 +0.001197,130 +0.001290,130 +0.001473,130 +0.001198,130 +0.001307,130 +0.001305,130 +0.001238,130 +0.001395,130 +0.001226,130 +0.001198,130 +0.001313,130 +0.001309,130 +0.001307,130 +0.001281,132 +0.001541,132 +0.001270,132 +0.001248,132 +0.001384,132 +0.001249,132 +0.001442,132 +0.001331,132 +0.001250,132 +0.001361,132 +0.001277,132 +0.001374,132 +0.001268,132 +0.001442,132 +0.001249,132 +0.001249,132 +0.001248,132 +0.001292,132 +0.001249,132 +0.001328,132 +0.001322,132 +0.001249,132 +0.001248,132 +0.001282,132 +0.001376,132 +0.001268,132 +0.001433,132 +0.001352,132 +0.001316,132 +0.001407,132 +0.001313,132 +0.001351,132 +0.001462,132 +0.001270,132 +0.001269,132 +0.001285,132 +0.001357,132 +0.001288,132 +0.001282,132 +0.001390,132 +0.001249,132 +0.001288,132 +0.001248,132 +0.001332,132 +0.001302,132 +0.001329,132 +0.001249,132 +0.001287,132 +0.001249,132 +0.001353,132 +0.001323,132 +0.001249,132 +0.001250,132 +0.001285,132 +0.001249,132 +0.001249,132 +0.001282,132 +0.001268,132 +0.001332,132 +0.001249,132 +0.001284,132 +0.001248,132 +0.001249,132 +0.001282,132 +0.001249,132 +0.001250,132 +0.001276,132 +0.001249,132 +0.001249,132 +0.001272,132 +0.001268,132 +0.001288,132 +0.001274,132 +0.001249,132 +0.001249,132 +0.001271,132 +0.001249,132 +0.001248,132 +0.001249,132 +0.001254,132 +0.001248,132 +0.001249,132 +0.001272,132 +0.001249,132 +0.001268,132 +0.001338,132 +0.001249,132 +0.001248,132 +0.001272,132 +0.001249,132 +0.001249,132 +0.001254,132 +0.001249,132 +0.001249,132 +0.001251,132 +0.001249,132 +0.001249,132 +0.001268,132 +0.001313,132 +0.001249,132 +0.001338,134 +0.001311,134 +0.001308,134 +0.001308,134 +0.001524,134 +0.001376,134 +0.001356,134 +0.001469,134 +0.001308,134 +0.001395,134 +0.001349,134 +0.001330,134 +0.001510,134 +0.001382,134 +0.001308,134 +0.001352,134 +0.001347,134 +0.001410,134 +0.001334,134 +0.001391,134 +0.001308,134 +0.001364,134 +0.001347,134 +0.001308,134 +0.001433,134 +0.001308,134 +0.001411,134 +0.001380,134 +0.001308,134 +0.001411,134 +0.001345,134 +0.001361,134 +0.001307,134 +0.001344,134 +0.001372,134 +0.001346,134 +0.001334,134 +0.001307,134 +0.001413,134 +0.001371,134 +0.001308,134 +0.001404,134 +0.001348,134 +0.001328,134 +0.001308,134 +0.001344,134 +0.001359,134 +0.001355,134 +0.001334,134 +0.001307,134 +0.001307,134 +0.001416,134 +0.001328,134 +0.001409,134 +0.001343,134 +0.001365,134 +0.001308,134 +0.001346,134 +0.001327,134 +0.001388,134 +0.001335,134 +0.001308,134 +0.001308,134 +0.001449,134 +0.001348,134 +0.001340,134 +0.001449,134 +0.001307,134 +0.001322,134 +0.001437,134 +0.001322,134 +0.001406,134 +0.001347,134 +0.001307,134 +0.001464,134 +0.001407,134 +0.001348,134 +0.001368,134 +0.001487,134 +0.001438,134 +0.001416,134 +0.001460,134 +0.001642,134 +0.001396,134 +0.001350,134 +0.001414,134 +0.001494,134 +0.001531,134 +0.001366,134 +0.001430,134 +0.001381,134 +0.001490,134 +0.001450,134 +0.001369,134 +0.001503,134 +0.001601,134 +0.001517,134 +0.001411,134 +0.001652,134 +0.001479,134 +0.001538,136 +0.001451,136 +0.001496,136 +0.001529,136 +0.001574,136 +0.001464,136 +0.001494,136 +0.001499,136 +0.001571,136 +0.001559,136 +0.001518,136 +0.001445,136 +0.001431,136 +0.001540,136 +0.001456,136 +0.001468,136 +0.001405,136 +0.001430,136 +0.001429,136 +0.001392,136 +0.001369,136 +0.001417,136 +0.001369,136 +0.001514,136 +0.001561,136 +0.001406,136 +0.001490,136 +0.001528,136 +0.001512,136 +0.001735,136 +0.001451,136 +0.001446,136 +0.001588,136 +0.001405,136 +0.001478,136 +0.001445,136 +0.001426,136 +0.001501,136 +0.001555,136 +0.001631,136 +0.001559,136 +0.001444,136 +0.001439,136 +0.001472,136 +0.001405,136 +0.002002,136 +0.001684,136 +0.001495,136 +0.001602,136 +0.001464,136 +0.001550,136 +0.001497,136 +0.001465,136 +0.001462,136 +0.001777,136 +0.002520,136 +0.002108,136 +0.001403,136 +0.001556,136 +0.001532,136 +0.001485,136 +0.001530,136 +0.001473,136 +0.001464,136 +0.001452,136 +0.001369,136 +0.002016,136 +0.001433,136 +0.001533,136 +0.001503,136 +0.001523,136 +0.001506,136 +0.001492,136 +0.001368,136 +0.001444,136 +0.001471,136 +0.001368,136 +0.001980,136 +0.001405,136 +0.001533,136 +0.001496,136 +0.001527,136 +0.001513,136 +0.001481,136 +0.001369,136 +0.001475,136 +0.001472,136 +0.001369,136 +0.002042,136 +0.001405,136 +0.001531,136 +0.001522,136 +0.001476,136 +0.001575,136 +0.001431,136 +0.001369,136 +0.001482,136 +0.001431,136 +0.001368,136 +0.002021,136 +0.001514,138 +0.001650,138 +0.001551,138 +0.001637,138 +0.001606,138 +0.001429,138 +0.001473,138 +0.001531,138 +0.001468,138 +0.001802,138 +0.001543,138 +0.001567,138 +0.001600,138 +0.001570,138 +0.001761,138 +0.001498,138 +0.001508,138 +0.001505,138 +0.001777,138 +0.002262,138 +0.001464,138 +0.001616,138 +0.001670,138 +0.001590,138 +0.001705,138 +0.001457,138 +0.001458,138 +0.001426,138 +0.001721,138 +0.001468,138 +0.001848,138 +0.001652,138 +0.001651,138 +0.001635,138 +0.001545,138 +0.001519,138 +0.001486,138 +0.001428,138 +0.001640,138 +0.001514,138 +0.001677,138 +0.001697,138 +0.001626,138 +0.001468,138 +0.001502,138 +0.001592,138 +0.001525,138 +0.001428,138 +0.001428,138 +0.001586,138 +0.001448,138 +0.001775,138 +0.001582,138 +0.001572,138 +0.001489,138 +0.001526,138 +0.001542,138 +0.001500,138 +0.001429,138 +0.001462,138 +0.001708,138 +0.001428,138 +0.001802,138 +0.001744,138 +0.001468,138 +0.001454,138 +0.001551,138 +0.001566,138 +0.001428,138 +0.001448,138 +0.001684,138 +0.001488,138 +0.001535,138 +0.001780,138 +0.001649,138 +0.001484,138 +0.001455,138 +0.001677,138 +0.001542,138 +0.001429,138 +0.001722,138 +0.001618,138 +0.001505,138 +0.001809,138 +0.001637,138 +0.001648,138 +0.001510,138 +0.001488,138 +0.001589,138 +0.001429,138 +0.001472,138 +0.001452,138 +0.001738,138 +0.001428,138 +0.001784,138 +0.001685,138 +0.001426,138 +0.001426,138 +0.001519,138 +0.001512,138 +0.001563,140 +0.001492,140 +0.001726,140 +0.001577,140 +0.001791,140 +0.001657,140 +0.001654,140 +0.001508,140 +0.001534,140 +0.001586,140 +0.001572,140 +0.001492,140 +0.001492,140 +0.001694,140 +0.001491,140 +0.001866,140 +0.001774,140 +0.001491,140 +0.001550,140 +0.001545,140 +0.001579,140 +0.001511,140 +0.001491,140 +0.001779,140 +0.001515,140 +0.001853,140 +0.001671,140 +0.001677,140 +0.001491,140 +0.001491,140 +0.001635,140 +0.001491,140 +0.001491,140 +0.001702,140 +0.001624,140 +0.001690,140 +0.001754,140 +0.001662,140 +0.001551,140 +0.001553,140 +0.001698,140 +0.001552,140 +0.001530,140 +0.001492,140 +0.001767,140 +0.001529,140 +0.001832,140 +0.001804,140 +0.001491,140 +0.001536,140 +0.001573,140 +0.001594,140 +0.001522,140 +0.001492,140 +0.001757,140 +0.001588,140 +0.001795,140 +0.001798,140 +0.001491,140 +0.001553,140 +0.001522,140 +0.001627,140 +0.001520,140 +0.001492,140 +0.001721,140 +0.001573,140 +0.001679,140 +0.001630,140 +0.001491,140 +0.001491,140 +0.001515,140 +0.001663,140 +0.001605,140 +0.001488,140 +0.001488,140 +0.001664,140 +0.001777,140 +0.001624,140 +0.001492,140 +0.001653,140 +0.001681,140 +0.001615,140 +0.001893,140 +0.001503,140 +0.001758,140 +0.001751,140 +0.001726,140 +0.001625,140 +0.001786,140 +0.001747,140 +0.001649,140 +0.001676,140 +0.001830,140 +0.001711,140 +0.001648,140 +0.001767,140 +0.001934,140 +0.002862,140 +0.002059,140 +0.001580,140 +0.001746,142 +0.001996,142 +0.001840,142 +0.001968,142 +0.002185,142 +0.002980,142 +0.001803,142 +0.001790,142 +0.001804,142 +0.001690,142 +0.001770,142 +0.001839,142 +0.001808,142 +0.002382,142 +0.002844,142 +0.001718,142 +0.001732,142 +0.001741,142 +0.001729,142 +0.001723,142 +0.001685,142 +0.001658,142 +0.002594,142 +0.002747,142 +0.001830,142 +0.001847,142 +0.001883,142 +0.001670,142 +0.001867,142 +0.001723,142 +0.002894,142 +0.002569,142 +0.001765,142 +0.001787,142 +0.001901,142 +0.001879,142 +0.002013,142 +0.001895,142 +0.001922,142 +0.002034,142 +0.001923,142 +0.001942,142 +0.001998,142 +0.002005,142 +0.002019,142 +0.001986,142 +0.001897,142 +0.001892,142 +0.001736,142 +0.001796,142 +0.001669,142 +0.001709,142 +0.001752,142 +0.001864,142 +0.001761,142 +0.002032,142 +0.001679,142 +0.001722,142 +0.001687,142 +0.001759,142 +0.001791,142 +0.001981,142 +0.002008,142 +0.002015,142 +0.002084,142 +0.002184,142 +0.002038,142 +0.002001,142 +0.002046,142 +0.002055,142 +0.002038,142 +0.001952,142 +0.001788,142 +0.002505,142 +0.001885,142 +0.001688,142 +0.001738,142 +0.001726,142 +0.001853,142 +0.001762,142 +0.001856,142 +0.001809,142 +0.002486,142 +0.001766,142 +0.001758,142 +0.001725,142 +0.001789,142 +0.001824,142 +0.001703,142 +0.001824,142 +0.001721,142 +0.002387,142 +0.001682,142 +0.001762,142 +0.001794,142 +0.001795,142 +0.001745,142 +0.001700,142 +0.001879,142 +0.001720,142 +0.001862,144 +0.001783,144 +0.001818,144 +0.001788,144 +0.001835,144 +0.001743,144 +0.001714,144 +0.001984,144 +0.001873,144 +0.002296,144 +0.001929,144 +0.001804,144 +0.001860,144 +0.001873,144 +0.002026,144 +0.001922,144 +0.001990,144 +0.001850,144 +0.001841,144 +0.001818,144 +0.001828,144 +0.001869,144 +0.001881,144 +0.001881,144 +0.001819,144 +0.001855,144 +0.001772,144 +0.001820,144 +0.001894,144 +0.001840,144 +0.001848,144 +0.001992,144 +0.001875,144 +0.001749,144 +0.001878,144 +0.001840,144 +0.001868,144 +0.001814,144 +0.001870,144 +0.001820,144 +0.001867,144 +0.001851,144 +0.001843,144 +0.001905,144 +0.001859,144 +0.001851,144 +0.001825,144 +0.001843,144 +0.001842,144 +0.001934,144 +0.001805,144 +0.001837,144 +0.001922,144 +0.001871,144 +0.001777,144 +0.001845,144 +0.001885,144 +0.001735,144 +0.001769,144 +0.001764,144 +0.001813,144 +0.001879,144 +0.001738,144 +0.001768,144 +0.001809,144 +0.001720,144 +0.001778,144 +0.001797,144 +0.001730,144 +0.001760,144 +0.001766,144 +0.001806,144 +0.001822,144 +0.001879,144 +0.001857,144 +0.001858,144 +0.001913,144 +0.002014,144 +0.001948,144 +0.001844,144 +0.001948,144 +0.001865,144 +0.001881,144 +0.001819,144 +0.001908,144 +0.001920,144 +0.002060,144 +0.001885,144 +0.002011,144 +0.001915,144 +0.001939,144 +0.001870,144 +0.001824,144 +0.001755,144 +0.001816,144 +0.001959,144 +0.001760,144 +0.001881,144 +0.001774,144 +0.001748,144 +0.001905,146 +0.001885,146 +0.001791,146 +0.001961,146 +0.001898,146 +0.001862,146 +0.001960,146 +0.001887,146 +0.001832,146 +0.001839,146 +0.001875,146 +0.001855,146 +0.001900,146 +0.001870,146 +0.001909,146 +0.001862,146 +0.001840,146 +0.001859,146 +0.001834,146 +0.001819,146 +0.001862,146 +0.002148,146 +0.002027,146 +0.001807,146 +0.001939,146 +0.001817,146 +0.001863,146 +0.001835,146 +0.001857,146 +0.001835,146 +0.001915,146 +0.001869,146 +0.001875,146 +0.001886,146 +0.001841,146 +0.001889,146 +0.001834,146 +0.001888,146 +0.001857,146 +0.001886,146 +0.001835,146 +0.001885,146 +0.001837,146 +0.001852,146 +0.001886,146 +0.001918,146 +0.001821,146 +0.001919,146 +0.001934,146 +0.001846,146 +0.001958,146 +0.001918,146 +0.001878,146 +0.001852,146 +0.001881,146 +0.001852,146 +0.001906,146 +0.001880,146 +0.001850,146 +0.001868,146 +0.001860,146 +0.001854,146 +0.001806,146 +0.001794,146 +0.001779,146 +0.001919,146 +0.001855,146 +0.001830,146 +0.002055,146 +0.001954,146 +0.002077,146 +0.001872,146 +0.001821,146 +0.001880,146 +0.001840,146 +0.001889,146 +0.001818,146 +0.001952,146 +0.001826,146 +0.001766,146 +0.001839,146 +0.001794,146 +0.001780,146 +0.001905,146 +0.002034,146 +0.001896,146 +0.001952,146 +0.001833,146 +0.001926,146 +0.002057,146 +0.001924,146 +0.001887,146 +0.001996,146 +0.001829,146 +0.001916,146 +0.001874,146 +0.001916,146 +0.001858,146 +0.001760,146 +0.001866,146 +0.001911,148 +0.001937,148 +0.001896,148 +0.001991,148 +0.001954,148 +0.001922,148 +0.001847,148 +0.001874,148 +0.001895,148 +0.001870,148 +0.001988,148 +0.002018,148 +0.001926,148 +0.001982,148 +0.001928,148 +0.001948,148 +0.001908,148 +0.001924,148 +0.001959,148 +0.001879,148 +0.001966,148 +0.002189,148 +0.001985,148 +0.001938,148 +0.001946,148 +0.001902,148 +0.002000,148 +0.001996,148 +0.001961,148 +0.002127,148 +0.002068,148 +0.001933,148 +0.001979,148 +0.001960,148 +0.002116,148 +0.001997,148 +0.001877,148 +0.002011,148 +0.001897,148 +0.001895,148 +0.001912,148 +0.001844,148 +0.001869,148 +0.001946,148 +0.002006,148 +0.001886,148 +0.001975,148 +0.001852,148 +0.001875,148 +0.001893,148 +0.001875,148 +0.001826,148 +0.001950,148 +0.001973,148 +0.001922,148 +0.001887,148 +0.001872,148 +0.001906,148 +0.001862,148 +0.001892,148 +0.001886,148 +0.002109,148 +0.002104,148 +0.002171,148 +0.002114,148 +0.002102,148 +0.002161,148 +0.002132,148 +0.001975,148 +0.001950,148 +0.001905,148 +0.001915,148 +0.002150,148 +0.001955,148 +0.001946,148 +0.001897,148 +0.001895,148 +0.001987,148 +0.001925,148 +0.001853,148 +0.001973,148 +0.001946,148 +0.001916,148 +0.001968,148 +0.001909,148 +0.001935,148 +0.002010,148 +0.002004,148 +0.001991,148 +0.002028,148 +0.001887,148 +0.001935,148 +0.001936,148 +0.001911,148 +0.001951,148 +0.002074,148 +0.001929,148 +0.001922,148 +0.001936,148 +0.001940,148 +0.002027,150 +0.002057,150 +0.001981,150 +0.002110,150 +0.002039,150 +0.002057,150 +0.002001,150 +0.002028,150 +0.002001,150 +0.002032,150 +0.001992,150 +0.002110,150 +0.001971,150 +0.002019,150 +0.001990,150 +0.002015,150 +0.001988,150 +0.002021,150 +0.001989,150 +0.002062,150 +0.002077,150 +0.001940,150 +0.001878,150 +0.002521,150 +0.002403,150 +0.002418,150 +0.002415,150 +0.002567,150 +0.002108,150 +0.002078,150 +0.002005,150 +0.001971,150 +0.002000,150 +0.001971,150 +0.001997,150 +0.002000,150 +0.002029,150 +0.002118,150 +0.002058,150 +0.002057,150 +0.002034,150 +0.002066,150 +0.002027,150 +0.002163,150 +0.002074,150 +0.002055,150 +0.002094,150 +0.002064,150 +0.002016,150 +0.002077,150 +0.002030,150 +0.002068,150 +0.002005,150 +0.002058,150 +0.002059,150 +0.002117,150 +0.001977,150 +0.001992,150 +0.001878,150 +0.002084,150 +0.001979,150 +0.001900,150 +0.001888,150 +0.002066,150 +0.001897,150 +0.001901,150 +0.001878,150 +0.002055,150 +0.002006,150 +0.001984,150 +0.001986,150 +0.001984,150 +0.002203,150 +0.002178,150 +0.002021,150 +0.001956,150 +0.002305,150 +0.002120,150 +0.002166,150 +0.002037,150 +0.001950,150 +0.002068,150 +0.002040,150 +0.002059,150 +0.002266,150 +0.002048,150 +0.002175,150 +0.002061,150 +0.002094,150 +0.002019,150 +0.002019,150 +0.001992,150 +0.002071,150 +0.001998,150 +0.002128,150 +0.001998,150 +0.002015,150 +0.001990,150 +0.002015,150 +0.001970,150 +0.002200,152 +0.002076,152 +0.002105,152 +0.002039,152 +0.002095,152 +0.002090,152 +0.002091,152 +0.002069,152 +0.002131,152 +0.002110,152 +0.002183,152 +0.002061,152 +0.002054,152 +0.002089,152 +0.002094,152 +0.002085,152 +0.002159,152 +0.002121,152 +0.002076,152 +0.002097,152 +0.002164,152 +0.002036,152 +0.002078,152 +0.002105,152 +0.002139,152 +0.002058,152 +0.002102,152 +0.002118,152 +0.002106,152 +0.002109,152 +0.002084,152 +0.002113,152 +0.002190,152 +0.002055,152 +0.002096,152 +0.002005,152 +0.002036,152 +0.002107,152 +0.002181,152 +0.002116,152 +0.002285,152 +0.002039,152 +0.002262,152 +0.002090,152 +0.002231,152 +0.002144,152 +0.002184,152 +0.002273,152 +0.002246,152 +0.002231,152 +0.002192,152 +0.002114,152 +0.002050,152 +0.002106,152 +0.002111,152 +0.002076,152 +0.002286,152 +0.002248,152 +0.002134,152 +0.002184,152 +0.002176,152 +0.002189,152 +0.002162,152 +0.002302,152 +0.002142,152 +0.002109,152 +0.002065,152 +0.002287,152 +0.002049,152 +0.002108,152 +0.002177,152 +0.002280,152 +0.002104,152 +0.002209,152 +0.002108,152 +0.002147,152 +0.002118,152 +0.002184,152 +0.002196,152 +0.002164,152 +0.002194,152 +0.002148,152 +0.002143,152 +0.002141,152 +0.002147,152 +0.002101,152 +0.002256,152 +0.002117,152 +0.002181,152 +0.002088,152 +0.002180,152 +0.002101,152 +0.002134,152 +0.002111,152 +0.002216,152 +0.002035,152 +0.002099,152 +0.002077,152 +0.002105,152 +0.002024,152 +0.002205,154 +0.002190,154 +0.002186,154 +0.002065,154 +0.002048,154 +0.002059,154 +0.002026,154 +0.002009,154 +0.001975,154 +0.002009,154 +0.002163,154 +0.002015,154 +0.002106,154 +0.002094,154 +0.001976,154 +0.002104,154 +0.002224,154 +0.002124,154 +0.002059,154 +0.002012,154 +0.002226,154 +0.001976,154 +0.001998,154 +0.001976,154 +0.001989,154 +0.001985,154 +0.002102,154 +0.001976,154 +0.002004,154 +0.001975,154 +0.001980,154 +0.001975,154 +0.001976,154 +0.001998,154 +0.001995,154 +0.002019,154 +0.002007,154 +0.002143,154 +0.001982,154 +0.001975,154 +0.001977,154 +0.001975,154 +0.002017,154 +0.002015,154 +0.001980,154 +0.001975,154 +0.001978,154 +0.001976,154 +0.001975,154 +0.001980,154 +0.001976,154 +0.002051,154 +0.002339,154 +0.002092,154 +0.002002,154 +0.002347,154 +0.002136,154 +0.001975,154 +0.002238,154 +0.002441,154 +0.002197,154 +0.002141,154 +0.002148,154 +0.002398,154 +0.002253,154 +0.002308,154 +0.002461,154 +0.002718,154 +0.002731,154 +0.002189,154 +0.002179,154 +0.002139,154 +0.002173,154 +0.002120,154 +0.002183,154 +0.002250,154 +0.002336,154 +0.002298,154 +0.002206,154 +0.002207,154 +0.002210,154 +0.002277,154 +0.002222,154 +0.002231,154 +0.002267,154 +0.002106,154 +0.002195,154 +0.002223,154 +0.002300,154 +0.002120,154 +0.002334,154 +0.002182,154 +0.002288,154 +0.002189,154 +0.002181,154 +0.002210,154 +0.002194,154 +0.002154,154 +0.002150,154 +0.002142,154 +0.002376,156 +0.002262,156 +0.002311,156 +0.002263,156 +0.002213,156 +0.002254,156 +0.002220,156 +0.002106,156 +0.002391,156 +0.002241,156 +0.002224,156 +0.002339,156 +0.002249,156 +0.002301,156 +0.002222,156 +0.002229,156 +0.002243,156 +0.002346,156 +0.002434,156 +0.002223,156 +0.002353,156 +0.002201,156 +0.002275,156 +0.002206,156 +0.002239,156 +0.002356,156 +0.002366,156 +0.002641,156 +0.002381,156 +0.002473,156 +0.002343,156 +0.002298,156 +0.002497,156 +0.002293,156 +0.002359,156 +0.002295,156 +0.002125,156 +0.002263,156 +0.002106,156 +0.002339,156 +0.002133,156 +0.002147,156 +0.002106,156 +0.002135,156 +0.002081,156 +0.002091,156 +0.002085,156 +0.002130,156 +0.002126,156 +0.002204,156 +0.002221,156 +0.002126,156 +0.002280,156 +0.002198,156 +0.002085,156 +0.002255,156 +0.002091,156 +0.002327,156 +0.002051,156 +0.002094,156 +0.002051,156 +0.002077,156 +0.002052,156 +0.002180,156 +0.002051,156 +0.002089,156 +0.002052,156 +0.002074,156 +0.002052,156 +0.002077,156 +0.002051,156 +0.002152,156 +0.002051,156 +0.002076,156 +0.002104,156 +0.002080,156 +0.002051,156 +0.002227,156 +0.002463,156 +0.002595,156 +0.002532,156 +0.003101,156 +0.002759,156 +0.002161,156 +0.002417,156 +0.002332,156 +0.002852,156 +0.002693,156 +0.002307,156 +0.002412,156 +0.002374,156 +0.002192,156 +0.002388,156 +0.002278,156 +0.003178,156 +0.002101,156 +0.002126,156 +0.002054,156 +0.002092,156 +0.002539,156 +0.002303,158 +0.002466,158 +0.002339,158 +0.002641,158 +0.002272,158 +0.002744,158 +0.003238,158 +0.002335,158 +0.002136,158 +0.002323,158 +0.002201,158 +0.002193,158 +0.002135,158 +0.002461,158 +0.002361,158 +0.002260,158 +0.003240,158 +0.002305,158 +0.002172,158 +0.002209,158 +0.002263,158 +0.002313,158 +0.002137,158 +0.002317,158 +0.002133,158 +0.002175,158 +0.002191,158 +0.002377,158 +0.002175,158 +0.002267,158 +0.002179,158 +0.002133,158 +0.002176,158 +0.002133,158 +0.002209,158 +0.002266,158 +0.002210,158 +0.002161,158 +0.002142,158 +0.002178,158 +0.002133,158 +0.002160,158 +0.002271,158 +0.002217,158 +0.002173,158 +0.002162,158 +0.002133,158 +0.002167,158 +0.002149,158 +0.002142,158 +0.002248,158 +0.002133,158 +0.002205,158 +0.002133,158 +0.002195,158 +0.002154,158 +0.002170,158 +0.002215,158 +0.002360,158 +0.002375,158 +0.002395,158 +0.002297,158 +0.002173,158 +0.002307,158 +0.002133,158 +0.002237,158 +0.002158,158 +0.002175,158 +0.002201,158 +0.002134,158 +0.002160,158 +0.002134,158 +0.002178,158 +0.002211,158 +0.002206,158 +0.002133,158 +0.002575,158 +0.002161,158 +0.002392,158 +0.002265,158 +0.002695,158 +0.002399,158 +0.002348,158 +0.002369,158 +0.002395,158 +0.002360,158 +0.002311,158 +0.002464,158 +0.002301,158 +0.002392,158 +0.002272,158 +0.002316,158 +0.002278,158 +0.002309,158 +0.002581,158 +0.002331,158 +0.002421,158 +0.002307,158 +0.002320,158 +0.002327,158 +0.002463,160 +0.002505,160 +0.002359,160 +0.002524,160 +0.002461,160 +0.002479,160 +0.002418,160 +0.002422,160 +0.002452,160 +0.002601,160 +0.002474,160 +0.002475,160 +0.002478,160 +0.002396,160 +0.002523,160 +0.002472,160 +0.002613,160 +0.002480,160 +0.002518,160 +0.002428,160 +0.002499,160 +0.002458,160 +0.002499,160 +0.002613,160 +0.002459,160 +0.002426,160 +0.002437,160 +0.002506,160 +0.002578,160 +0.002446,160 +0.002623,160 +0.002540,160 +0.002366,160 +0.002348,160 +0.002400,160 +0.002920,160 +0.004547,160 +0.004423,160 +0.003569,160 +0.003106,160 +0.003154,160 +0.003011,160 +0.003072,160 +0.002556,160 +0.002439,160 +0.002655,160 +0.002619,160 +0.002688,160 +0.002485,160 +0.002435,160 +0.002441,160 +0.002513,160 +0.002632,160 +0.002688,160 +0.003292,160 +0.002384,160 +0.002356,160 +0.002372,160 +0.002708,160 +0.002480,160 +0.002963,160 +0.002525,160 +0.002414,160 +0.002482,160 +0.002506,160 +0.003104,160 +0.002652,160 +0.002795,160 +0.002947,160 +0.002402,160 +0.003490,160 +0.004557,160 +0.004375,160 +0.002576,160 +0.002360,160 +0.002570,160 +0.002459,160 +0.002533,160 +0.002415,160 +0.002338,160 +0.002298,160 +0.002332,160 +0.002609,160 +0.002467,160 +0.002602,160 +0.002552,160 +0.002393,160 +0.002369,160 +0.002540,160 +0.002677,160 +0.002618,160 +0.002612,160 +0.002328,160 +0.002444,160 +0.002353,160 +0.002467,160 +0.002377,160 +0.002676,160 +0.002682,160 +0.002423,160 +0.002458,162 +0.002465,162 +0.002565,162 +0.002438,162 +0.002644,162 +0.002481,162 +0.002587,162 +0.002390,162 +0.002430,162 +0.002528,162 +0.002642,162 +0.002521,162 +0.002361,162 +0.002344,162 +0.002378,162 +0.002534,162 +0.002318,162 +0.003067,162 +0.002505,162 +0.002380,162 +0.002328,162 +0.002320,162 +0.002513,162 +0.002474,162 +0.002453,162 +0.002954,162 +0.002338,162 +0.002295,162 +0.002423,162 +0.002627,162 +0.002587,162 +0.002435,162 +0.002342,162 +0.002335,162 +0.002330,162 +0.002354,162 +0.002589,162 +0.002554,162 +0.002455,162 +0.002357,162 +0.002449,162 +0.002420,162 +0.002573,162 +0.002431,162 +0.002588,162 +0.002398,162 +0.002329,162 +0.002333,162 +0.002294,162 +0.002598,162 +0.002323,162 +0.002690,162 +0.002464,162 +0.002294,162 +0.002771,162 +0.002616,162 +0.002931,162 +0.003634,162 +0.002846,162 +0.002458,162 +0.002573,162 +0.002642,162 +0.002514,162 +0.003737,162 +0.003512,162 +0.003035,162 +0.003066,162 +0.002736,162 +0.002737,162 +0.002603,162 +0.002509,162 +0.002611,162 +0.002552,162 +0.002661,162 +0.002711,162 +0.002889,162 +0.003110,162 +0.002515,162 +0.002469,162 +0.002588,162 +0.002489,162 +0.002732,162 +0.002544,162 +0.002478,162 +0.002470,162 +0.002426,162 +0.002709,162 +0.002556,162 +0.003016,162 +0.002833,162 +0.002612,162 +0.002586,162 +0.003024,162 +0.003874,162 +0.003492,162 +0.002413,162 +0.002456,162 +0.002437,162 +0.002531,162 +0.002685,162 +0.002841,164 +0.002593,164 +0.002665,164 +0.002604,164 +0.002649,164 +0.002738,164 +0.003488,164 +0.002777,164 +0.002709,164 +0.002529,164 +0.002603,164 +0.002617,164 +0.003292,164 +0.002670,164 +0.002666,164 +0.002505,164 +0.002738,164 +0.002864,164 +0.003250,164 +0.002514,164 +0.002488,164 +0.002493,164 +0.002708,164 +0.002615,164 +0.002986,164 +0.002846,164 +0.002503,164 +0.002438,164 +0.002594,164 +0.002479,164 +0.002857,164 +0.002583,164 +0.002393,164 +0.002433,164 +0.002428,164 +0.002610,164 +0.002759,164 +0.002656,164 +0.002452,164 +0.002440,164 +0.002392,164 +0.002609,164 +0.002540,164 +0.002820,164 +0.002591,164 +0.002432,164 +0.002392,164 +0.002440,164 +0.002621,164 +0.002605,164 +0.002709,164 +0.002562,164 +0.002392,164 +0.002479,164 +0.002531,164 +0.002717,164 +0.002825,164 +0.002509,164 +0.002443,164 +0.002438,164 +0.002413,164 +0.002588,164 +0.002580,164 +0.002837,164 +0.002538,164 +0.002570,164 +0.002403,164 +0.002497,164 +0.002969,164 +0.004485,164 +0.003401,164 +0.002712,164 +0.002849,164 +0.002621,164 +0.003173,164 +0.002910,164 +0.002450,164 +0.002395,164 +0.002477,164 +0.002771,164 +0.002645,164 +0.003699,164 +0.003640,164 +0.002623,164 +0.002579,164 +0.002465,164 +0.002700,164 +0.003043,164 +0.002441,164 +0.002434,164 +0.002557,164 +0.002601,164 +0.002718,164 +0.002494,164 +0.002504,164 +0.002392,164 +0.002434,164 +0.002742,164 +0.002516,164 +0.002553,164 +0.002738,166 +0.002476,166 +0.002514,166 +0.002703,166 +0.002657,166 +0.002698,166 +0.003604,166 +0.002634,166 +0.002706,166 +0.002551,166 +0.002656,166 +0.002929,166 +0.002677,166 +0.002507,166 +0.002471,166 +0.002623,166 +0.002824,166 +0.002874,166 +0.002632,166 +0.002579,166 +0.002471,166 +0.002507,166 +0.002705,166 +0.002622,166 +0.002675,166 +0.002678,166 +0.002513,166 +0.002505,166 +0.002617,166 +0.002702,166 +0.002998,166 +0.002612,166 +0.002503,166 +0.002504,166 +0.002470,166 +0.002719,166 +0.002926,166 +0.002678,166 +0.002527,166 +0.002514,166 +0.002471,166 +0.002740,166 +0.002619,166 +0.002670,166 +0.002584,166 +0.002524,166 +0.002471,166 +0.002555,166 +0.002610,166 +0.002841,166 +0.002664,166 +0.002538,166 +0.002503,166 +0.002506,166 +0.002670,166 +0.002847,166 +0.002579,166 +0.002567,166 +0.002508,166 +0.002510,166 +0.002541,166 +0.002613,166 +0.002932,166 +0.002606,166 +0.002507,166 +0.002521,166 +0.002587,166 +0.002757,166 +0.002953,166 +0.002857,166 +0.002527,166 +0.002512,166 +0.002471,166 +0.002696,166 +0.002884,166 +0.002576,166 +0.002886,166 +0.002597,166 +0.002490,166 +0.002935,166 +0.003359,166 +0.003268,166 +0.002690,166 +0.002614,166 +0.002847,166 +0.002813,166 +0.002894,166 +0.002733,166 +0.002573,166 +0.002665,166 +0.002583,166 +0.002776,166 +0.002903,166 +0.002703,166 +0.002711,166 +0.002610,166 +0.002714,166 +0.002732,166 +0.002941,166 +0.002962,166 +0.002736,168 +0.002825,168 +0.002639,168 +0.002875,168 +0.002828,168 +0.002788,168 +0.002643,168 +0.002624,168 +0.002544,168 +0.002716,168 +0.002653,168 +0.002544,168 +0.002551,168 +0.002544,168 +0.002881,168 +0.002690,168 +0.002870,168 +0.002913,168 +0.002768,168 +0.002799,168 +0.002712,168 +0.002900,168 +0.002896,168 +0.002720,168 +0.002800,168 +0.002811,168 +0.002858,168 +0.002821,168 +0.002969,168 +0.002816,168 +0.002808,168 +0.002847,168 +0.002900,168 +0.002948,168 +0.002776,168 +0.002771,168 +0.003002,168 +0.003304,168 +0.002708,168 +0.002777,168 +0.002802,168 +0.002781,168 +0.002704,168 +0.002751,168 +0.002722,168 +0.003114,168 +0.002848,168 +0.002933,168 +0.002750,168 +0.002655,168 +0.002786,168 +0.002758,168 +0.002819,168 +0.002703,168 +0.002546,168 +0.002857,168 +0.002661,168 +0.003118,168 +0.002598,168 +0.002592,168 +0.002546,168 +0.002840,168 +0.002623,168 +0.002816,168 +0.002566,168 +0.002572,168 +0.002546,168 +0.002573,168 +0.002557,168 +0.002585,168 +0.002585,168 +0.002764,168 +0.002634,168 +0.002619,168 +0.002578,168 +0.002627,168 +0.002832,168 +0.002795,168 +0.002843,168 +0.002642,168 +0.002729,168 +0.002546,168 +0.002848,168 +0.002600,168 +0.002840,168 +0.002853,168 +0.002670,168 +0.002753,168 +0.003022,168 +0.002839,168 +0.002700,168 +0.002935,168 +0.002957,168 +0.002801,168 +0.002843,168 +0.002698,168 +0.002752,168 +0.002640,168 +0.002613,168 +0.002647,168 +0.003061,170 +0.002651,170 +0.002658,170 +0.002652,170 +0.002647,170 +0.002654,170 +0.002785,170 +0.002689,170 +0.002653,170 +0.002655,170 +0.002646,170 +0.002654,170 +0.002727,170 +0.002850,170 +0.002827,170 +0.002848,170 +0.002685,170 +0.002646,170 +0.002706,170 +0.002687,170 +0.002646,170 +0.002678,170 +0.002681,170 +0.002695,170 +0.002732,170 +0.002667,170 +0.002646,170 +0.002651,170 +0.002661,170 +0.002646,170 +0.002715,170 +0.002683,170 +0.002646,170 +0.002788,170 +0.002699,170 +0.002647,170 +0.002671,170 +0.002750,170 +0.002646,170 +0.002657,170 +0.003080,170 +0.002791,170 +0.002717,170 +0.003166,170 +0.002987,170 +0.002883,170 +0.002937,170 +0.002889,170 +0.002878,170 +0.002980,170 +0.003034,170 +0.003052,170 +0.002931,170 +0.002900,170 +0.003430,170 +0.004351,170 +0.003347,170 +0.002914,170 +0.002895,170 +0.002961,170 +0.003166,170 +0.002951,170 +0.002805,170 +0.002811,170 +0.002858,170 +0.002897,170 +0.003924,170 +0.003026,170 +0.003066,170 +0.003075,170 +0.003396,170 +0.002965,170 +0.002926,170 +0.002870,170 +0.002842,170 +0.002817,170 +0.002862,170 +0.002790,170 +0.002856,170 +0.002864,170 +0.002897,170 +0.002913,170 +0.002899,170 +0.002927,170 +0.002776,170 +0.002737,170 +0.002863,170 +0.003196,170 +0.003169,170 +0.003174,170 +0.002972,170 +0.002853,170 +0.002820,170 +0.002859,170 +0.003361,170 +0.003052,170 +0.002939,170 +0.002847,170 +0.002919,170 +0.003103,170 +0.003902,172 +0.003090,172 +0.003185,172 +0.003100,172 +0.003481,172 +0.003511,172 +0.002919,172 +0.002885,172 +0.002846,172 +0.002990,172 +0.003973,172 +0.003140,172 +0.003148,172 +0.003481,172 +0.004020,172 +0.003712,172 +0.003309,172 +0.004044,172 +0.003654,172 +0.003374,172 +0.003559,172 +0.003092,172 +0.003741,172 +0.003325,172 +0.003688,172 +0.003125,172 +0.002883,172 +0.002962,172 +0.003089,172 +0.003673,172 +0.003146,172 +0.002918,172 +0.002874,172 +0.003277,172 +0.003582,172 +0.003203,172 +0.002840,172 +0.002826,172 +0.002969,172 +0.002873,172 +0.003742,172 +0.002978,172 +0.002747,172 +0.002790,172 +0.002956,172 +0.003446,172 +0.003046,172 +0.003076,172 +0.002815,172 +0.002822,172 +0.003267,172 +0.003442,172 +0.003169,172 +0.002880,172 +0.003011,172 +0.002947,172 +0.003491,172 +0.003078,172 +0.003057,172 +0.002833,172 +0.002914,172 +0.003242,172 +0.003967,172 +0.003268,172 +0.003196,172 +0.003737,172 +0.003576,172 +0.003445,172 +0.003383,172 +0.003298,172 +0.003517,172 +0.003472,172 +0.003764,172 +0.003244,172 +0.003295,172 +0.003393,172 +0.004356,172 +0.002991,172 +0.003097,172 +0.002999,172 +0.003230,172 +0.003457,172 +0.003304,172 +0.003088,172 +0.003121,172 +0.003199,172 +0.003288,172 +0.003158,172 +0.003051,172 +0.003034,172 +0.003097,172 +0.003490,172 +0.003527,172 +0.003157,172 +0.003086,172 +0.003062,172 +0.003758,172 +0.003198,172 +0.003024,172 +0.003026,172 +0.003241,174 +0.003326,174 +0.003523,174 +0.003166,174 +0.003049,174 +0.002951,174 +0.003015,174 +0.003492,174 +0.003125,174 +0.003071,174 +0.002934,174 +0.003152,174 +0.003262,174 +0.003171,174 +0.002934,174 +0.002902,174 +0.002950,174 +0.003223,174 +0.003100,174 +0.003020,174 +0.002920,174 +0.002898,174 +0.003007,174 +0.003383,174 +0.003026,174 +0.002891,174 +0.002854,174 +0.002931,174 +0.003208,174 +0.003114,174 +0.003021,174 +0.002915,174 +0.002917,174 +0.003070,174 +0.003445,174 +0.003060,174 +0.002881,174 +0.002894,174 +0.002915,174 +0.003362,174 +0.003250,174 +0.003025,174 +0.003080,174 +0.002871,174 +0.003250,174 +0.003490,174 +0.003080,174 +0.002888,174 +0.002854,174 +0.003048,174 +0.003322,174 +0.003161,174 +0.002920,174 +0.002912,174 +0.002892,174 +0.003085,174 +0.003400,174 +0.003015,174 +0.002890,174 +0.002886,174 +0.003020,174 +0.003468,174 +0.003093,174 +0.002877,174 +0.002899,174 +0.002854,174 +0.003218,174 +0.002946,174 +0.003106,174 +0.002854,174 +0.002877,174 +0.002981,174 +0.003005,174 +0.003079,174 +0.003046,174 +0.003034,174 +0.002933,174 +0.003010,174 +0.003004,174 +0.002890,174 +0.002854,174 +0.002896,174 +0.002927,174 +0.003026,174 +0.002854,174 +0.002879,174 +0.002907,174 +0.002924,174 +0.002894,174 +0.002987,174 +0.002896,174 +0.002855,174 +0.002856,174 +0.002856,174 +0.002995,174 +0.002946,174 +0.004948,174 +0.002848,174 +0.002884,174 +0.002914,174 +0.003203,176 +0.003099,176 +0.002981,176 +0.003032,176 +0.002989,176 +0.003070,176 +0.003019,176 +0.003216,176 +0.003142,176 +0.002963,176 +0.003031,176 +0.003067,176 +0.002967,176 +0.002943,176 +0.002967,176 +0.002990,176 +0.003060,176 +0.002943,176 +0.002949,176 +0.002953,176 +0.002950,176 +0.002994,176 +0.003031,176 +0.002969,176 +0.002945,176 +0.002943,176 +0.002947,176 +0.003173,176 +0.002968,176 +0.002944,176 +0.002946,176 +0.002950,176 +0.002985,176 +0.003058,176 +0.002969,176 +0.002945,176 +0.002946,176 +0.002943,176 +0.002997,176 +0.003061,176 +0.003302,176 +0.003073,176 +0.003229,176 +0.003052,176 +0.003085,176 +0.002981,176 +0.002943,176 +0.002989,176 +0.002990,176 +0.003089,176 +0.002975,176 +0.002985,176 +0.002972,176 +0.002969,176 +0.002983,176 +0.003100,176 +0.002970,176 +0.002974,176 +0.002973,176 +0.002974,176 +0.003029,176 +0.003057,176 +0.002944,176 +0.002946,176 +0.002946,176 +0.002983,176 +0.003064,176 +0.002967,176 +0.002949,176 +0.002943,176 +0.002946,176 +0.003116,176 +0.003328,176 +0.003176,176 +0.003190,176 +0.003030,176 +0.003068,176 +0.003127,176 +0.002944,176 +0.002978,176 +0.002968,176 +0.002979,176 +0.002988,176 +0.003028,176 +0.002983,176 +0.002976,176 +0.002943,176 +0.003021,176 +0.003105,176 +0.002970,176 +0.003105,176 +0.002968,176 +0.002970,176 +0.003030,176 +0.003230,176 +0.002944,176 +0.002966,176 +0.002977,176 +0.002982,176 +0.003142,176 +0.003227,178 +0.003164,178 +0.003159,178 +0.003164,178 +0.003305,178 +0.003147,178 +0.003396,178 +0.003352,178 +0.003144,178 +0.003265,178 +0.003232,178 +0.003124,178 +0.003167,178 +0.003149,178 +0.003172,178 +0.003259,178 +0.003167,178 +0.003154,178 +0.003137,178 +0.003170,178 +0.003277,178 +0.003146,178 +0.003123,178 +0.003121,178 +0.003156,178 +0.003296,178 +0.003127,178 +0.003123,178 +0.003121,178 +0.003126,178 +0.003172,178 +0.003277,178 +0.003134,178 +0.003121,178 +0.003148,178 +0.003178,178 +0.003252,178 +0.003293,178 +0.003244,178 +0.003292,178 +0.003203,178 +0.003303,178 +0.003163,178 +0.003120,178 +0.003144,178 +0.003205,178 +0.003268,178 +0.003182,178 +0.003121,178 +0.003144,178 +0.003146,178 +0.003319,178 +0.003147,178 +0.003180,178 +0.003282,178 +0.003147,178 +0.003277,178 +0.003407,178 +0.003121,178 +0.003155,178 +0.003144,178 +0.003228,178 +0.003333,178 +0.003121,178 +0.003161,178 +0.003155,178 +0.003195,178 +0.003336,178 +0.003121,178 +0.003438,178 +0.003315,178 +0.003203,178 +0.003288,178 +0.003128,178 +0.003120,178 +0.003143,178 +0.003150,178 +0.003320,178 +0.003161,178 +0.003120,178 +0.003125,178 +0.003127,178 +0.003172,178 +0.003242,178 +0.003126,178 +0.003123,178 +0.003132,178 +0.003182,178 +0.003343,178 +0.003130,178 +0.003122,178 +0.003124,178 +0.003168,178 +0.003281,178 +0.003143,178 +0.003134,178 +0.003125,178 +0.003134,178 +0.003321,178 +0.003504,178 +0.003532,180 +0.003527,180 +0.003495,180 +0.004005,180 +0.003884,180 +0.003513,180 +0.003805,180 +0.004142,180 +0.003700,180 +0.003624,180 +0.003559,180 +0.003563,180 +0.004337,180 +0.003487,180 +0.003685,180 +0.003598,180 +0.003867,180 +0.003445,180 +0.003491,180 +0.003522,180 +0.003481,180 +0.003945,180 +0.003953,180 +0.004146,180 +0.004174,180 +0.004212,180 +0.004009,180 +0.003485,180 +0.003538,180 +0.003646,180 +0.003549,180 +0.003461,180 +0.003395,180 +0.003463,180 +0.003542,180 +0.003426,180 +0.003518,180 +0.003413,180 +0.003602,180 +0.003509,180 +0.003408,180 +0.003412,180 +0.003377,180 +0.003336,180 +0.003671,180 +0.003293,180 +0.003453,180 +0.003358,180 +0.003344,180 +0.003603,180 +0.003481,180 +0.003429,180 +0.003489,180 +0.003376,180 +0.003597,180 +0.003199,180 +0.006071,180 +0.004131,180 +0.003369,180 +0.003196,180 +0.003210,180 +0.003194,180 +0.003199,180 +0.003336,180 +0.003196,180 +0.003194,180 +0.003187,180 +0.003171,180 +0.003301,180 +0.003201,180 +0.003163,180 +0.003162,180 +0.003171,180 +0.003267,180 +0.003166,180 +0.003167,180 +0.003166,180 +0.003159,180 +0.003270,180 +0.003200,180 +0.003164,180 +0.003162,180 +0.003159,180 +0.003192,180 +0.003267,180 +0.003193,180 +0.005630,180 +0.004376,180 +0.003275,180 +0.003530,180 +0.003186,180 +0.003178,180 +0.003557,180 +0.003336,180 +0.003194,180 +0.003186,180 +0.003168,180 +0.003224,180 +0.003370,180 +0.003219,180 +0.003419,182 +0.003360,182 +0.003445,182 +0.003421,182 +0.003299,182 +0.003305,182 +0.003301,182 +0.003343,182 +0.003424,182 +0.003325,182 +0.003298,182 +0.003322,182 +0.003373,182 +0.003489,182 +0.003304,182 +0.005269,182 +0.005044,182 +0.003425,182 +0.003322,182 +0.003903,182 +0.003365,182 +0.003537,182 +0.003340,182 +0.003298,182 +0.003336,182 +0.003341,182 +0.003955,182 +0.003324,182 +0.003321,182 +0.003531,182 +0.003343,182 +0.003573,182 +0.003330,182 +0.003325,182 +0.003301,182 +0.003342,182 +0.003532,182 +0.003298,182 +0.003303,182 +0.003549,182 +0.003413,182 +0.003438,182 +0.003696,182 +0.003524,182 +0.003702,182 +0.003760,182 +0.003347,182 +0.003355,182 +0.003342,182 +0.003384,182 +0.003610,182 +0.003367,182 +0.003298,182 +0.003330,182 +0.003324,182 +0.003480,182 +0.003303,182 +0.003301,182 +0.003298,182 +0.003307,182 +0.003458,182 +0.003303,182 +0.003301,182 +0.003303,182 +0.003298,182 +0.003439,182 +0.003310,182 +0.003300,182 +0.003303,182 +0.003300,182 +0.003435,182 +0.003303,182 +0.003391,182 +0.003518,182 +0.003521,182 +0.003498,182 +0.003325,182 +0.003298,182 +0.003301,182 +0.003323,182 +0.003512,182 +0.003333,182 +0.003322,182 +0.003591,182 +0.003476,182 +0.004173,182 +0.003645,182 +0.003635,182 +0.003644,182 +0.003882,182 +0.003617,182 +0.003687,182 +0.003340,182 +0.003958,182 +0.003804,182 +0.003327,182 +0.003628,182 +0.003332,182 +0.003860,182 +0.003440,182 +0.003478,184 +0.003872,184 +0.003574,184 +0.003834,184 +0.003615,184 +0.003471,184 +0.003375,184 +0.003846,184 +0.003612,184 +0.003411,184 +0.003410,184 +0.003546,184 +0.003638,184 +0.003450,184 +0.003373,184 +0.003526,184 +0.003471,184 +0.003868,184 +0.003409,184 +0.003431,184 +0.003712,184 +0.003757,184 +0.003919,184 +0.003743,184 +0.003877,184 +0.004446,184 +0.003781,184 +0.003494,184 +0.003574,184 +0.003515,184 +0.003843,184 +0.003487,184 +0.003726,184 +0.003475,184 +0.003640,184 +0.003964,184 +0.003477,184 +0.003568,184 +0.003411,184 +0.003638,184 +0.003699,184 +0.003571,184 +0.003672,184 +0.003516,184 +0.004054,184 +0.003407,184 +0.003674,184 +0.003867,184 +0.003679,184 +0.003599,184 +0.003693,184 +0.003736,184 +0.003553,184 +0.003677,184 +0.003643,184 +0.003409,184 +0.003831,184 +0.003547,184 +0.003797,184 +0.003437,184 +0.003663,184 +0.003375,184 +0.003873,184 +0.003873,184 +0.003577,184 +0.003461,184 +0.003798,184 +0.003677,184 +0.003596,184 +0.003566,184 +0.003559,184 +0.003469,184 +0.003993,184 +0.003479,184 +0.003687,184 +0.003701,184 +0.003874,184 +0.003523,184 +0.003456,184 +0.003757,184 +0.003408,184 +0.003917,184 +0.003623,184 +0.003624,184 +0.003523,184 +0.003855,184 +0.003613,184 +0.003494,184 +0.003663,184 +0.003490,184 +0.003807,184 +0.003417,184 +0.003416,184 +0.003683,184 +0.003648,184 +0.003582,184 +0.003410,184 +0.003647,184 +0.003441,184 +0.003741,184 +0.003845,186 +0.003610,186 +0.003840,186 +0.003755,186 +0.003996,186 +0.003626,186 +0.003662,186 +0.003616,186 +0.003837,186 +0.003807,186 +0.003575,186 +0.003698,186 +0.003855,186 +0.004090,186 +0.003746,186 +0.003654,186 +0.003662,186 +0.003753,186 +0.003679,186 +0.003729,186 +0.003555,186 +0.004084,186 +0.003842,186 +0.004042,186 +0.003867,186 +0.003646,186 +0.004074,186 +0.003782,186 +0.003805,186 +0.003689,186 +0.004057,186 +0.003623,186 +0.003747,186 +0.003948,186 +0.003816,186 +0.003689,186 +0.003701,186 +0.004021,186 +0.003745,186 +0.004078,186 +0.003749,186 +0.003831,186 +0.003884,186 +0.003938,186 +0.003788,186 +0.003805,186 +0.003843,186 +0.003815,186 +0.004775,186 +0.003963,186 +0.003874,186 +0.003864,186 +0.003969,186 +0.003972,186 +0.003923,186 +0.003896,186 +0.003969,186 +0.003879,186 +0.003893,186 +0.003916,186 +0.004147,186 +0.003865,186 +0.004189,186 +0.004018,186 +0.003830,186 +0.004140,186 +0.003803,186 +0.003855,186 +0.003847,186 +0.003834,186 +0.003831,186 +0.003836,186 +0.003793,186 +0.003835,186 +0.003768,186 +0.003816,186 +0.003799,186 +0.003921,186 +0.003870,186 +0.004070,186 +0.003696,186 +0.003704,186 +0.003752,186 +0.003701,186 +0.003696,186 +0.003698,186 +0.003802,186 +0.003829,186 +0.003843,186 +0.003912,186 +0.003834,186 +0.003880,186 +0.003977,186 +0.003990,186 +0.003975,186 +0.004196,186 +0.003918,186 +0.003972,186 +0.003786,186 +0.003989,186 +0.004024,188 +0.003897,188 +0.004031,188 +0.004214,188 +0.004064,188 +0.004241,188 +0.004052,188 +0.004212,188 +0.003884,188 +0.003797,188 +0.003846,188 +0.004174,188 +0.003773,188 +0.003844,188 +0.003915,188 +0.003933,188 +0.003868,188 +0.004128,188 +0.003906,188 +0.003799,188 +0.004139,188 +0.003761,188 +0.003768,188 +0.003649,188 +0.004111,188 +0.003630,188 +0.003623,188 +0.003623,188 +0.004186,188 +0.003697,188 +0.003625,188 +0.003631,188 +0.003623,188 +0.003940,188 +0.003590,188 +0.003624,188 +0.003612,188 +0.004065,188 +0.003658,188 +0.003619,188 +0.004117,188 +0.003771,188 +0.003812,188 +0.004109,188 +0.004308,188 +0.004025,188 +0.004218,188 +0.004310,188 +0.004067,188 +0.004055,188 +0.004184,188 +0.003942,188 +0.003944,188 +0.003933,188 +0.004197,188 +0.003830,188 +0.003792,188 +0.003786,188 +0.003824,188 +0.003799,188 +0.004284,188 +0.004693,188 +0.004667,188 +0.004699,188 +0.004437,188 +0.004234,188 +0.004512,188 +0.004764,188 +0.003925,188 +0.003896,188 +0.003828,188 +0.003627,188 +0.003622,188 +0.004032,188 +0.003930,188 +0.003808,188 +0.003687,188 +0.003625,188 +0.004004,188 +0.004522,188 +0.003834,188 +0.003986,188 +0.003676,188 +0.004082,188 +0.003910,188 +0.003707,188 +0.004000,188 +0.003937,188 +0.003630,188 +0.003981,188 +0.004197,188 +0.004261,188 +0.004293,188 +0.003882,188 +0.003632,188 +0.003609,188 +0.003895,188 +0.003628,188 +0.003638,188 +0.003625,188 +0.004031,190 +0.003732,190 +0.003713,190 +0.004069,190 +0.003967,190 +0.003814,190 +0.003748,190 +0.003742,190 +0.003794,190 +0.003921,190 +0.003743,190 +0.003948,190 +0.003822,190 +0.003917,190 +0.004039,190 +0.003837,190 +0.003886,190 +0.004334,190 +0.004670,190 +0.003918,190 +0.003767,190 +0.003926,190 +0.004045,190 +0.003812,190 +0.003883,190 +0.004148,190 +0.003789,190 +0.003733,190 +0.003982,190 +0.003831,190 +0.004218,190 +0.003887,190 +0.004065,190 +0.003829,190 +0.004073,190 +0.003854,190 +0.003864,190 +0.004040,190 +0.003908,190 +0.003708,190 +0.003750,190 +0.003847,190 +0.003919,190 +0.004953,190 +0.003872,190 +0.003915,190 +0.003805,190 +0.003935,190 +0.003760,190 +0.003736,190 +0.003736,190 +0.003952,190 +0.003751,190 +0.003966,190 +0.003744,190 +0.004105,190 +0.004057,190 +0.003848,190 +0.004103,190 +0.004007,190 +0.003991,190 +0.003958,190 +0.003858,190 +0.003898,190 +0.004309,190 +0.003779,190 +0.004400,190 +0.003842,190 +0.004690,190 +0.004212,190 +0.003952,190 +0.003825,190 +0.004132,190 +0.003949,190 +0.003970,190 +0.003901,190 +0.004336,190 +0.004022,190 +0.004203,190 +0.004286,190 +0.004137,190 +0.003975,190 +0.004159,190 +0.004018,190 +0.004249,190 +0.003971,190 +0.004063,190 +0.004069,190 +0.004161,190 +0.004036,190 +0.004065,190 +0.004090,190 +0.004051,190 +0.005002,190 +0.004184,190 +0.004001,190 +0.004155,190 +0.004062,190 +0.004114,190 +0.003998,190 +0.004504,192 +0.004226,192 +0.004231,192 +0.004154,192 +0.004391,192 +0.004256,192 +0.004164,192 +0.004621,192 +0.004542,192 +0.004177,192 +0.004269,192 +0.004290,192 +0.004861,192 +0.004628,192 +0.004849,192 +0.004740,192 +0.005128,192 +0.004511,192 +0.004285,192 +0.004344,192 +0.004368,192 +0.004324,192 +0.004270,192 +0.004247,192 +0.004214,192 +0.004177,192 +0.004196,192 +0.004271,192 +0.004291,192 +0.004231,192 +0.004307,192 +0.004301,192 +0.004323,192 +0.004325,192 +0.004395,192 +0.004233,192 +0.004210,192 +0.004187,192 +0.004353,192 +0.004866,192 +0.004385,192 +0.004047,192 +0.004525,192 +0.003945,192 +0.004156,192 +0.004179,192 +0.004386,192 +0.003930,192 +0.004117,192 +0.004327,192 +0.004368,192 +0.004014,192 +0.003910,192 +0.003904,192 +0.004190,192 +0.003906,192 +0.003925,192 +0.004126,192 +0.004216,192 +0.003886,192 +0.004132,192 +0.003998,192 +0.004251,192 +0.004098,192 +0.004112,192 +0.004504,192 +0.004272,192 +0.003909,192 +0.004141,192 +0.003941,192 +0.004337,192 +0.003940,192 +0.004117,192 +0.003910,192 +0.004424,192 +0.003919,192 +0.003898,192 +0.003902,192 +0.004022,192 +0.004072,192 +0.004431,192 +0.003967,192 +0.003941,192 +0.004591,192 +0.003937,192 +0.003917,192 +0.004209,192 +0.004130,192 +0.004293,192 +0.004051,192 +0.003910,192 +0.004307,192 +0.004201,192 +0.004005,192 +0.003908,192 +0.004203,192 +0.003900,192 +0.003901,192 +0.003943,192 +0.004501,192 +0.004094,194 +0.003974,194 +0.003975,194 +0.004121,194 +0.003976,194 +0.003980,194 +0.004015,194 +0.004034,194 +0.003976,194 +0.003973,194 +0.004004,194 +0.004086,194 +0.004075,194 +0.004420,194 +0.004343,194 +0.004312,194 +0.004001,194 +0.004387,194 +0.004344,194 +0.004544,194 +0.004207,194 +0.004339,194 +0.004008,194 +0.004578,194 +0.004317,194 +0.004009,194 +0.004012,194 +0.004546,194 +0.004054,194 +0.004310,194 +0.004004,194 +0.004506,194 +0.004113,194 +0.004008,194 +0.004088,194 +0.004520,194 +0.004227,194 +0.004167,194 +0.004084,194 +0.004735,194 +0.004056,194 +0.004024,194 +0.004008,194 +0.004922,194 +0.004059,194 +0.004162,194 +0.004479,194 +0.004472,194 +0.004063,194 +0.004017,194 +0.004182,194 +0.004476,194 +0.004032,194 +0.004005,194 +0.004184,194 +0.004252,194 +0.004021,194 +0.004021,194 +0.004307,194 +0.004103,194 +0.004144,194 +0.004259,194 +0.004192,194 +0.004050,194 +0.003998,194 +0.004037,194 +0.004022,194 +0.004178,194 +0.003980,194 +0.003993,194 +0.003995,194 +0.004106,194 +0.004053,194 +0.003975,194 +0.003972,194 +0.004192,194 +0.003993,194 +0.004004,194 +0.003973,194 +0.004068,194 +0.003973,194 +0.003975,194 +0.003972,194 +0.004128,194 +0.003974,194 +0.004098,194 +0.004575,194 +0.004296,194 +0.004130,194 +0.004183,194 +0.004120,194 +0.004470,194 +0.004030,194 +0.004261,194 +0.004005,194 +0.004232,194 +0.004353,194 +0.004020,194 +0.004014,194 +0.004370,194 +0.004545,196 +0.004109,196 +0.004114,196 +0.004780,196 +0.004173,196 +0.004120,196 +0.004174,196 +0.004525,196 +0.004153,196 +0.004320,196 +0.004240,196 +0.004641,196 +0.004273,196 +0.004153,196 +0.004230,196 +0.005091,196 +0.004129,196 +0.004116,196 +0.004529,196 +0.004654,196 +0.004161,196 +0.004103,196 +0.004477,196 +0.004167,196 +0.004105,196 +0.004087,196 +0.004363,196 +0.004107,196 +0.004086,196 +0.004084,196 +0.004302,196 +0.004159,196 +0.004212,196 +0.004335,196 +0.004361,196 +0.004112,196 +0.004103,196 +0.004086,196 +0.004496,196 +0.004112,196 +0.004112,196 +0.004083,196 +0.004287,196 +0.004234,196 +0.004107,196 +0.004129,196 +0.004353,196 +0.004115,196 +0.004112,196 +0.004107,196 +0.004223,196 +0.004106,196 +0.004081,196 +0.004080,196 +0.004291,196 +0.004178,196 +0.004245,196 +0.004458,196 +0.004203,196 +0.004119,196 +0.004101,196 +0.004108,196 +0.004204,196 +0.004112,196 +0.004143,196 +0.004096,196 +0.004264,196 +0.004084,196 +0.004080,196 +0.004083,196 +0.004164,196 +0.004152,196 +0.004085,196 +0.004126,196 +0.004152,196 +0.004085,196 +0.004088,196 +0.004084,196 +0.004290,196 +0.004087,196 +0.004122,196 +0.004348,196 +0.004431,196 +0.004117,196 +0.004116,196 +0.004105,196 +0.004325,196 +0.004107,196 +0.004109,196 +0.004101,196 +0.004195,196 +0.004197,196 +0.004107,196 +0.004083,196 +0.004143,196 +0.004084,196 +0.004081,196 +0.004082,196 +0.004170,196 +0.004112,196 +0.004318,198 +0.004213,198 +0.004337,198 +0.004214,198 +0.004221,198 +0.004428,198 +0.004661,198 +0.004246,198 +0.004222,198 +0.004220,198 +0.004276,198 +0.004216,198 +0.004216,198 +0.004216,198 +0.004276,198 +0.004217,198 +0.004213,198 +0.004215,198 +0.004296,198 +0.004217,198 +0.004212,198 +0.004212,198 +0.004280,198 +0.004213,198 +0.004212,198 +0.004426,198 +0.004250,198 +0.004213,198 +0.004275,198 +0.004559,198 +0.004351,198 +0.004217,198 +0.004215,198 +0.004253,198 +0.004269,198 +0.004281,198 +0.004236,198 +0.004277,198 +0.004218,198 +0.004223,198 +0.004214,198 +0.004282,198 +0.004261,198 +0.004236,198 +0.004212,198 +0.004287,198 +0.004214,198 +0.004212,198 +0.004216,198 +0.004355,198 +0.004310,198 +0.004226,198 +0.004401,198 +0.004622,198 +0.004228,198 +0.004243,198 +0.004255,198 +0.004280,198 +0.004212,198 +0.004213,198 +0.004215,198 +0.004380,198 +0.004283,198 +0.004212,198 +0.004255,198 +0.004258,198 +0.004219,198 +0.004212,198 +0.004250,198 +0.004269,198 +0.004219,198 +0.004212,198 +0.004329,198 +0.004275,198 +0.004237,198 +0.004275,198 +0.004463,198 +0.004471,198 +0.004213,198 +0.004217,198 +0.004276,198 +0.004217,198 +0.004242,198 +0.004213,198 +0.004380,198 +0.004281,198 +0.004233,198 +0.004236,198 +0.004297,198 +0.004251,198 +0.004215,198 +0.004216,198 +0.004283,198 +0.004217,198 +0.004213,198 +0.004256,198 +0.004317,198 +0.004218,198 +0.004213,198 +0.004384,198 +0.004875,200 +0.004366,200 +0.004361,200 +0.004399,200 +0.004415,200 +0.004386,200 +0.004407,200 +0.004432,200 +0.004415,200 +0.004395,200 +0.004359,200 +0.004429,200 +0.004360,200 +0.004360,200 +0.004363,200 +0.004422,200 +0.004364,200 +0.004360,200 +0.004365,200 +0.004492,200 +0.004363,200 +0.004359,200 +0.004645,200 +0.004694,200 +0.004384,200 +0.004401,200 +0.004458,200 +0.004390,200 +0.004361,200 +0.004362,200 +0.004420,200 +0.004363,200 +0.004360,200 +0.004362,200 +0.004421,200 +0.004365,200 +0.004360,200 +0.004395,200 +0.004394,200 +0.004364,200 +0.004419,200 +0.004473,200 +0.004394,200 +0.004363,200 +0.004360,200 +0.004659,200 +0.004696,200 +0.004363,200 +0.004363,200 +0.004435,200 +0.004360,200 +0.004365,200 +0.004362,200 +0.004423,200 +0.004365,200 +0.004360,200 +0.004391,200 +0.004401,200 +0.004360,200 +0.004360,200 +0.004427,200 +0.004361,200 +0.004364,200 +0.004360,200 +0.004512,200 +0.004462,200 +0.004412,200 +0.004441,200 +0.004719,200 +0.004610,200 +0.004381,200 +0.004391,200 +0.004394,200 +0.004364,200 +0.004359,200 +0.004427,200 +0.004363,200 +0.004368,200 +0.004362,200 +0.004423,200 +0.004364,200 +0.004360,200 +0.004360,200 +0.004427,200 +0.004361,200 +0.004359,200 +0.004365,200 +0.004485,200 +0.004360,200 +0.004359,200 +0.004434,200 +0.004607,200 +0.004493,200 +0.004360,200 +0.004424,200 +0.004388,200 +0.004379,200 +0.004362,200 +0.004463,200 +0.004364,200 +0.004613,202 +0.004510,202 +0.004569,202 +0.004569,202 +0.004556,202 +0.004572,202 +0.004568,202 +0.004506,202 +0.004510,202 +0.004647,202 +0.004511,202 +0.004512,202 +0.004506,202 +0.004837,202 +0.004759,202 +0.004527,202 +0.004569,202 +0.004513,202 +0.004506,202 +0.004507,202 +0.004567,202 +0.004573,202 +0.004506,202 +0.004505,202 +0.004572,202 +0.004508,202 +0.004508,202 +0.004534,202 +0.004607,202 +0.004505,202 +0.004505,202 +0.004670,202 +0.004512,202 +0.004506,202 +0.004507,202 +0.004731,202 +0.004904,202 +0.004541,202 +0.004570,202 +0.004554,202 +0.004550,202 +0.004508,202 +0.004588,202 +0.004510,202 +0.004506,202 +0.004534,202 +0.004548,202 +0.004505,202 +0.004509,202 +0.004566,202 +0.004510,202 +0.004506,202 +0.004505,202 +0.004651,202 +0.004515,202 +0.004506,202 +0.004507,202 +0.004745,202 +0.004779,202 +0.004541,202 +0.005156,202 +0.004703,202 +0.004594,202 +0.004549,202 +0.004622,202 +0.004536,202 +0.004507,202 +0.004540,202 +0.004541,202 +0.004506,202 +0.004577,202 +0.004567,202 +0.004510,202 +0.004508,202 +0.004508,202 +0.004650,202 +0.004569,202 +0.004506,202 +0.004534,202 +0.004766,202 +0.004821,202 +0.004531,202 +0.004595,202 +0.004530,202 +0.004506,202 +0.004537,202 +0.004541,202 +0.004552,202 +0.004505,202 +0.004571,202 +0.004506,202 +0.004541,202 +0.004512,202 +0.004737,202 +0.004575,202 +0.005103,202 +0.004676,202 +0.004671,202 +0.004511,202 +0.004506,202 +0.005009,204 +0.004842,204 +0.004876,204 +0.004731,204 +0.004710,204 +0.004678,204 +0.004683,204 +0.004779,204 +0.004634,204 +0.004630,204 +0.004762,204 +0.004729,204 +0.004662,204 +0.004660,204 +0.004727,204 +0.004658,204 +0.004705,204 +0.004630,204 +0.004776,204 +0.004630,204 +0.004630,204 +0.004693,204 +0.004734,204 +0.004899,204 +0.004656,204 +0.004711,204 +0.004653,204 +0.004658,204 +0.004669,204 +0.004662,204 +0.004720,204 +0.004629,204 +0.004696,204 +0.004633,204 +0.004635,204 +0.004657,204 +0.004666,204 +0.004630,204 +0.004630,204 +0.004703,204 +0.004710,204 +0.004629,204 +0.004632,204 +0.004732,204 +0.004913,204 +0.004954,204 +0.004754,204 +0.004660,204 +0.004650,204 +0.004663,204 +0.004727,204 +0.004678,204 +0.004629,204 +0.004697,204 +0.004631,204 +0.004630,204 +0.004633,204 +0.004696,204 +0.004629,204 +0.004630,204 +0.004660,204 +0.004747,204 +0.004632,204 +0.004634,204 +0.004871,204 +0.004808,204 +0.004954,204 +0.004905,204 +0.004718,204 +0.004630,204 +0.004633,204 +0.004883,204 +0.004657,204 +0.004652,204 +0.004680,204 +0.004664,204 +0.004670,204 +0.004635,204 +0.004735,204 +0.004636,204 +0.004629,204 +0.004642,204 +0.004760,204 +0.004714,204 +0.004629,204 +0.004696,204 +0.004633,204 +0.004911,204 +0.004861,204 +0.004721,204 +0.004634,204 +0.004653,204 +0.004802,204 +0.004630,204 +0.004630,204 +0.004633,204 +0.004692,204 +0.004636,204 +0.004629,204 +0.004660,204 +0.004924,206 +0.004774,206 +0.004782,206 +0.004954,206 +0.004774,206 +0.004768,206 +0.004833,206 +0.004776,206 +0.005023,206 +0.005055,206 +0.004881,206 +0.004827,206 +0.004799,206 +0.004937,206 +0.004790,206 +0.004772,206 +0.004799,206 +0.004842,206 +0.004774,206 +0.004841,206 +0.004854,206 +0.004783,206 +0.004769,206 +0.004809,206 +0.004883,206 +0.004772,206 +0.004780,206 +0.004834,206 +0.004769,206 +0.005048,206 +0.005067,206 +0.004833,206 +0.004809,206 +0.004795,206 +0.004867,206 +0.004885,206 +0.004772,206 +0.004829,206 +0.004773,206 +0.004769,206 +0.004774,206 +0.004830,206 +0.004772,206 +0.004769,206 +0.004840,206 +0.004875,206 +0.004769,206 +0.004771,206 +0.004831,206 +0.004773,206 +0.005113,206 +0.007995,206 +0.008452,206 +0.008079,206 +0.004899,206 +0.004804,206 +0.004890,206 +0.004867,206 +0.004817,206 +0.004849,206 +0.004793,206 +0.004769,206 +0.004773,206 +0.004853,206 +0.004848,206 +0.004771,206 +0.004855,206 +0.004816,206 +0.004872,206 +0.005138,206 +0.004869,206 +0.004817,206 +0.004909,206 +0.004867,206 +0.004769,206 +0.004772,206 +0.004822,206 +0.004817,206 +0.004771,206 +0.004769,206 +0.004853,206 +0.004775,206 +0.004769,206 +0.004810,206 +0.004889,206 +0.004830,206 +0.004773,206 +0.004847,206 +0.004771,206 +0.004953,206 +0.005091,206 +0.004828,206 +0.004772,206 +0.004789,206 +0.004878,206 +0.004794,206 +0.004769,206 +0.004853,206 +0.004769,206 +0.004771,206 +0.005036,208 +0.005039,208 +0.004925,208 +0.004919,208 +0.005021,208 +0.005021,208 +0.004919,208 +0.004978,208 +0.004968,208 +0.004918,208 +0.005219,208 +0.005136,208 +0.004977,208 +0.005095,208 +0.005023,208 +0.004945,208 +0.004943,208 +0.005017,208 +0.004997,208 +0.004923,208 +0.004930,208 +0.005022,208 +0.004922,208 +0.004961,208 +0.004998,208 +0.004979,208 +0.004918,208 +0.004960,208 +0.004986,208 +0.004919,208 +0.005191,208 +0.005119,208 +0.004947,208 +0.004944,208 +0.004981,208 +0.004919,208 +0.005006,208 +0.004949,208 +0.004951,208 +0.004922,208 +0.004920,208 +0.004983,208 +0.004919,208 +0.004918,208 +0.004981,208 +0.005008,208 +0.004927,208 +0.004949,208 +0.004953,208 +0.004924,208 +0.005130,208 +0.005277,208 +0.004958,208 +0.004919,208 +0.005014,208 +0.004946,208 +0.004918,208 +0.004952,208 +0.004955,208 +0.004919,208 +0.004920,208 +0.004986,208 +0.004918,208 +0.004918,208 +0.004971,208 +0.004995,208 +0.004938,208 +0.005102,208 +0.005016,208 +0.004951,208 +0.005049,208 +0.005315,208 +0.004940,208 +0.004971,208 +0.005001,208 +0.004947,208 +0.004945,208 +0.004969,208 +0.005006,208 +0.004923,208 +0.004919,208 +0.004984,208 +0.004922,208 +0.004919,208 +0.004948,208 +0.005040,208 +0.005027,208 +0.004921,208 +0.004980,208 +0.004925,208 +0.004918,208 +0.005315,208 +0.005033,208 +0.004925,208 +0.004946,208 +0.004956,208 +0.004919,208 +0.004922,208 +0.004980,208 +0.004922,208 +0.005214,210 +0.005162,210 +0.005099,210 +0.005105,210 +0.005186,210 +0.005162,210 +0.005276,210 +0.005236,210 +0.005176,210 +0.005095,210 +0.005244,210 +0.005476,210 +0.005100,210 +0.005196,210 +0.005180,210 +0.005102,210 +0.005095,210 +0.005179,210 +0.005141,210 +0.005170,210 +0.005148,210 +0.005152,210 +0.005102,210 +0.005099,210 +0.005162,210 +0.005164,210 +0.005137,210 +0.005179,210 +0.005100,210 +0.005098,210 +0.005395,210 +0.005238,210 +0.005161,210 +0.005177,210 +0.005125,210 +0.005229,210 +0.005146,210 +0.005129,210 +0.005099,210 +0.005098,210 +0.005160,210 +0.005096,210 +0.005100,210 +0.005157,210 +0.005181,210 +0.005095,210 +0.005163,210 +0.005100,210 +0.005097,210 +0.005175,210 +0.005415,210 +0.005359,210 +0.005202,210 +0.005224,210 +0.005125,210 +0.005177,210 +0.005315,210 +0.005119,210 +0.005096,210 +0.005162,210 +0.005102,210 +0.005095,210 +0.005125,210 +0.005134,210 +0.005175,210 +0.005097,210 +0.005196,210 +0.005098,210 +0.005097,210 +0.005353,210 +0.005342,210 +0.005119,210 +0.005177,210 +0.005102,210 +0.005146,210 +0.005160,210 +0.005101,210 +0.005107,210 +0.005126,210 +0.005128,210 +0.005100,210 +0.005098,210 +0.005166,210 +0.005230,210 +0.005131,210 +0.005158,210 +0.005099,210 +0.005097,210 +0.005200,210 +0.005421,210 +0.005113,210 +0.005148,210 +0.005129,210 +0.005099,210 +0.005100,210 +0.005155,210 +0.005172,210 +0.005104,210 +0.005160,210 +0.005100,210 +0.005338,212 +0.005299,212 +0.005295,212 +0.005210,212 +0.005338,212 +0.005213,212 +0.005208,212 +0.005261,212 +0.005489,212 +0.005501,212 +0.005398,212 +0.005309,212 +0.005229,212 +0.005254,212 +0.005347,212 +0.005216,212 +0.005218,212 +0.005280,212 +0.005212,212 +0.005255,212 +0.005271,212 +0.005316,212 +0.005210,212 +0.005294,212 +0.005210,212 +0.005210,212 +0.005296,212 +0.005481,212 +0.005432,212 +0.005325,212 +0.005243,212 +0.005295,212 +0.005212,212 +0.005296,212 +0.005209,212 +0.005213,212 +0.005270,212 +0.005212,212 +0.005210,212 +0.005275,212 +0.005297,212 +0.005215,212 +0.005271,212 +0.005213,212 +0.005209,212 +0.005241,212 +0.005435,212 +0.005482,212 +0.005306,212 +0.005241,212 +0.005210,212 +0.005216,212 +0.005293,212 +0.005209,212 +0.005214,212 +0.005270,212 +0.005212,212 +0.005214,212 +0.005270,212 +0.005257,212 +0.005216,212 +0.005388,212 +0.005245,212 +0.005221,212 +0.005250,212 +0.005424,212 +0.005478,212 +0.005264,212 +0.005265,212 +0.005257,212 +0.005250,212 +0.005272,212 +0.005208,212 +0.005213,212 +0.005271,212 +0.005214,212 +0.005270,212 +0.005321,212 +0.005319,212 +0.005250,212 +0.005280,212 +0.005211,212 +0.005216,212 +0.005238,212 +0.005358,212 +0.005522,212 +0.005261,212 +0.005268,212 +0.005213,212 +0.005252,212 +0.005271,212 +0.005213,212 +0.005221,212 +0.005293,212 +0.005210,212 +0.005214,212 +0.005291,212 +0.005254,212 +0.005251,212 +0.005415,212 +0.005511,214 +0.005377,214 +0.005431,214 +0.005497,214 +0.005634,214 +0.005582,214 +0.005380,214 +0.005369,214 +0.005434,214 +0.005454,214 +0.005416,214 +0.005450,214 +0.005415,214 +0.005371,214 +0.005402,214 +0.005410,214 +0.005471,214 +0.005407,214 +0.005401,214 +0.005369,214 +0.005376,214 +0.005434,214 +0.005608,214 +0.005504,214 +0.005458,214 +0.005459,214 +0.005456,214 +0.005460,214 +0.005475,214 +0.005412,214 +0.005440,214 +0.005371,214 +0.005371,214 +0.005431,214 +0.005435,214 +0.005369,214 +0.005473,214 +0.005393,214 +0.005372,214 +0.005430,214 +0.005473,214 +0.005797,214 +0.005643,214 +0.005410,214 +0.005420,214 +0.005513,214 +0.005400,214 +0.005405,214 +0.005477,214 +0.005369,214 +0.005369,214 +0.005436,214 +0.005374,214 +0.005494,214 +0.005534,214 +0.005442,214 +0.005402,214 +0.005645,214 +0.005529,214 +0.005776,214 +0.005501,214 +0.005429,214 +0.005412,214 +0.005443,214 +0.005445,214 +0.005392,214 +0.005399,214 +0.005408,214 +0.005370,214 +0.005399,214 +0.005412,214 +0.005515,214 +0.005474,214 +0.005406,214 +0.005369,214 +0.005374,214 +0.005431,214 +0.005568,214 +0.005725,214 +0.005470,214 +0.005413,214 +0.005427,214 +0.005471,214 +0.005412,214 +0.005399,214 +0.005446,214 +0.005378,214 +0.005411,214 +0.005457,214 +0.005401,214 +0.005452,214 +0.005452,214 +0.005376,214 +0.005369,214 +0.005473,214 +0.005397,214 +0.005785,214 +0.005732,214 +0.005391,214 +0.005625,214 +0.006151,216 +0.005788,216 +0.006171,216 +0.006296,216 +0.006094,216 +0.006567,216 +0.008187,216 +0.006341,216 +0.006257,216 +0.006222,216 +0.006249,216 +0.006635,216 +0.007265,216 +0.006322,216 +0.006406,216 +0.006345,216 +0.006161,216 +0.006079,216 +0.007007,216 +0.006613,216 +0.006141,216 +0.006247,216 +0.006074,216 +0.007351,216 +0.005990,216 +0.006103,216 +0.007244,216 +0.007006,216 +0.008089,216 +0.006477,216 +0.007051,216 +0.007433,216 +0.007063,216 +0.006501,216 +0.006232,216 +0.006415,216 +0.006916,216 +0.007117,216 +0.007403,216 +0.006350,216 +0.007760,216 +0.006184,216 +0.005968,216 +0.007188,216 +0.006074,216 +0.007077,216 +0.005790,216 +0.006115,216 +0.008246,216 +0.007490,216 +0.007457,216 +0.005645,216 +0.006889,216 +0.006281,216 +0.006042,216 +0.006582,216 +0.006166,216 +0.006802,216 +0.006558,216 +0.006041,216 +0.006568,216 +0.006179,216 +0.006179,216 +0.006787,216 +0.007046,216 +0.008044,216 +0.006161,216 +0.006380,216 +0.006220,216 +0.005972,216 +0.007988,216 +0.006318,216 +0.007219,216 +0.007577,216 +0.007820,216 +0.006773,216 +0.006201,216 +0.006750,216 +0.006430,216 +0.006074,216 +0.006347,216 +0.005806,216 +0.006344,216 +0.006285,216 +0.006094,216 +0.006686,216 +0.005977,216 +0.005836,216 +0.006300,216 +0.007047,216 +0.006276,216 +0.006208,216 +0.005685,216 +0.006487,216 +0.006019,216 +0.005781,216 +0.007648,216 +0.005997,216 +0.007177,216 +0.006766,216 +0.006210,218 +0.007256,218 +0.005898,218 +0.006264,218 +0.009736,218 +0.005934,218 +0.006642,218 +0.005758,218 +0.006376,218 +0.006204,218 +0.005705,218 +0.006358,218 +0.005827,218 +0.005790,218 +0.006412,218 +0.005781,218 +0.006085,218 +0.006048,218 +0.005698,218 +0.006003,218 +0.006033,218 +0.005719,218 +0.005811,218 +0.005729,218 +0.005720,218 +0.005784,218 +0.005733,218 +0.005670,218 +0.005820,218 +0.005687,218 +0.005769,218 +0.005788,218 +0.005663,218 +0.005668,218 +0.005807,218 +0.005668,218 +0.005742,218 +0.006086,218 +0.005812,218 +0.005815,218 +0.005765,218 +0.005701,218 +0.005771,218 +0.005702,218 +0.005669,218 +0.005714,218 +0.005747,218 +0.005663,218 +0.005804,218 +0.005729,218 +0.005664,218 +0.005859,218 +0.005708,218 +0.005690,218 +0.005978,218 +0.006048,218 +0.005702,218 +0.005724,218 +0.005713,218 +0.005784,218 +0.006000,218 +0.005901,218 +0.005784,218 +0.006205,218 +0.005706,218 +0.005842,218 +0.005730,218 +0.005667,218 +0.005869,218 +0.005789,218 +0.005679,218 +0.005993,218 +0.006072,218 +0.005793,218 +0.005816,218 +0.006076,218 +0.005689,218 +0.005872,218 +0.006006,218 +0.005817,218 +0.005734,218 +0.005828,218 +0.005804,218 +0.005768,218 +0.005742,218 +0.005726,218 +0.005716,218 +0.005692,218 +0.005666,218 +0.006121,218 +0.005762,218 +0.005669,218 +0.005726,218 +0.005705,218 +0.005708,218 +0.005705,218 +0.005665,218 +0.005668,218 +0.005781,218 +0.005691,218 +0.006165,220 +0.005818,220 +0.005839,220 +0.005879,220 +0.005838,220 +0.005813,220 +0.006274,220 +0.005964,220 +0.005843,220 +0.005911,220 +0.005859,220 +0.005875,220 +0.005888,220 +0.005807,220 +0.005817,220 +0.005982,220 +0.005889,220 +0.006092,220 +0.005858,220 +0.005828,220 +0.005898,220 +0.005814,220 +0.005815,220 +0.006025,220 +0.005997,220 +0.005881,220 +0.005914,220 +0.005823,220 +0.005818,220 +0.005881,220 +0.005815,220 +0.005816,220 +0.005895,220 +0.005814,220 +0.005960,220 +0.005851,220 +0.005817,220 +0.005895,220 +0.005836,220 +0.005965,220 +0.006084,220 +0.005981,220 +0.005879,220 +0.005960,220 +0.005945,220 +0.005819,220 +0.005910,220 +0.005815,220 +0.006064,220 +0.005851,220 +0.005837,220 +0.006360,220 +0.005851,220 +0.005961,220 +0.006022,220 +0.005815,220 +0.005884,220 +0.006152,220 +0.006042,220 +0.005933,220 +0.005918,220 +0.005819,220 +0.005834,220 +0.005856,220 +0.005812,220 +0.005853,220 +0.005851,220 +0.005817,220 +0.005985,220 +0.005819,220 +0.005813,220 +0.005885,220 +0.005815,220 +0.005817,220 +0.006085,220 +0.006280,220 +0.005859,220 +0.005925,220 +0.005816,220 +0.005828,220 +0.005856,220 +0.005813,220 +0.005826,220 +0.005852,220 +0.005817,220 +0.005921,220 +0.005824,220 +0.005839,220 +0.005873,220 +0.005821,220 +0.005856,220 +0.006110,220 +0.006147,220 +0.005837,220 +0.005921,220 +0.005834,220 +0.005838,220 +0.005865,220 +0.005813,220 +0.005827,220 +0.006199,222 +0.006047,222 +0.006113,222 +0.005991,222 +0.005998,222 +0.006044,222 +0.005992,222 +0.005992,222 +0.006332,222 +0.006240,222 +0.006050,222 +0.006050,222 +0.006035,222 +0.006060,222 +0.006039,222 +0.006035,222 +0.006087,222 +0.005991,222 +0.006057,222 +0.006044,222 +0.005994,222 +0.006002,222 +0.006035,222 +0.006061,222 +0.006153,222 +0.006487,222 +0.006039,222 +0.006085,222 +0.006020,222 +0.006097,222 +0.006120,222 +0.006067,222 +0.006035,222 +0.006069,222 +0.005991,222 +0.006187,222 +0.005994,222 +0.005995,222 +0.006040,222 +0.005995,222 +0.005993,222 +0.006250,222 +0.006297,222 +0.006125,222 +0.006036,222 +0.006073,222 +0.006072,222 +0.005997,222 +0.005991,222 +0.006043,222 +0.005993,222 +0.006054,222 +0.006039,222 +0.005995,222 +0.006002,222 +0.006036,222 +0.005991,222 +0.006044,222 +0.006302,222 +0.006241,222 +0.006090,222 +0.006012,222 +0.006042,222 +0.006062,222 +0.005993,222 +0.006003,222 +0.006059,222 +0.005991,222 +0.006520,222 +0.005994,222 +0.006099,222 +0.006051,222 +0.006056,222 +0.006015,222 +0.006136,222 +0.006390,222 +0.006093,222 +0.006011,222 +0.006018,222 +0.006080,222 +0.006039,222 +0.006015,222 +0.006043,222 +0.005996,222 +0.006123,222 +0.006034,222 +0.005996,222 +0.006089,222 +0.005991,222 +0.005995,222 +0.006039,222 +0.006226,222 +0.006255,222 +0.006094,222 +0.006012,222 +0.006004,222 +0.006030,222 +0.005996,222 +0.006041,222 +0.005995,222 +0.006544,224 +0.006214,224 +0.006159,224 +0.006201,224 +0.006209,224 +0.006269,224 +0.006196,224 +0.006284,224 +0.006576,224 +0.006228,224 +0.006259,224 +0.006181,224 +0.006204,224 +0.006160,224 +0.006206,224 +0.006182,224 +0.006215,224 +0.006209,224 +0.006159,224 +0.006160,224 +0.006209,224 +0.006219,224 +0.006184,224 +0.006200,224 +0.006813,224 +0.006231,224 +0.006438,224 +0.006208,224 +0.006394,224 +0.006190,224 +0.006206,224 +0.006190,224 +0.006220,224 +0.006259,224 +0.006164,224 +0.006159,224 +0.006209,224 +0.006155,224 +0.006170,224 +0.006197,224 +0.006456,224 +0.006614,224 +0.006198,224 +0.006202,224 +0.006229,224 +0.006181,224 +0.006217,224 +0.006183,224 +0.006216,224 +0.006229,224 +0.006287,224 +0.006185,224 +0.006209,224 +0.006493,224 +0.006197,224 +0.006170,224 +0.006525,224 +0.006446,224 +0.006177,224 +0.006217,224 +0.006214,224 +0.006162,224 +0.006206,224 +0.006165,224 +0.006261,224 +0.006237,224 +0.006162,224 +0.006220,224 +0.006216,224 +0.006155,224 +0.006170,224 +0.006198,224 +0.006455,224 +0.006439,224 +0.006188,224 +0.006182,224 +0.006247,224 +0.006160,224 +0.006166,224 +0.006200,224 +0.006179,224 +0.006269,224 +0.006159,224 +0.006158,224 +0.006210,224 +0.006179,224 +0.006262,224 +0.006195,224 +0.006400,224 +0.006445,224 +0.006241,224 +0.006192,224 +0.006266,224 +0.006244,224 +0.006168,224 +0.006225,224 +0.006156,224 +0.006312,224 +0.006159,224 +0.006161,224 +0.006549,226 +0.006319,226 +0.006334,226 +0.006360,226 +0.006602,226 +0.006872,226 +0.006318,226 +0.006371,226 +0.006378,226 +0.006344,226 +0.006397,226 +0.006370,226 +0.006379,226 +0.006397,226 +0.006319,226 +0.006400,226 +0.006359,226 +0.006319,226 +0.006389,226 +0.006320,226 +0.006569,226 +0.006630,226 +0.006340,226 +0.006420,226 +0.006365,226 +0.006322,226 +0.006366,226 +0.006323,226 +0.006906,226 +0.006387,226 +0.006637,226 +0.006371,226 +0.006345,226 +0.006332,226 +0.006357,226 +0.006324,226 +0.006945,226 +0.006377,226 +0.006349,226 +0.006376,226 +0.006559,226 +0.006351,226 +0.006320,226 +0.006376,226 +0.006434,226 +0.006335,226 +0.006330,226 +0.006359,226 +0.006322,226 +0.006369,226 +0.006323,226 +0.006419,226 +0.006789,226 +0.006450,226 +0.006401,226 +0.006351,226 +0.006318,226 +0.006375,226 +0.006323,226 +0.006379,226 +0.006371,226 +0.006317,226 +0.006370,226 +0.006323,226 +0.006361,226 +0.006372,226 +0.006318,226 +0.006571,226 +0.006741,226 +0.006366,226 +0.006431,226 +0.006340,226 +0.006364,226 +0.006402,226 +0.006318,226 +0.006461,226 +0.006320,226 +0.006319,226 +0.006371,226 +0.006320,226 +0.006330,226 +0.006366,226 +0.006392,226 +0.006721,226 +0.006562,226 +0.006344,226 +0.006403,226 +0.006320,226 +0.006370,226 +0.006322,226 +0.006342,226 +0.006452,226 +0.006320,226 +0.006332,226 +0.006359,226 +0.006359,226 +0.006367,226 +0.006324,226 +0.006318,226 +0.006649,226 +0.007106,228 +0.006580,228 +0.006485,228 +0.006484,228 +0.006534,228 +0.006483,228 +0.006636,228 +0.006547,228 +0.006541,228 +0.006579,228 +0.006543,228 +0.006496,228 +0.006526,228 +0.006482,228 +0.006787,228 +0.006789,228 +0.006515,228 +0.006587,228 +0.006502,228 +0.006544,228 +0.006491,228 +0.006656,228 +0.006526,228 +0.006488,228 +0.006556,228 +0.006483,228 +0.006483,228 +0.006536,228 +0.006488,228 +0.006665,228 +0.006857,228 +0.006545,228 +0.006555,228 +0.006531,228 +0.006544,228 +0.006483,228 +0.006527,228 +0.006643,228 +0.006481,228 +0.006529,228 +0.006496,228 +0.006636,228 +0.006586,228 +0.006502,228 +0.006495,228 +0.007019,228 +0.006552,228 +0.006599,228 +0.006554,228 +0.006495,228 +0.006529,228 +0.006485,228 +0.006610,228 +0.006486,228 +0.006483,228 +0.006535,228 +0.006484,228 +0.006531,228 +0.006488,228 +0.006585,228 +0.006792,228 +0.006762,228 +0.006576,228 +0.006481,228 +0.006486,228 +0.006535,228 +0.006481,228 +0.006615,228 +0.006484,228 +0.006499,228 +0.006538,228 +0.006495,228 +0.006501,228 +0.006530,228 +0.006481,228 +0.006686,228 +0.006840,228 +0.006519,228 +0.006612,228 +0.006503,228 +0.006565,228 +0.006530,228 +0.006877,228 +0.006551,228 +0.006489,228 +0.006533,228 +0.006620,228 +0.006507,228 +0.006530,228 +0.006486,228 +0.006534,228 +0.006951,228 +0.006530,228 +0.006585,228 +0.006482,228 +0.006564,228 +0.006488,228 +0.006579,228 +0.006645,228 +0.006481,228 +0.006906,230 +0.006664,230 +0.006654,230 +0.006708,230 +0.006732,230 +0.007061,230 +0.007030,230 +0.007347,230 +0.007360,230 +0.007459,230 +0.007354,230 +0.007573,230 +0.007686,230 +0.007985,230 +0.007109,230 +0.007216,230 +0.007353,230 +0.008097,230 +0.009631,230 +0.007771,230 +0.009133,230 +0.007343,230 +0.008509,230 +0.007966,230 +0.007210,230 +0.008854,230 +0.008231,230 +0.007544,230 +0.008028,230 +0.007625,230 +0.007927,230 +0.008986,230 +0.008489,230 +0.009163,230 +0.011969,230 +0.011834,230 +0.008479,230 +0.007426,230 +0.007346,230 +0.008399,230 +0.008797,230 +0.007532,230 +0.007414,230 +0.006996,230 +0.007756,230 +0.006975,230 +0.007077,230 +0.007386,230 +0.007467,230 +0.007776,230 +0.007609,230 +0.007568,230 +0.007361,230 +0.007952,230 +0.007071,230 +0.008761,230 +0.007205,230 +0.008618,230 +0.007297,230 +0.007950,230 +0.007024,230 +0.008121,230 +0.007081,230 +0.007821,230 +0.007059,230 +0.006998,230 +0.007775,230 +0.007005,230 +0.008090,230 +0.007026,230 +0.007915,230 +0.007400,230 +0.007968,230 +0.007076,230 +0.006918,230 +0.007954,230 +0.006799,230 +0.008414,230 +0.006951,230 +0.008150,230 +0.007105,230 +0.008124,230 +0.006950,230 +0.006990,230 +0.008277,230 +0.006900,230 +0.007570,230 +0.007040,230 +0.007710,230 +0.007099,230 +0.006936,230 +0.007400,230 +0.006832,230 +0.006759,230 +0.006929,230 +0.006787,230 +0.006863,230 +0.006921,230 +0.007279,230 +0.008303,230 +0.007663,232 +0.008658,232 +0.006971,232 +0.007331,232 +0.007265,232 +0.007715,232 +0.008007,232 +0.007884,232 +0.007827,232 +0.008317,232 +0.007851,232 +0.008945,232 +0.008069,232 +0.008027,232 +0.008219,232 +0.010375,232 +0.009157,232 +0.007510,232 +0.008506,232 +0.007659,232 +0.007794,232 +0.008050,232 +0.007744,232 +0.008130,232 +0.008074,232 +0.009084,232 +0.007656,232 +0.007832,232 +0.007544,232 +0.007925,232 +0.007558,232 +0.008052,232 +0.007596,232 +0.007857,232 +0.007764,232 +0.008353,232 +0.007662,232 +0.007970,232 +0.007488,232 +0.007856,232 +0.007517,232 +0.007807,232 +0.007618,232 +0.007640,232 +0.007767,232 +0.007442,232 +0.008778,232 +0.008466,232 +0.009341,232 +0.007269,232 +0.007878,232 +0.007136,232 +0.007985,232 +0.007516,232 +0.008181,232 +0.007519,232 +0.007891,232 +0.007465,232 +0.008925,232 +0.007472,232 +0.007641,232 +0.008206,232 +0.007339,232 +0.008165,232 +0.007036,232 +0.008310,232 +0.007241,232 +0.007607,232 +0.007111,232 +0.007456,232 +0.007123,232 +0.007018,232 +0.007113,232 +0.006921,232 +0.007212,232 +0.007295,232 +0.006936,232 +0.006939,232 +0.007001,232 +0.006917,232 +0.006998,232 +0.006892,232 +0.006963,232 +0.006877,232 +0.006901,232 +0.006871,232 +0.006835,232 +0.006900,232 +0.006971,232 +0.007192,232 +0.006898,232 +0.006905,232 +0.006866,232 +0.006936,232 +0.007135,232 +0.006877,232 +0.006894,232 +0.006838,232 +0.006897,232 +0.006900,232 +0.007237,234 +0.007229,234 +0.007226,234 +0.007570,234 +0.007112,234 +0.007043,234 +0.007135,234 +0.007101,234 +0.007239,234 +0.007078,234 +0.007109,234 +0.007069,234 +0.007125,234 +0.007131,234 +0.007047,234 +0.007088,234 +0.007028,234 +0.007460,234 +0.007143,234 +0.007030,234 +0.007112,234 +0.007027,234 +0.007208,234 +0.007024,234 +0.007050,234 +0.007111,234 +0.007026,234 +0.007117,234 +0.007020,234 +0.007249,234 +0.007210,234 +0.007394,234 +0.007278,234 +0.007165,234 +0.007221,234 +0.007963,234 +0.009203,234 +0.008000,234 +0.007206,234 +0.007376,234 +0.007202,234 +0.007165,234 +0.007109,234 +0.007178,234 +0.007352,234 +0.007577,234 +0.007112,234 +0.007174,234 +0.007093,234 +0.007694,234 +0.007190,234 +0.007050,234 +0.007141,234 +0.007084,234 +0.007142,234 +0.007064,234 +0.007727,234 +0.007223,234 +0.007325,234 +0.007454,234 +0.007197,234 +0.007191,234 +0.007104,234 +0.007222,234 +0.007170,234 +0.007125,234 +0.007088,234 +0.007044,234 +0.007124,234 +0.007086,234 +0.007128,234 +0.007025,234 +0.007278,234 +0.007411,234 +0.007062,234 +0.007125,234 +0.007030,234 +0.007122,234 +0.007101,234 +0.007102,234 +0.007911,234 +0.007742,234 +0.008329,234 +0.010380,234 +0.008026,234 +0.008500,234 +0.008256,234 +0.008138,234 +0.008184,234 +0.008851,234 +0.008628,234 +0.009289,234 +0.008313,234 +0.007911,234 +0.007843,234 +0.008029,234 +0.007784,234 +0.007991,234 +0.008368,234 +0.008967,234 +0.008834,236 +0.008266,236 +0.008228,236 +0.008136,236 +0.007759,236 +0.007821,236 +0.007737,236 +0.008175,236 +0.007579,236 +0.007759,236 +0.007853,236 +0.008212,236 +0.007521,236 +0.007879,236 +0.007829,236 +0.008431,236 +0.007612,236 +0.007583,236 +0.007709,236 +0.007579,236 +0.007473,236 +0.007549,236 +0.007520,236 +0.007821,236 +0.007461,236 +0.007356,236 +0.007291,236 +0.007332,236 +0.007349,236 +0.007236,236 +0.007218,236 +0.007238,236 +0.007243,236 +0.007231,236 +0.007609,236 +0.007350,236 +0.007396,236 +0.007753,236 +0.007261,236 +0.007650,236 +0.007419,236 +0.007379,236 +0.007389,236 +0.007298,236 +0.007704,236 +0.007321,236 +0.007505,236 +0.007313,236 +0.007608,236 +0.007351,236 +0.007657,236 +0.007536,236 +0.007321,236 +0.008096,236 +0.007385,236 +0.007427,236 +0.007215,236 +0.007849,236 +0.007234,236 +0.007367,236 +0.007348,236 +0.007299,236 +0.007194,236 +0.007443,236 +0.007902,236 +0.007590,236 +0.007554,236 +0.007431,236 +0.007748,236 +0.007674,236 +0.007683,236 +0.007500,236 +0.007520,236 +0.007672,236 +0.007701,236 +0.007689,236 +0.007781,236 +0.007872,236 +0.007630,236 +0.007828,236 +0.007667,236 +0.008095,236 +0.008005,236 +0.007886,236 +0.011243,236 +0.008679,236 +0.007297,236 +0.007512,236 +0.007207,236 +0.007647,236 +0.007748,236 +0.007369,236 +0.007605,236 +0.007382,236 +0.008036,236 +0.007378,236 +0.007765,236 +0.007261,236 +0.008214,236 +0.007343,236 +0.008624,238 +0.007429,238 +0.008038,238 +0.007670,238 +0.007491,238 +0.007370,238 +0.007469,238 +0.007570,238 +0.007449,238 +0.007586,238 +0.007496,238 +0.007464,238 +0.007847,238 +0.007520,238 +0.007370,238 +0.007655,238 +0.007782,238 +0.007511,238 +0.007451,238 +0.007444,238 +0.007455,238 +0.007374,238 +0.007449,238 +0.007378,238 +0.007449,238 +0.007370,238 +0.007508,238 +0.007370,238 +0.007410,238 +0.007805,238 +0.007561,238 +0.007425,238 +0.007431,238 +0.007451,238 +0.007467,238 +0.007449,238 +0.007414,238 +0.007432,238 +0.007401,238 +0.007409,238 +0.007371,238 +0.007368,238 +0.007521,238 +0.007874,238 +0.007490,238 +0.007442,238 +0.007476,238 +0.007785,238 +0.007454,238 +0.007751,238 +0.007405,238 +0.007598,238 +0.007370,238 +0.007409,238 +0.007369,238 +0.007427,238 +0.008021,238 +0.007421,238 +0.007365,238 +0.007567,238 +0.008946,238 +0.008478,238 +0.010571,238 +0.009349,238 +0.011127,238 +0.009461,238 +0.008439,238 +0.008230,238 +0.008482,238 +0.009090,238 +0.008313,238 +0.008916,238 +0.009600,238 +0.009170,238 +0.008555,238 +0.008817,238 +0.008428,238 +0.008248,238 +0.008378,238 +0.008190,238 +0.008983,238 +0.010074,238 +0.009864,238 +0.009125,238 +0.008735,238 +0.007859,238 +0.007874,238 +0.007669,238 +0.007687,238 +0.007573,238 +0.008210,238 +0.008295,238 +0.008358,238 +0.007898,238 +0.008410,238 +0.007990,238 +0.007957,238 +0.008097,238 +0.008056,238 +0.007972,238 +0.008653,240 +0.008411,240 +0.009443,240 +0.010387,240 +0.009186,240 +0.009200,240 +0.008355,240 +0.008307,240 +0.008691,240 +0.009048,240 +0.009448,240 +0.008462,240 +0.010544,240 +0.009193,240 +0.010076,240 +0.008931,240 +0.008495,240 +0.008309,240 +0.008280,240 +0.008282,240 +0.008086,240 +0.008305,240 +0.008257,240 +0.008537,240 +0.007775,240 +0.008803,240 +0.008156,240 +0.008703,240 +0.007829,240 +0.009971,240 +0.010236,240 +0.011200,240 +0.008115,240 +0.009301,240 +0.007973,240 +0.008482,240 +0.007937,240 +0.008784,240 +0.013206,240 +0.008126,240 +0.008587,240 +0.008093,240 +0.008492,240 +0.007942,240 +0.008638,240 +0.007867,240 +0.008002,240 +0.007985,240 +0.008097,240 +0.008768,240 +0.008668,240 +0.007959,240 +0.008045,240 +0.007915,240 +0.007964,240 +0.009017,240 +0.010591,240 +0.010042,240 +0.011167,240 +0.010816,240 +0.008555,240 +0.010858,240 +0.009223,240 +0.010121,240 +0.008837,240 +0.008203,240 +0.008618,240 +0.008413,240 +0.008477,240 +0.008723,240 +0.008598,240 +0.008431,240 +0.008652,240 +0.008653,240 +0.008365,240 +0.008711,240 +0.008385,240 +0.008926,240 +0.008361,240 +0.008319,240 +0.008091,240 +0.008054,240 +0.008121,240 +0.008434,240 +0.010000,240 +0.011078,240 +0.009180,240 +0.008554,240 +0.008533,240 +0.008538,240 +0.008345,240 +0.008361,240 +0.009772,240 +0.009039,240 +0.008347,240 +0.010383,240 +0.011302,240 +0.009205,240 +0.012062,240 +0.009639,240 +0.010181,242 +0.009269,242 +0.009006,242 +0.009717,242 +0.008504,242 +0.010585,242 +0.008997,242 +0.011064,242 +0.010893,242 +0.009848,242 +0.010563,242 +0.009299,242 +0.010176,242 +0.009776,242 +0.013347,242 +0.009719,242 +0.009009,242 +0.009491,242 +0.009756,242 +0.008917,242 +0.009300,242 +0.008440,242 +0.009133,242 +0.008241,242 +0.008374,242 +0.008364,242 +0.008505,242 +0.008798,242 +0.008924,242 +0.009366,242 +0.009250,242 +0.008463,242 +0.008386,242 +0.009386,242 +0.008959,242 +0.008696,242 +0.008675,242 +0.009764,242 +0.008470,242 +0.008959,242 +0.008126,242 +0.008964,242 +0.007957,242 +0.008368,242 +0.007936,242 +0.008271,242 +0.007890,242 +0.008236,242 +0.008135,242 +0.008964,242 +0.007986,242 +0.008580,242 +0.008036,242 +0.008817,242 +0.007993,242 +0.008811,242 +0.008000,242 +0.008834,242 +0.007999,242 +0.008670,242 +0.008321,242 +0.008742,242 +0.008018,242 +0.008544,242 +0.007957,242 +0.008447,242 +0.008035,242 +0.008698,242 +0.007998,242 +0.009916,242 +0.008943,242 +0.008820,242 +0.008849,242 +0.008685,242 +0.009261,242 +0.010206,242 +0.009261,242 +0.008096,242 +0.008463,242 +0.007979,242 +0.008195,242 +0.007949,242 +0.008773,242 +0.008035,242 +0.009100,242 +0.008042,242 +0.008596,242 +0.008102,242 +0.008360,242 +0.008007,242 +0.008242,242 +0.007991,242 +0.008185,242 +0.007931,242 +0.008300,242 +0.007946,242 +0.009118,242 +0.008265,242 +0.008771,242 +0.008246,242 +0.008730,244 +0.008402,244 +0.009118,244 +0.008417,244 +0.009298,244 +0.008481,244 +0.009313,244 +0.008668,244 +0.008875,244 +0.008600,244 +0.008772,244 +0.009428,244 +0.008755,244 +0.009235,244 +0.009010,244 +0.010082,244 +0.008771,244 +0.010093,244 +0.008906,244 +0.009613,244 +0.009461,244 +0.009210,244 +0.010194,244 +0.009208,244 +0.011270,244 +0.009555,244 +0.009779,244 +0.010409,244 +0.009468,244 +0.009655,244 +0.008584,244 +0.008506,244 +0.008732,244 +0.008071,244 +0.008374,244 +0.008024,244 +0.008208,244 +0.008216,244 +0.008539,244 +0.008170,244 +0.008311,244 +0.009333,244 +0.010456,244 +0.009038,244 +0.009488,244 +0.008646,244 +0.008772,244 +0.008282,244 +0.008996,244 +0.013515,244 +0.011108,244 +0.009122,244 +0.009141,244 +0.010592,244 +0.012973,244 +0.010900,244 +0.008776,244 +0.008599,244 +0.008271,244 +0.008535,244 +0.008380,244 +0.008547,244 +0.008541,244 +0.009122,244 +0.009425,244 +0.009985,244 +0.008869,244 +0.009671,244 +0.008826,244 +0.009167,244 +0.009475,244 +0.010463,244 +0.008845,244 +0.009068,244 +0.009923,244 +0.008686,244 +0.009351,244 +0.008841,244 +0.009443,244 +0.009230,244 +0.009117,244 +0.009444,244 +0.008598,244 +0.011855,244 +0.013583,244 +0.009072,244 +0.009092,244 +0.009185,244 +0.014677,244 +0.011672,244 +0.009429,244 +0.008713,244 +0.008714,244 +0.009273,244 +0.010116,244 +0.009393,244 +0.010491,244 +0.008408,244 +0.009318,244 +0.008508,244 +0.009858,246 +0.009395,246 +0.008938,246 +0.011050,246 +0.008977,246 +0.009164,246 +0.009213,246 +0.009397,246 +0.009276,246 +0.009221,246 +0.009539,246 +0.008873,246 +0.009992,246 +0.009103,246 +0.009691,246 +0.010062,246 +0.009052,246 +0.009601,246 +0.009269,246 +0.009436,246 +0.008698,246 +0.008780,246 +0.008658,246 +0.008635,246 +0.009383,246 +0.008811,246 +0.009192,246 +0.008760,246 +0.009154,246 +0.008547,246 +0.009660,246 +0.010609,246 +0.009080,246 +0.009131,246 +0.009144,246 +0.009341,246 +0.013315,246 +0.009230,246 +0.009309,246 +0.009871,246 +0.008865,246 +0.008572,246 +0.010704,246 +0.008672,246 +0.009686,246 +0.011265,246 +0.009018,246 +0.009531,246 +0.008655,246 +0.010740,246 +0.008935,246 +0.008863,246 +0.008870,246 +0.009304,246 +0.009020,246 +0.008978,246 +0.009087,246 +0.008751,246 +0.009580,246 +0.008960,246 +0.009217,246 +0.008830,246 +0.009173,246 +0.008646,246 +0.009105,246 +0.009314,246 +0.008384,246 +0.009238,246 +0.008834,246 +0.009322,246 +0.008750,246 +0.009035,246 +0.008676,246 +0.009955,246 +0.008648,246 +0.009108,246 +0.008685,246 +0.008831,246 +0.009185,246 +0.009365,246 +0.009642,246 +0.008500,246 +0.009377,246 +0.008589,246 +0.008932,246 +0.008653,246 +0.008815,246 +0.008795,246 +0.009015,246 +0.008711,246 +0.009558,246 +0.009287,246 +0.008655,246 +0.008782,246 +0.008563,246 +0.010632,246 +0.008627,246 +0.009575,246 +0.008599,246 +0.009215,246 +0.009130,248 +0.009244,248 +0.009282,248 +0.008789,248 +0.009308,248 +0.008727,248 +0.009762,248 +0.008719,248 +0.008883,248 +0.008873,248 +0.008978,248 +0.008867,248 +0.010259,248 +0.009395,248 +0.008633,248 +0.009338,248 +0.008758,248 +0.009328,248 +0.009498,248 +0.008909,248 +0.009063,248 +0.009817,248 +0.009740,248 +0.009207,248 +0.009438,248 +0.012479,248 +0.010154,248 +0.009249,248 +0.009299,248 +0.010087,248 +0.009723,248 +0.009695,248 +0.010362,248 +0.010546,248 +0.010629,248 +0.010528,248 +0.015329,248 +0.012274,248 +0.011152,248 +0.009396,248 +0.009280,248 +0.009034,248 +0.012744,248 +0.015582,248 +0.015658,248 +0.015078,248 +0.010024,248 +0.009239,248 +0.009943,248 +0.009773,248 +0.014537,248 +0.017530,248 +0.015920,248 +0.011957,248 +0.009105,248 +0.009083,248 +0.009202,248 +0.009940,248 +0.010099,248 +0.009476,248 +0.009598,248 +0.010707,248 +0.009195,248 +0.009424,248 +0.008605,248 +0.009276,248 +0.008892,248 +0.009204,248 +0.008877,248 +0.009213,248 +0.011625,248 +0.009214,248 +0.009382,248 +0.009043,248 +0.009214,248 +0.008909,248 +0.010248,248 +0.009246,248 +0.009236,248 +0.009438,248 +0.008784,248 +0.011077,248 +0.010114,248 +0.009304,248 +0.009221,248 +0.008766,248 +0.009307,248 +0.008864,248 +0.009873,248 +0.008852,248 +0.009311,248 +0.008867,248 +0.009239,248 +0.009388,248 +0.009156,248 +0.009197,248 +0.008510,248 +0.009130,248 +0.008669,248 +0.009244,248 +0.009025,250 +0.009350,250 +0.008872,250 +0.009456,250 +0.009317,250 +0.008936,250 +0.009422,250 +0.008982,250 +0.009744,250 +0.008988,250 +0.009696,250 +0.009359,250 +0.009167,250 +0.012349,250 +0.009517,250 +0.009812,250 +0.009119,250 +0.009061,250 +0.009260,250 +0.009456,250 +0.009952,250 +0.008818,250 +0.009474,250 +0.008798,250 +0.009091,250 +0.009133,250 +0.009540,250 +0.009433,250 +0.009249,250 +0.010214,250 +0.008713,250 +0.010148,250 +0.008962,250 +0.009849,250 +0.009456,250 +0.009602,250 +0.009677,250 +0.008792,250 +0.009677,250 +0.008841,250 +0.009685,250 +0.009485,250 +0.008924,250 +0.009592,250 +0.008825,250 +0.009603,250 +0.009132,250 +0.009784,250 +0.009045,250 +0.009499,250 +0.009518,250 +0.009109,250 +0.009879,250 +0.008919,250 +0.009706,250 +0.008915,250 +0.009780,250 +0.009812,250 +0.009038,250 +0.009642,250 +0.009030,250 +0.009746,250 +0.008882,250 +0.009732,250 +0.009126,250 +0.009544,250 +0.009785,250 +0.009096,250 +0.009853,250 +0.008885,250 +0.009660,250 +0.009002,250 +0.009631,250 +0.009679,250 +0.008955,250 +0.009704,250 +0.008887,250 +0.013027,250 +0.010948,250 +0.008987,250 +0.009630,250 +0.008881,250 +0.009727,250 +0.009298,250 +0.009833,250 +0.009567,250 +0.009455,250 +0.010065,250 +0.009454,250 +0.010091,250 +0.009412,250 +0.009077,250 +0.009636,250 +0.009303,250 +0.009526,250 +0.008877,250 +0.009605,250 +0.009191,250 +0.010011,250 +0.009709,250 +0.010231,252 +0.012990,252 +0.009854,252 +0.010859,252 +0.014675,252 +0.015726,252 +0.012810,252 +0.014456,252 +0.009736,252 +0.010464,252 +0.010532,252 +0.012710,252 +0.010361,252 +0.009999,252 +0.009827,252 +0.013812,252 +0.010463,252 +0.010301,252 +0.009966,252 +0.009810,252 +0.009776,252 +0.009550,252 +0.009727,252 +0.009798,252 +0.009014,252 +0.011330,252 +0.010802,252 +0.009600,252 +0.010121,252 +0.011557,252 +0.009966,252 +0.010390,252 +0.009430,252 +0.009848,252 +0.010062,252 +0.012363,252 +0.012036,252 +0.009869,252 +0.009844,252 +0.010969,252 +0.011726,252 +0.011246,252 +0.011567,252 +0.009282,252 +0.010693,252 +0.010142,252 +0.009920,252 +0.012229,252 +0.010075,252 +0.009732,252 +0.010298,252 +0.009082,252 +0.010190,252 +0.009417,252 +0.009715,252 +0.015873,252 +0.016372,252 +0.016583,252 +0.015830,252 +0.016000,252 +0.011421,252 +0.010158,252 +0.010739,252 +0.009456,252 +0.012964,252 +0.012191,252 +0.012941,252 +0.011451,252 +0.011859,252 +0.013485,252 +0.011426,252 +0.011688,252 +0.016568,252 +0.016182,252 +0.016828,252 +0.016195,252 +0.016573,252 +0.016100,252 +0.010000,252 +0.009507,252 +0.010536,252 +0.010492,252 +0.009154,252 +0.013518,252 +0.010619,252 +0.012216,252 +0.010740,252 +0.009764,252 +0.009365,252 +0.009776,252 +0.010528,252 +0.009679,252 +0.009761,252 +0.009547,252 +0.010305,252 +0.012599,252 +0.011673,252 +0.009893,252 +0.010159,252 +0.009324,252 +0.010555,254 +0.009937,254 +0.010597,254 +0.010326,254 +0.009800,254 +0.010106,254 +0.009499,254 +0.010620,254 +0.010066,254 +0.009924,254 +0.011003,254 +0.009747,254 +0.009786,254 +0.009392,254 +0.010399,254 +0.011080,254 +0.009258,254 +0.010474,254 +0.009610,254 +0.010054,254 +0.011508,254 +0.009480,254 +0.009833,254 +0.009961,254 +0.009436,254 +0.012692,254 +0.009641,254 +0.010464,254 +0.011081,254 +0.009649,254 +0.010144,254 +0.010091,254 +0.009405,254 +0.009991,254 +0.010172,254 +0.010449,254 +0.010108,254 +0.010207,254 +0.010032,254 +0.009369,254 +0.010225,254 +0.009678,254 +0.016870,254 +0.016472,254 +0.010452,254 +0.011093,254 +0.010473,254 +0.009599,254 +0.014770,254 +0.016677,254 +0.017813,254 +0.017380,254 +0.016409,254 +0.017041,254 +0.016572,254 +0.016370,254 +0.016605,254 +0.016964,254 +0.017444,254 +0.017205,254 +0.016628,254 +0.013205,254 +0.010322,254 +0.009270,254 +0.009769,254 +0.009492,254 +0.009941,254 +0.010107,254 +0.010101,254 +0.010084,254 +0.010374,254 +0.012121,254 +0.012037,254 +0.009778,254 +0.010571,254 +0.009853,254 +0.009496,254 +0.009743,254 +0.009096,254 +0.009745,254 +0.009021,254 +0.010155,254 +0.010309,254 +0.009889,254 +0.011350,254 +0.010828,254 +0.010240,254 +0.009932,254 +0.009917,254 +0.010543,254 +0.010089,254 +0.013366,254 +0.016995,254 +0.017477,254 +0.016690,254 +0.016894,254 +0.018866,254 +0.014139,254 +0.010406,254 +0.009661,254 +0.009779,256 +0.010680,256 +0.010421,256 +0.010054,256 +0.010939,256 +0.009451,256 +0.013862,256 +0.010243,256 +0.009519,256 +0.010374,256 +0.009982,256 +0.010124,256 +0.011400,256 +0.010499,256 +0.009763,256 +0.010973,256 +0.009887,256 +0.010968,256 +0.011389,256 +0.013785,256 +0.009945,256 +0.010088,256 +0.010515,256 +0.010346,256 +0.010209,256 +0.009981,256 +0.010826,256 +0.009649,256 +0.011957,256 +0.010635,256 +0.009541,256 +0.010679,256 +0.010541,256 +0.009604,256 +0.010616,256 +0.009487,256 +0.010491,256 +0.010836,256 +0.013541,256 +0.017591,256 +0.014169,256 +0.012726,256 +0.013956,256 +0.011220,256 +0.010190,256 +0.011644,256 +0.010571,256 +0.010247,256 +0.010495,256 +0.010289,256 +0.010695,256 +0.010168,256 +0.009805,256 +0.011205,256 +0.010342,256 +0.010553,256 +0.010728,256 +0.009985,256 +0.010386,256 +0.010392,256 +0.010682,256 +0.011283,256 +0.011353,256 +0.010878,256 +0.015319,256 +0.015399,256 +0.010297,256 +0.010587,256 +0.017157,256 +0.017762,256 +0.017091,256 +0.017641,256 +0.013289,256 +0.011448,256 +0.011872,256 +0.011224,256 +0.010420,256 +0.011012,256 +0.011475,256 +0.015462,256 +0.012049,256 +0.011826,256 +0.011497,256 +0.011092,256 +0.011921,256 +0.011552,256 +0.011640,256 +0.010822,256 +0.011117,256 +0.010751,256 +0.010827,256 +0.010403,256 +0.009689,256 +0.011013,256 +0.012598,256 +0.009945,256 +0.010082,256 +0.014993,256 +0.009717,256 +0.009882,256 +0.010107,258 +0.009770,258 +0.009796,258 +0.009472,258 +0.009749,258 +0.009416,258 +0.010430,258 +0.009918,258 +0.009482,258 +0.009579,258 +0.009374,258 +0.009683,258 +0.009468,258 +0.009405,258 +0.009450,258 +0.009404,258 +0.009560,258 +0.009866,258 +0.009767,258 +0.009467,258 +0.009433,258 +0.009574,258 +0.009596,258 +0.009561,258 +0.009546,258 +0.009753,258 +0.009619,258 +0.009744,258 +0.010196,258 +0.010095,258 +0.010383,258 +0.010210,258 +0.010262,258 +0.010389,258 +0.010256,258 +0.009983,258 +0.009761,258 +0.009582,258 +0.010053,258 +0.009413,258 +0.009532,258 +0.009446,258 +0.009426,258 +0.009423,258 +0.009346,258 +0.009422,258 +0.009347,258 +0.009394,258 +0.009674,258 +0.009704,258 +0.009396,258 +0.009351,258 +0.009391,258 +0.009346,258 +0.009475,258 +0.009598,258 +0.010080,258 +0.010452,258 +0.010871,258 +0.010423,258 +0.010513,258 +0.010116,258 +0.010210,258 +0.009958,258 +0.009968,258 +0.010047,258 +0.010058,258 +0.010037,258 +0.010153,258 +0.011575,258 +0.012614,258 +0.010947,258 +0.009669,258 +0.009714,258 +0.009688,258 +0.010026,258 +0.009516,258 +0.009797,258 +0.009955,258 +0.010176,258 +0.009922,258 +0.010324,258 +0.010263,258 +0.009942,258 +0.010075,258 +0.010010,258 +0.010313,258 +0.010602,258 +0.010260,258 +0.010234,258 +0.010394,258 +0.010284,258 +0.013337,258 +0.010676,258 +0.010417,258 +0.010114,258 +0.010350,258 +0.012891,258 +0.013548,258 +0.010766,258 +0.011532,260 +0.010968,260 +0.010756,260 +0.010761,260 +0.010170,260 +0.010459,260 +0.013812,260 +0.011390,260 +0.009759,260 +0.010005,260 +0.009683,260 +0.009912,260 +0.009788,260 +0.009833,260 +0.012760,260 +0.019698,260 +0.018735,260 +0.018137,260 +0.018051,260 +0.018126,260 +0.016454,260 +0.010452,260 +0.009917,260 +0.009712,260 +0.010646,260 +0.010046,260 +0.010721,260 +0.010848,260 +0.010831,260 +0.011017,260 +0.010318,260 +0.010154,260 +0.009890,260 +0.009848,260 +0.010152,260 +0.009949,260 +0.009642,260 +0.009848,260 +0.010376,260 +0.010758,260 +0.011059,260 +0.010853,260 +0.012435,260 +0.010276,260 +0.010300,260 +0.012000,260 +0.013294,260 +0.012111,260 +0.011801,260 +0.010755,260 +0.011994,260 +0.011919,260 +0.010789,260 +0.012048,260 +0.011977,260 +0.012300,260 +0.012509,260 +0.012142,260 +0.010451,260 +0.010635,260 +0.010448,260 +0.010917,260 +0.010891,260 +0.010783,260 +0.010708,260 +0.010749,260 +0.010585,260 +0.010855,260 +0.011117,260 +0.010729,260 +0.010794,260 +0.010692,260 +0.010542,260 +0.010503,260 +0.010549,260 +0.010460,260 +0.010503,260 +0.010593,260 +0.010516,260 +0.010728,260 +0.010585,260 +0.010632,260 +0.010700,260 +0.013832,260 +0.011336,260 +0.010597,260 +0.010557,260 +0.010810,260 +0.011117,260 +0.011006,260 +0.011358,260 +0.010412,260 +0.010276,260 +0.011562,260 +0.012203,260 +0.015970,260 +0.009911,260 +0.011294,260 +0.011579,260 +0.012378,260 +0.011885,262 +0.011688,262 +0.012098,262 +0.017249,262 +0.012328,262 +0.017765,262 +0.022648,262 +0.018523,262 +0.011370,262 +0.012250,262 +0.011140,262 +0.010837,262 +0.010156,262 +0.010665,262 +0.010573,262 +0.012050,262 +0.011725,262 +0.011434,262 +0.011467,262 +0.011308,262 +0.012422,262 +0.010747,262 +0.011455,262 +0.012212,262 +0.010871,262 +0.011883,262 +0.011414,262 +0.011060,262 +0.011012,262 +0.011690,262 +0.013613,262 +0.010994,262 +0.011202,262 +0.013261,262 +0.012546,262 +0.013007,262 +0.011315,262 +0.011240,262 +0.010581,262 +0.012079,262 +0.011860,262 +0.011337,262 +0.011544,262 +0.013034,262 +0.011081,262 +0.010664,262 +0.010906,262 +0.012053,262 +0.010731,262 +0.014121,262 +0.011711,262 +0.013684,262 +0.012036,262 +0.012383,262 +0.011715,262 +0.010776,262 +0.011244,262 +0.011810,262 +0.010253,262 +0.010740,262 +0.010743,262 +0.011492,262 +0.011037,262 +0.011238,262 +0.010825,262 +0.011052,262 +0.011090,262 +0.010108,262 +0.011135,262 +0.011111,262 +0.011944,262 +0.011301,262 +0.011062,262 +0.010266,262 +0.012399,262 +0.011177,262 +0.009959,262 +0.010554,262 +0.010458,262 +0.010451,262 +0.010572,262 +0.010284,262 +0.011125,262 +0.011215,262 +0.010490,262 +0.011294,262 +0.010950,262 +0.010181,262 +0.010554,262 +0.010798,262 +0.010588,262 +0.010938,262 +0.011195,262 +0.010304,262 +0.016095,262 +0.013226,262 +0.010853,262 +0.010454,262 +0.010427,262 +0.010101,262 +0.010794,264 +0.011579,264 +0.011372,264 +0.013671,264 +0.012693,264 +0.012298,264 +0.011387,264 +0.010932,264 +0.012185,264 +0.012093,264 +0.010862,264 +0.013355,264 +0.013758,264 +0.012014,264 +0.010772,264 +0.013846,264 +0.010442,264 +0.010146,264 +0.010189,264 +0.010453,264 +0.010165,264 +0.010202,264 +0.010154,264 +0.010184,264 +0.016234,264 +0.010232,264 +0.010653,264 +0.010957,264 +0.010317,264 +0.010160,264 +0.010207,264 +0.010154,264 +0.010074,264 +0.015739,264 +0.010218,264 +0.010167,264 +0.010198,264 +0.010039,264 +0.011495,264 +0.010973,264 +0.010209,264 +0.010213,264 +0.010392,264 +0.010206,264 +0.010219,264 +0.010150,264 +0.010204,264 +0.010077,264 +0.010029,264 +0.010081,264 +0.010087,264 +0.010062,264 +0.010284,264 +0.010231,264 +0.010156,264 +0.010122,264 +0.010094,264 +0.010179,264 +0.009974,264 +0.010217,264 +0.010331,264 +0.010127,264 +0.010511,264 +0.010212,264 +0.010175,264 +0.010099,264 +0.010354,264 +0.010094,264 +0.010020,264 +0.010053,264 +0.010128,264 +0.010016,264 +0.010424,264 +0.010017,264 +0.010142,264 +0.010322,264 +0.009975,264 +0.011610,264 +0.010608,264 +0.010153,264 +0.010441,264 +0.010130,264 +0.010610,264 +0.010203,264 +0.010101,264 +0.010052,264 +0.010070,264 +0.010221,264 +0.010127,264 +0.010209,264 +0.010113,264 +0.010248,264 +0.010656,264 +0.010227,264 +0.010537,264 +0.010463,264 +0.010206,264 +0.009976,264 +0.010978,264 +0.012841,264 +0.011457,266 +0.011325,266 +0.012660,266 +0.011298,266 +0.010768,266 +0.011054,266 +0.010783,266 +0.010563,266 +0.010470,266 +0.010377,266 +0.010594,266 +0.010372,266 +0.010286,266 +0.010322,266 +0.010281,266 +0.010319,266 +0.010380,266 +0.010277,266 +0.010316,266 +0.010538,266 +0.010632,266 +0.010314,266 +0.010246,266 +0.010298,266 +0.010313,266 +0.010222,266 +0.010392,266 +0.010303,266 +0.010258,266 +0.011083,266 +0.011373,266 +0.011394,266 +0.011423,266 +0.011494,266 +0.011362,266 +0.011225,266 +0.011327,266 +0.011162,266 +0.011533,266 +0.012106,266 +0.011551,266 +0.011496,266 +0.012078,266 +0.010990,266 +0.011217,266 +0.011571,266 +0.011147,266 +0.010625,266 +0.011689,266 +0.012289,266 +0.011349,266 +0.012935,266 +0.012327,266 +0.011804,266 +0.011409,266 +0.011983,266 +0.011368,266 +0.011151,266 +0.011225,266 +0.010653,266 +0.010704,266 +0.011275,266 +0.011230,266 +0.011698,266 +0.013166,266 +0.015349,266 +0.018412,266 +0.017065,266 +0.013121,266 +0.011527,266 +0.010822,266 +0.011982,266 +0.011018,266 +0.010638,266 +0.011363,266 +0.012734,266 +0.010482,266 +0.010728,266 +0.010993,266 +0.011482,266 +0.011666,266 +0.011318,266 +0.011667,266 +0.011474,266 +0.012265,266 +0.012166,266 +0.011736,266 +0.012148,266 +0.012070,266 +0.011598,266 +0.013895,266 +0.012129,266 +0.014653,266 +0.012137,266 +0.014748,266 +0.015828,266 +0.013458,266 +0.014819,266 +0.012846,266 +0.016506,266 +0.012439,268 +0.011157,268 +0.012181,268 +0.012792,268 +0.018302,268 +0.012486,268 +0.011053,268 +0.011819,268 +0.012515,268 +0.014427,268 +0.018408,268 +0.021454,268 +0.012570,268 +0.011423,268 +0.011239,268 +0.011432,268 +0.011399,268 +0.011265,268 +0.012256,268 +0.011688,268 +0.011787,268 +0.011798,268 +0.011951,268 +0.011667,268 +0.011537,268 +0.012007,268 +0.010827,268 +0.011254,268 +0.011534,268 +0.011232,268 +0.010853,268 +0.011462,268 +0.011062,268 +0.010949,268 +0.011541,268 +0.011058,268 +0.011035,268 +0.011518,268 +0.011622,268 +0.010679,268 +0.011386,268 +0.012035,268 +0.014004,268 +0.011193,268 +0.012148,268 +0.011543,268 +0.012519,268 +0.011213,268 +0.014361,268 +0.013364,268 +0.013924,268 +0.012259,268 +0.013628,268 +0.012660,268 +0.012574,268 +0.012317,268 +0.012326,268 +0.011779,268 +0.012059,268 +0.011431,268 +0.011946,268 +0.013517,268 +0.015301,268 +0.014987,268 +0.012013,268 +0.012194,268 +0.011377,268 +0.011686,268 +0.011386,268 +0.012465,268 +0.015420,268 +0.020418,268 +0.015497,268 +0.012483,268 +0.011771,268 +0.013726,268 +0.012621,268 +0.012090,268 +0.010986,268 +0.012368,268 +0.011458,268 +0.011811,268 +0.011334,268 +0.017564,268 +0.014490,268 +0.016207,268 +0.013307,268 +0.012526,268 +0.011412,268 +0.012655,268 +0.011794,268 +0.011151,268 +0.012182,268 +0.012015,268 +0.011588,268 +0.011319,268 +0.011843,268 +0.011518,268 +0.013115,268 +0.011957,268 +0.013827,270 +0.011480,270 +0.011624,270 +0.011960,270 +0.013117,270 +0.013719,270 +0.012665,270 +0.014312,270 +0.018070,270 +0.012840,270 +0.013579,270 +0.013749,270 +0.011697,270 +0.011351,270 +0.012223,270 +0.017580,270 +0.011414,270 +0.011318,270 +0.011599,270 +0.011700,270 +0.012627,270 +0.011451,270 +0.011609,270 +0.011333,270 +0.011392,270 +0.010944,270 +0.010892,270 +0.011558,270 +0.011820,270 +0.011908,270 +0.011294,270 +0.011460,270 +0.013014,270 +0.014360,270 +0.011905,270 +0.011698,270 +0.011326,270 +0.011469,270 +0.011072,270 +0.011061,270 +0.012363,270 +0.011825,270 +0.012339,270 +0.011823,270 +0.014907,270 +0.011328,270 +0.011481,270 +0.011953,270 +0.014402,270 +0.014933,270 +0.011434,270 +0.011730,270 +0.011142,270 +0.011680,270 +0.011440,270 +0.011634,270 +0.011048,270 +0.012270,270 +0.011313,270 +0.011724,270 +0.011649,270 +0.014341,270 +0.017158,270 +0.013464,270 +0.011567,270 +0.011611,270 +0.011913,270 +0.013445,270 +0.011918,270 +0.015169,270 +0.014472,270 +0.011883,270 +0.012696,270 +0.012013,270 +0.011942,270 +0.011916,270 +0.011145,270 +0.013960,270 +0.012014,270 +0.011429,270 +0.011623,270 +0.013834,270 +0.011994,270 +0.011362,270 +0.010976,270 +0.011128,270 +0.010985,270 +0.011327,270 +0.011608,270 +0.013648,270 +0.011881,270 +0.011458,270 +0.011348,270 +0.011615,270 +0.012125,270 +0.011188,270 +0.013129,270 +0.011223,270 +0.011644,270 +0.011201,270 +0.011853,272 +0.012187,272 +0.012305,272 +0.013455,272 +0.012277,272 +0.012017,272 +0.015585,272 +0.012174,272 +0.011242,272 +0.011910,272 +0.011257,272 +0.011207,272 +0.011918,272 +0.011065,272 +0.011464,272 +0.012213,272 +0.011118,272 +0.011124,272 +0.011316,272 +0.011282,272 +0.011464,272 +0.011202,272 +0.011479,272 +0.011615,272 +0.011943,272 +0.011892,272 +0.011300,272 +0.013015,272 +0.011799,272 +0.012453,272 +0.011830,272 +0.015279,272 +0.013138,272 +0.011969,272 +0.012412,272 +0.013635,272 +0.011874,272 +0.012776,272 +0.012803,272 +0.012065,272 +0.012143,272 +0.011485,272 +0.011841,272 +0.012257,272 +0.012161,272 +0.011664,272 +0.012727,272 +0.012390,272 +0.011519,272 +0.012903,272 +0.012968,272 +0.011564,272 +0.011474,272 +0.012503,272 +0.013555,272 +0.011861,272 +0.017892,272 +0.012202,272 +0.011796,272 +0.011900,272 +0.011608,272 +0.011639,272 +0.012110,272 +0.011517,272 +0.011523,272 +0.011379,272 +0.011210,272 +0.011205,272 +0.011195,272 +0.011060,272 +0.011284,272 +0.011000,272 +0.011011,272 +0.011319,272 +0.010966,272 +0.011012,272 +0.011026,272 +0.010966,272 +0.010985,272 +0.011140,272 +0.010966,272 +0.011092,272 +0.011223,272 +0.010995,272 +0.011014,272 +0.010989,272 +0.010997,272 +0.010986,272 +0.011621,272 +0.010976,272 +0.011770,272 +0.011894,272 +0.012049,272 +0.012264,272 +0.012022,272 +0.011747,272 +0.012237,272 +0.012840,272 +0.012496,272 +0.018836,272 +0.012484,274 +0.011528,274 +0.011521,274 +0.011412,274 +0.011490,274 +0.011426,274 +0.011435,274 +0.017460,274 +0.011924,274 +0.011255,274 +0.011323,274 +0.011351,274 +0.011352,274 +0.011390,274 +0.011604,274 +0.014364,274 +0.014529,274 +0.011399,274 +0.011264,274 +0.011219,274 +0.011388,274 +0.011373,274 +0.011226,274 +0.011304,274 +0.017376,274 +0.011361,274 +0.011385,274 +0.011204,274 +0.011264,274 +0.011887,274 +0.011308,274 +0.011339,274 +0.017406,274 +0.013205,274 +0.012187,274 +0.011445,274 +0.011474,274 +0.011793,274 +0.011532,274 +0.011725,274 +0.017909,274 +0.011546,274 +0.012766,274 +0.011466,274 +0.011593,274 +0.011637,274 +0.011641,274 +0.013013,274 +0.018135,274 +0.013629,274 +0.011539,274 +0.012274,274 +0.012491,274 +0.011918,274 +0.012186,274 +0.011985,274 +0.017766,274 +0.011750,274 +0.011517,274 +0.011799,274 +0.011707,274 +0.011869,274 +0.012377,274 +0.012414,274 +0.011907,274 +0.012177,274 +0.011493,274 +0.011761,274 +0.012167,274 +0.012437,274 +0.011576,274 +0.011602,274 +0.012961,274 +0.011365,274 +0.011398,274 +0.011277,274 +0.011328,274 +0.011243,274 +0.011415,274 +0.011370,274 +0.011262,274 +0.013047,274 +0.011328,274 +0.011282,274 +0.011300,274 +0.011189,274 +0.011350,274 +0.011451,274 +0.011256,274 +0.011985,274 +0.012333,274 +0.011306,274 +0.011182,274 +0.011293,274 +0.011283,274 +0.011312,274 +0.011405,274 +0.011258,274 +0.012624,274 +0.011732,274 +0.011626,276 +0.011830,276 +0.011472,276 +0.011444,276 +0.012230,276 +0.011908,276 +0.011449,276 +0.013251,276 +0.011545,276 +0.011906,276 +0.011556,276 +0.011654,276 +0.011653,276 +0.011543,276 +0.011620,276 +0.014764,276 +0.012550,276 +0.011524,276 +0.011551,276 +0.011626,276 +0.011757,276 +0.012318,276 +0.011735,276 +0.012132,276 +0.012866,276 +0.011526,276 +0.011551,276 +0.011645,276 +0.011461,276 +0.011700,276 +0.011646,276 +0.011464,276 +0.013195,276 +0.011691,276 +0.011567,276 +0.011444,276 +0.011548,276 +0.011577,276 +0.011507,276 +0.011613,276 +0.011945,276 +0.013265,276 +0.011492,276 +0.011523,276 +0.011529,276 +0.011488,276 +0.011626,276 +0.011577,276 +0.011430,276 +0.013222,276 +0.011690,276 +0.011585,276 +0.011442,276 +0.011534,276 +0.011572,276 +0.011527,276 +0.011698,276 +0.011460,276 +0.013457,276 +0.011480,276 +0.011521,276 +0.011593,276 +0.011477,276 +0.011625,276 +0.011618,276 +0.011504,276 +0.013268,276 +0.011676,276 +0.011595,276 +0.011449,276 +0.011510,276 +0.011694,276 +0.011560,276 +0.011675,276 +0.011486,276 +0.013421,276 +0.011482,276 +0.011500,276 +0.011549,276 +0.011423,276 +0.011618,276 +0.011554,276 +0.011484,276 +0.013115,276 +0.011791,276 +0.011593,276 +0.011446,276 +0.011472,276 +0.011623,276 +0.011769,276 +0.011809,276 +0.011456,276 +0.013300,276 +0.011511,276 +0.011486,276 +0.011532,276 +0.011444,276 +0.011601,276 +0.011573,276 +0.011466,276 +0.014016,278 +0.012821,278 +0.011816,278 +0.011791,278 +0.011814,278 +0.011808,278 +0.011876,278 +0.011704,278 +0.012423,278 +0.013013,278 +0.011796,278 +0.011863,278 +0.011816,278 +0.012011,278 +0.011901,278 +0.011876,278 +0.011801,278 +0.013614,278 +0.012472,278 +0.011975,278 +0.011879,278 +0.011779,278 +0.011925,278 +0.011799,278 +0.011921,278 +0.013394,278 +0.012003,278 +0.011716,278 +0.011783,278 +0.011709,278 +0.011817,278 +0.011915,278 +0.011706,278 +0.012678,278 +0.012789,278 +0.011801,278 +0.011737,278 +0.011810,278 +0.011883,278 +0.011786,278 +0.011824,278 +0.011753,278 +0.013593,278 +0.011803,278 +0.011789,278 +0.011834,278 +0.011888,278 +0.011825,278 +0.011847,278 +0.011877,278 +0.013396,278 +0.011984,278 +0.011737,278 +0.011921,278 +0.011703,278 +0.011848,278 +0.012008,278 +0.012461,278 +0.013065,278 +0.015012,278 +0.011799,278 +0.011843,278 +0.011725,278 +0.011822,278 +0.011867,278 +0.011685,278 +0.012549,278 +0.017619,278 +0.012041,278 +0.011872,278 +0.011734,278 +0.011846,278 +0.011907,278 +0.011726,278 +0.013490,278 +0.016518,278 +0.012111,278 +0.011972,278 +0.011709,278 +0.011893,278 +0.011847,278 +0.011849,278 +0.013321,278 +0.017125,278 +0.011849,278 +0.012183,278 +0.011838,278 +0.011931,278 +0.011931,278 +0.011880,278 +0.016327,278 +0.013564,278 +0.011901,278 +0.011785,278 +0.012227,278 +0.012016,278 +0.015415,278 +0.012437,278 +0.018601,278 +0.011967,278 +0.012358,280 +0.012528,280 +0.012497,280 +0.012089,280 +0.012103,280 +0.013682,280 +0.016582,280 +0.011985,280 +0.012008,280 +0.012124,280 +0.012076,280 +0.012043,280 +0.012039,280 +0.015314,280 +0.015128,280 +0.011979,280 +0.012000,280 +0.012176,280 +0.012002,280 +0.012048,280 +0.011957,280 +0.017007,280 +0.013269,280 +0.011976,280 +0.012094,280 +0.012067,280 +0.012082,280 +0.012120,280 +0.011987,280 +0.018353,280 +0.012012,280 +0.012067,280 +0.011959,280 +0.012076,280 +0.012149,280 +0.011906,280 +0.012002,280 +0.018332,280 +0.012014,280 +0.012062,280 +0.011926,280 +0.012084,280 +0.012065,280 +0.012078,280 +0.011952,280 +0.018367,280 +0.012072,280 +0.011984,280 +0.012042,280 +0.012131,280 +0.012037,280 +0.012020,280 +0.011885,280 +0.018517,280 +0.012033,280 +0.011994,280 +0.012136,280 +0.012023,280 +0.012108,280 +0.012008,280 +0.012312,280 +0.019490,280 +0.012129,280 +0.012053,280 +0.012023,280 +0.012058,280 +0.011982,280 +0.012002,280 +0.015990,280 +0.014953,280 +0.012328,280 +0.012194,280 +0.012157,280 +0.012081,280 +0.012064,280 +0.011945,280 +0.018334,280 +0.012104,280 +0.011964,280 +0.012029,280 +0.012046,280 +0.012069,280 +0.012067,280 +0.012037,280 +0.018357,280 +0.011993,280 +0.012012,280 +0.012035,280 +0.012176,280 +0.011944,280 +0.011945,280 +0.012023,280 +0.018378,280 +0.012070,280 +0.011964,280 +0.012046,280 +0.012120,280 +0.011925,280 +0.011982,280 +0.012008,280 +0.018777,282 +0.012455,282 +0.012229,282 +0.012423,282 +0.012639,282 +0.012323,282 +0.012197,282 +0.017554,282 +0.013383,282 +0.012235,282 +0.012296,282 +0.012469,282 +0.012245,282 +0.012271,282 +0.012269,282 +0.018619,282 +0.012279,282 +0.012240,282 +0.012295,282 +0.012357,282 +0.012275,282 +0.012292,282 +0.012448,282 +0.018508,282 +0.012233,282 +0.012294,282 +0.012277,282 +0.012265,282 +0.012279,282 +0.012284,282 +0.016910,282 +0.014048,282 +0.012333,282 +0.012298,282 +0.012427,282 +0.012202,282 +0.012237,282 +0.012336,282 +0.019885,282 +0.012457,282 +0.012339,282 +0.012278,282 +0.012321,282 +0.012412,282 +0.012197,282 +0.015114,282 +0.016011,282 +0.012308,282 +0.012356,282 +0.012507,282 +0.012255,282 +0.012235,282 +0.012698,282 +0.019801,282 +0.013296,282 +0.013066,282 +0.012764,282 +0.012640,282 +0.012618,282 +0.012736,282 +0.016990,282 +0.014150,282 +0.012346,282 +0.012283,282 +0.012471,282 +0.012238,282 +0.012256,282 +0.012278,282 +0.018771,282 +0.012374,282 +0.012408,282 +0.012287,282 +0.012941,282 +0.012385,282 +0.012293,282 +0.014701,282 +0.016269,282 +0.012355,282 +0.012353,282 +0.012427,282 +0.012444,282 +0.012636,282 +0.013100,282 +0.020059,282 +0.013754,282 +0.015306,282 +0.013966,282 +0.013118,282 +0.013573,282 +0.013209,282 +0.013211,282 +0.013682,282 +0.013451,282 +0.013830,282 +0.016563,282 +0.014275,282 +0.013191,282 +0.014931,282 +0.013361,282 +0.013060,282 +0.013946,284 +0.013994,284 +0.013735,284 +0.013689,284 +0.015005,284 +0.013579,284 +0.013733,284 +0.013731,284 +0.014022,284 +0.013994,284 +0.013784,284 +0.013775,284 +0.013650,284 +0.013812,284 +0.013409,284 +0.013660,284 +0.013485,284 +0.013261,284 +0.012729,284 +0.013414,284 +0.012799,284 +0.012514,284 +0.012703,284 +0.012598,284 +0.012822,284 +0.012455,284 +0.012624,284 +0.012976,284 +0.012607,284 +0.012557,284 +0.012518,284 +0.012584,284 +0.012541,284 +0.013689,284 +0.013699,284 +0.013100,284 +0.013475,284 +0.012920,284 +0.013383,284 +0.014202,284 +0.014666,284 +0.014012,284 +0.013489,284 +0.013736,284 +0.013426,284 +0.013414,284 +0.013479,284 +0.013610,284 +0.013781,284 +0.013853,284 +0.014394,284 +0.013401,284 +0.013368,284 +0.013851,284 +0.013561,284 +0.013997,284 +0.013764,284 +0.015446,284 +0.013561,284 +0.013659,284 +0.013920,284 +0.013185,284 +0.013524,284 +0.013365,284 +0.015054,284 +0.014309,284 +0.013730,284 +0.013936,284 +0.013663,284 +0.013726,284 +0.013492,284 +0.014247,284 +0.013913,284 +0.013512,284 +0.013265,284 +0.013152,284 +0.012955,284 +0.012899,284 +0.012563,284 +0.012663,284 +0.012529,284 +0.012587,284 +0.012622,284 +0.012544,284 +0.012493,284 +0.012484,284 +0.012470,284 +0.012798,284 +0.012542,284 +0.012523,284 +0.012628,284 +0.012525,284 +0.012440,284 +0.012487,284 +0.012466,284 +0.012660,284 +0.012507,284 +0.012504,284 +0.012633,284 +0.012492,284 +0.012885,286 +0.012740,286 +0.012743,286 +0.012959,286 +0.012753,286 +0.012818,286 +0.012940,286 +0.012742,286 +0.012681,286 +0.012706,286 +0.012818,286 +0.013008,286 +0.012674,286 +0.012738,286 +0.013173,286 +0.012881,286 +0.012797,286 +0.013203,286 +0.013836,286 +0.013470,286 +0.013405,286 +0.013145,286 +0.013560,286 +0.013173,286 +0.012748,286 +0.012981,286 +0.013443,286 +0.013051,286 +0.012730,286 +0.012914,286 +0.012685,286 +0.012631,286 +0.012703,286 +0.012712,286 +0.013049,286 +0.012640,286 +0.012690,286 +0.012926,286 +0.012703,286 +0.012614,286 +0.012685,286 +0.012711,286 +0.013000,286 +0.012728,286 +0.012750,286 +0.012863,286 +0.012725,286 +0.012820,286 +0.012615,286 +0.012768,286 +0.012977,286 +0.012775,286 +0.012779,286 +0.012877,286 +0.012749,286 +0.012727,286 +0.012663,286 +0.012842,286 +0.012997,286 +0.012824,286 +0.012818,286 +0.012674,286 +0.012758,286 +0.012853,286 +0.012863,286 +0.012864,286 +0.012988,286 +0.012823,286 +0.012866,286 +0.012704,286 +0.012687,286 +0.012745,286 +0.012806,286 +0.013069,286 +0.012840,286 +0.012767,286 +0.012968,286 +0.012784,286 +0.012612,286 +0.012711,286 +0.012723,286 +0.013276,286 +0.012728,286 +0.012752,286 +0.012881,286 +0.012702,286 +0.012743,286 +0.012612,286 +0.012753,286 +0.013214,286 +0.012757,286 +0.012776,286 +0.012821,286 +0.012775,286 +0.012750,286 +0.012712,286 +0.012857,286 +0.013142,286 +0.012788,286 +0.012879,286 +0.013201,288 +0.012976,288 +0.013002,288 +0.012988,288 +0.013214,288 +0.013187,288 +0.013072,288 +0.013409,288 +0.013022,288 +0.012897,288 +0.013063,288 +0.012993,288 +0.013472,288 +0.013100,288 +0.012897,288 +0.013178,288 +0.013025,288 +0.013024,288 +0.013205,288 +0.013200,288 +0.013378,288 +0.013053,288 +0.013097,288 +0.014063,288 +0.013531,288 +0.013111,288 +0.012972,288 +0.013326,288 +0.013193,288 +0.013007,288 +0.013126,288 +0.013079,288 +0.013020,288 +0.013074,288 +0.013201,288 +0.013680,288 +0.013155,288 +0.013164,288 +0.013608,288 +0.013087,288 +0.013348,288 +0.013029,288 +0.013178,288 +0.013346,288 +0.013070,288 +0.013138,288 +0.013156,288 +0.013135,288 +0.013054,288 +0.013051,288 +0.013585,288 +0.014019,288 +0.013054,288 +0.013111,288 +0.013063,288 +0.013061,288 +0.013035,288 +0.013075,288 +0.013358,288 +0.013098,288 +0.013045,288 +0.013083,288 +0.012938,288 +0.012982,288 +0.013000,288 +0.013198,288 +0.013349,288 +0.013032,288 +0.013157,288 +0.013035,288 +0.013016,288 +0.012915,288 +0.013047,288 +0.013452,288 +0.013033,288 +0.012995,288 +0.012971,288 +0.013044,288 +0.013024,288 +0.012997,288 +0.013056,288 +0.013446,288 +0.013038,288 +0.013153,288 +0.013140,288 +0.012877,288 +0.012974,288 +0.013012,288 +0.013184,288 +0.013406,288 +0.012904,288 +0.013190,288 +0.013045,288 +0.013018,288 +0.012908,288 +0.012955,288 +0.013446,288 +0.013057,288 +0.013114,288 +0.012941,288 +0.013481,290 +0.013334,290 +0.013320,290 +0.013323,290 +0.013687,290 +0.013270,290 +0.013456,290 +0.013301,290 +0.013286,290 +0.013170,290 +0.013281,290 +0.013732,290 +0.013544,290 +0.013473,290 +0.014077,290 +0.013593,290 +0.013379,290 +0.013369,290 +0.013526,290 +0.013858,290 +0.013238,290 +0.013551,290 +0.013339,290 +0.013329,290 +0.013351,290 +0.013180,290 +0.013894,290 +0.013400,290 +0.013488,290 +0.013460,290 +0.013149,290 +0.013432,290 +0.014937,290 +0.013927,290 +0.013685,290 +0.013380,290 +0.013409,290 +0.013391,290 +0.013376,290 +0.013751,290 +0.013292,290 +0.013819,290 +0.013339,290 +0.013473,290 +0.013314,290 +0.013291,290 +0.013173,290 +0.013790,290 +0.013684,290 +0.013551,290 +0.013448,290 +0.013325,290 +0.013243,290 +0.013352,290 +0.013321,290 +0.013306,290 +0.013955,290 +0.013242,290 +0.013509,290 +0.013295,290 +0.013302,290 +0.013305,290 +0.013144,290 +0.013688,290 +0.013629,290 +0.013456,290 +0.013424,290 +0.013146,290 +0.013349,290 +0.013292,290 +0.013466,290 +0.013820,290 +0.013269,290 +0.013694,290 +0.013465,290 +0.013425,290 +0.013293,290 +0.013317,290 +0.013721,290 +0.013529,290 +0.013479,290 +0.013367,290 +0.013148,290 +0.013268,290 +0.013541,290 +0.013400,290 +0.013686,290 +0.013212,290 +0.013478,290 +0.013329,290 +0.013299,290 +0.013286,290 +0.013170,290 +0.013637,290 +0.013704,290 +0.013489,290 +0.013450,290 +0.013332,290 +0.013141,290 +0.013324,290 +0.014173,292 +0.013964,292 +0.013706,292 +0.013608,292 +0.013528,292 +0.013538,292 +0.013556,292 +0.013539,292 +0.014056,292 +0.013518,292 +0.013774,292 +0.013569,292 +0.013601,292 +0.013535,292 +0.013463,292 +0.013851,292 +0.013804,292 +0.013714,292 +0.013679,292 +0.013573,292 +0.013422,292 +0.013563,292 +0.013673,292 +0.013962,292 +0.013572,292 +0.013598,292 +0.013531,292 +0.013587,292 +0.013540,292 +0.013535,292 +0.013977,292 +0.013441,292 +0.013751,292 +0.013548,292 +0.013621,292 +0.013551,292 +0.013401,292 +0.013880,292 +0.013904,292 +0.013742,292 +0.013665,292 +0.013593,292 +0.013414,292 +0.013546,292 +0.013682,292 +0.014659,292 +0.014596,292 +0.014658,292 +0.013872,292 +0.014497,292 +0.014095,292 +0.014564,292 +0.014594,292 +0.015230,292 +0.014673,292 +0.014149,292 +0.014151,292 +0.014572,292 +0.014287,292 +0.014656,292 +0.014418,292 +0.014275,292 +0.013836,292 +0.013588,292 +0.013943,292 +0.014227,292 +0.014491,292 +0.014003,292 +0.013849,292 +0.013481,292 +0.014047,292 +0.013839,292 +0.013693,292 +0.014099,292 +0.015242,292 +0.014441,292 +0.014667,292 +0.015529,292 +0.016512,292 +0.016460,292 +0.015420,292 +0.016760,292 +0.014867,292 +0.014562,292 +0.014597,292 +0.014859,292 +0.014662,292 +0.014812,292 +0.015283,292 +0.015188,292 +0.014670,292 +0.014191,292 +0.014242,292 +0.014280,292 +0.014270,292 +0.014309,292 +0.013729,292 +0.013819,292 +0.014126,292 +0.013795,292 +0.014795,294 +0.014027,294 +0.013913,294 +0.013824,294 +0.015135,294 +0.016026,294 +0.015641,294 +0.015718,294 +0.015860,294 +0.015509,294 +0.015591,294 +0.014985,294 +0.015005,294 +0.016038,294 +0.016855,294 +0.016140,294 +0.015329,294 +0.015619,294 +0.015057,294 +0.014654,294 +0.015085,294 +0.015368,294 +0.015454,294 +0.015917,294 +0.015275,294 +0.015016,294 +0.015117,294 +0.015881,294 +0.017002,294 +0.016115,294 +0.016410,294 +0.015987,294 +0.014855,294 +0.015974,294 +0.014814,294 +0.015446,294 +0.015848,294 +0.015758,294 +0.014875,294 +0.014658,294 +0.014860,294 +0.015297,294 +0.016768,294 +0.015180,294 +0.014770,294 +0.015168,294 +0.015061,294 +0.015951,294 +0.017409,294 +0.017436,294 +0.017312,294 +0.015754,294 +0.016206,294 +0.016827,294 +0.016502,294 +0.016044,294 +0.015842,294 +0.018897,294 +0.019509,294 +0.018065,294 +0.019213,294 +0.015811,294 +0.015241,294 +0.014296,294 +0.015615,294 +0.017037,294 +0.017171,294 +0.015242,294 +0.015142,294 +0.015733,294 +0.016041,294 +0.015273,294 +0.015189,294 +0.015082,294 +0.015422,294 +0.016060,294 +0.016130,294 +0.016446,294 +0.017918,294 +0.016325,294 +0.016780,294 +0.015085,294 +0.014598,294 +0.015548,294 +0.018661,294 +0.018239,294 +0.015832,294 +0.015122,294 +0.018574,294 +0.017859,294 +0.016707,294 +0.014995,294 +0.015211,294 +0.014929,294 +0.015035,294 +0.014774,294 +0.014655,294 +0.015027,294 +0.015038,294 +0.015198,294 +0.014681,296 +0.014288,296 +0.015142,296 +0.015681,296 +0.015230,296 +0.015222,296 +0.015204,296 +0.015051,296 +0.015135,296 +0.015832,296 +0.016320,296 +0.015317,296 +0.015174,296 +0.014283,296 +0.016614,296 +0.016972,296 +0.014858,296 +0.014459,296 +0.014602,296 +0.014277,296 +0.015539,296 +0.015612,296 +0.016112,296 +0.015737,296 +0.015104,296 +0.014696,296 +0.015561,296 +0.015715,296 +0.015489,296 +0.015198,296 +0.015239,296 +0.015045,296 +0.015285,296 +0.015164,296 +0.014412,296 +0.014795,296 +0.014220,296 +0.014082,296 +0.013997,296 +0.014116,296 +0.014535,296 +0.014673,296 +0.015166,296 +0.015054,296 +0.014801,296 +0.016423,296 +0.019121,296 +0.016707,296 +0.017321,296 +0.015645,296 +0.015656,296 +0.014643,296 +0.014348,296 +0.014928,296 +0.015420,296 +0.015165,296 +0.015154,296 +0.014837,296 +0.015405,296 +0.015458,296 +0.023828,296 +0.024815,296 +0.016970,296 +0.017982,296 +0.015732,296 +0.016239,296 +0.015299,296 +0.014810,296 +0.014520,296 +0.014830,296 +0.015901,296 +0.015074,296 +0.015274,296 +0.016604,296 +0.015285,296 +0.014779,296 +0.015344,296 +0.015064,296 +0.014944,296 +0.016107,296 +0.015013,296 +0.014853,296 +0.014481,296 +0.015386,296 +0.014975,296 +0.015724,296 +0.014866,296 +0.015657,296 +0.014461,296 +0.014291,296 +0.014056,296 +0.014826,296 +0.014428,296 +0.015374,296 +0.014666,296 +0.015026,296 +0.014345,296 +0.014619,296 +0.015102,296 +0.014787,296 +0.015666,298 +0.014854,298 +0.015187,298 +0.015992,298 +0.016170,298 +0.015382,298 +0.016049,298 +0.015758,298 +0.016153,298 +0.015938,298 +0.016403,298 +0.016760,298 +0.016727,298 +0.017336,298 +0.015007,298 +0.015812,298 +0.016600,298 +0.017088,298 +0.021346,298 +0.016721,298 +0.018078,298 +0.016002,298 +0.015634,298 +0.016869,298 +0.015550,298 +0.015720,298 +0.015011,298 +0.015664,298 +0.015481,298 +0.015510,298 +0.018328,298 +0.020421,298 +0.015091,298 +0.014703,298 +0.014954,298 +0.014855,298 +0.016252,298 +0.017516,298 +0.018290,298 +0.017556,298 +0.016717,298 +0.019328,298 +0.018002,298 +0.017207,298 +0.017260,298 +0.016040,298 +0.015982,298 +0.015778,298 +0.016230,298 +0.017668,298 +0.016499,298 +0.017272,298 +0.015800,298 +0.015261,298 +0.015103,298 +0.015956,298 +0.016004,298 +0.016785,298 +0.016497,298 +0.015962,298 +0.015830,298 +0.017555,298 +0.016003,298 +0.016073,298 +0.016233,298 +0.016343,298 +0.015528,298 +0.017081,298 +0.015666,298 +0.015200,298 +0.015575,298 +0.014971,298 +0.015492,298 +0.016195,298 +0.016266,298 +0.015414,298 +0.015653,298 +0.015342,298 +0.015384,298 +0.015154,298 +0.017177,298 +0.016570,298 +0.017330,298 +0.016724,298 +0.018397,298 +0.021554,298 +0.025023,298 +0.016175,298 +0.017001,298 +0.016864,298 +0.016334,298 +0.016042,298 +0.015923,298 +0.017484,298 +0.016283,298 +0.014971,298 +0.015364,298 +0.016135,298 +0.016538,298 +0.015348,298 diff --git a/buch/papers/multiplikation/code/meas/test/winograd.txt b/buch/papers/multiplikation/code/meas/test/winograd.txt new file mode 100644 index 0000000..d01fefd --- /dev/null +++ b/buch/papers/multiplikation/code/meas/test/winograd.txt @@ -0,0 +1,14900 @@ +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,2 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000010,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000010,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000000,4 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000010,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000011,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000010,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000001,6 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000012,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000011,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000012,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000011,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000014,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000011,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000015,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000011,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000011,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000011,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000002,8 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000013,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000012,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000013,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000005,10 +0.000005,10 +0.000005,10 +0.000014,10 +0.000004,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000003,10 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000015,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000014,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000005,12 +0.000008,14 +0.000008,14 +0.000018,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000017,14 +0.000012,14 +0.000013,14 +0.000009,14 +0.000011,14 +0.000014,14 +0.000010,14 +0.000008,14 +0.000008,14 +0.000014,14 +0.000013,14 +0.000010,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000015,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000012,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000009,14 +0.000010,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000017,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000008,14 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000022,16 +0.000011,16 +0.000011,16 +0.000020,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000021,16 +0.000011,16 +0.000011,16 +0.000020,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000011,16 +0.000016,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000027,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000015,18 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000026,20 +0.000028,20 +0.000031,20 +0.000031,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000031,20 +0.000052,20 +0.000021,20 +0.000021,20 +0.000030,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000028,20 +0.000025,20 +0.000032,20 +0.000036,20 +0.000031,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000021,20 +0.000031,20 +0.000021,20 +0.000030,20 +0.000031,20 +0.000048,22 +0.000038,22 +0.000028,22 +0.000037,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000035,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000035,22 +0.000037,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000029,22 +0.000042,22 +0.000042,22 +0.000036,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000027,22 +0.000036,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000052,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000047,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000048,24 +0.000070,24 +0.000045,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000046,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000035,24 +0.000043,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000034,24 +0.000044,26 +0.000043,26 +0.000052,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000044,26 +0.000057,26 +0.000045,26 +0.000044,26 +0.000044,26 +0.000052,26 +0.000043,26 +0.000043,26 +0.000084,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000061,26 +0.000062,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000053,26 +0.000053,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000067,26 +0.000073,26 +0.000044,26 +0.000072,26 +0.000074,26 +0.000053,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000061,26 +0.000057,26 +0.000053,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000043,26 +0.000065,26 +0.000091,26 +0.000047,26 +0.000044,26 +0.000044,26 +0.000048,26 +0.000044,26 +0.000044,26 +0.000049,26 +0.000048,26 +0.000053,26 +0.000043,26 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000084,28 +0.000084,28 +0.000098,28 +0.000063,28 +0.000054,28 +0.000054,28 +0.000064,28 +0.000084,28 +0.000064,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000081,28 +0.000063,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000053,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000053,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000064,28 +0.000074,28 +0.000085,28 +0.000095,28 +0.000063,28 +0.000054,28 +0.000064,28 +0.000073,28 +0.000085,28 +0.000064,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000053,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000053,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000062,28 +0.000092,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000054,28 +0.000067,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000066,30 +0.000066,30 +0.000065,30 +0.000098,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000066,30 +0.000065,30 +0.000066,30 +0.000066,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000104,30 +0.000077,30 +0.000127,30 +0.000075,30 +0.000065,30 +0.000066,30 +0.000095,30 +0.000086,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000076,30 +0.000087,30 +0.000140,30 +0.000075,30 +0.000066,30 +0.000085,30 +0.000106,30 +0.000076,30 +0.000066,30 +0.000065,30 +0.000066,30 +0.000101,30 +0.000065,30 +0.000065,30 +0.000066,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000066,30 +0.000065,30 +0.000066,30 +0.000066,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000074,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000067,30 +0.000098,30 +0.000108,30 +0.000075,30 +0.000065,30 +0.000085,30 +0.000106,30 +0.000076,30 +0.000066,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000065,30 +0.000066,30 +0.000066,30 +0.000065,30 +0.000065,30 +0.000066,30 +0.000065,30 +0.000065,30 +0.000076,30 +0.000081,30 +0.000103,30 +0.000096,30 +0.000069,30 +0.000091,30 +0.000080,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000090,32 +0.000089,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000110,32 +0.000138,32 +0.000099,32 +0.000079,32 +0.000099,32 +0.000120,32 +0.000089,32 +0.000079,32 +0.000119,32 +0.000121,32 +0.000081,32 +0.000085,32 +0.000086,32 +0.000093,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000114,32 +0.000110,32 +0.000155,32 +0.000089,32 +0.000079,32 +0.000090,32 +0.000120,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000109,32 +0.000112,32 +0.000132,32 +0.000079,32 +0.000079,32 +0.000121,32 +0.000089,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000105,32 +0.000089,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000079,32 +0.000103,32 +0.000089,32 +0.000096,34 +0.000094,34 +0.000094,34 +0.000125,34 +0.000139,34 +0.000115,34 +0.000114,34 +0.000136,34 +0.000104,34 +0.000094,34 +0.000104,34 +0.000119,34 +0.000094,34 +0.000094,34 +0.000094,34 +0.000094,34 +0.000094,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000126,34 +0.000168,34 +0.000104,34 +0.000115,34 +0.000136,34 +0.000105,34 +0.000095,34 +0.000139,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000106,34 +0.000159,34 +0.000134,34 +0.000095,34 +0.000125,34 +0.000116,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000131,34 +0.000095,34 +0.000095,34 +0.000125,34 +0.000165,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000095,34 +0.000125,34 +0.000143,34 +0.000149,34 +0.000095,34 +0.000115,34 +0.000136,34 +0.000104,34 +0.000095,34 +0.000105,34 +0.000133,34 +0.000152,34 +0.000095,34 +0.000105,34 +0.000135,34 +0.000094,34 +0.000094,34 +0.000094,34 +0.000094,34 +0.000094,34 +0.000094,34 +0.000095,34 +0.000112,36 +0.000123,36 +0.000175,36 +0.000120,36 +0.000146,36 +0.000125,36 +0.000115,36 +0.000115,36 +0.000131,36 +0.000124,36 +0.000124,36 +0.000124,36 +0.000124,36 +0.000140,36 +0.000129,36 +0.000124,36 +0.000159,36 +0.000135,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000114,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000115,36 +0.000150,36 +0.000122,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000133,36 +0.000151,36 +0.000163,36 +0.000153,36 +0.000152,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000145,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000152,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000123,36 +0.000148,36 +0.000127,36 +0.000123,36 +0.000163,36 +0.000121,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000132,36 +0.000111,36 +0.000112,36 +0.000112,36 +0.000112,36 +0.000133,38 +0.000131,38 +0.000131,38 +0.000173,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000141,38 +0.000189,38 +0.000178,38 +0.000140,38 +0.000182,38 +0.000141,38 +0.000131,38 +0.000138,38 +0.000181,38 +0.000175,38 +0.000181,38 +0.000162,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000146,38 +0.000174,38 +0.000230,38 +0.000194,38 +0.000195,38 +0.000222,38 +0.000131,38 +0.000134,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000132,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000132,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000132,38 +0.000131,38 +0.000175,38 +0.000197,38 +0.000144,38 +0.000176,38 +0.000175,38 +0.000134,38 +0.000135,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000182,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000152,38 +0.000131,38 +0.000141,38 +0.000189,38 +0.000179,38 +0.000172,38 +0.000171,38 +0.000131,38 +0.000169,38 +0.000131,38 +0.000141,38 +0.000140,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000131,38 +0.000177,38 +0.000163,38 +0.000161,38 +0.000182,38 +0.000131,38 +0.000131,38 +0.000149,38 +0.000209,40 +0.000172,40 +0.000213,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000192,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000153,40 +0.000217,40 +0.000162,40 +0.000203,40 +0.000209,40 +0.000152,40 +0.000152,40 +0.000152,40 +0.000174,40 +0.000152,40 +0.000152,40 +0.000163,40 +0.000179,40 +0.000210,40 +0.000172,40 +0.000225,40 +0.000160,40 +0.000200,40 +0.000195,40 +0.000184,40 +0.000167,40 +0.000154,40 +0.000174,40 +0.000181,40 +0.000166,40 +0.000162,40 +0.000153,40 +0.000165,40 +0.000165,40 +0.000153,40 +0.000164,40 +0.000157,40 +0.000157,40 +0.000157,40 +0.000157,40 +0.000157,40 +0.000163,40 +0.000153,40 +0.000153,40 +0.000153,40 +0.000164,40 +0.000195,40 +0.000158,40 +0.000153,40 +0.000185,40 +0.000165,40 +0.000153,40 +0.000153,40 +0.000163,40 +0.000165,40 +0.000152,40 +0.000153,40 +0.000153,40 +0.000153,40 +0.000169,40 +0.000272,40 +0.000177,40 +0.000195,40 +0.000196,40 +0.000162,40 +0.000210,40 +0.000177,40 +0.000166,40 +0.000176,40 +0.000258,40 +0.000241,40 +0.000176,40 +0.000166,40 +0.000156,40 +0.000156,40 +0.000156,40 +0.000156,40 +0.000156,40 +0.000156,40 +0.000156,40 +0.000156,40 +0.000184,40 +0.000184,40 +0.000198,40 +0.000158,40 +0.000158,40 +0.000158,40 +0.000158,40 +0.000184,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000238,42 +0.000302,42 +0.000215,42 +0.000192,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000206,42 +0.000199,42 +0.000188,42 +0.000203,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000206,42 +0.000309,42 +0.000182,42 +0.000222,42 +0.000182,42 +0.000219,42 +0.000280,42 +0.000212,42 +0.000225,42 +0.000187,42 +0.000187,42 +0.000187,42 +0.000191,42 +0.000187,42 +0.000187,42 +0.000305,42 +0.000270,42 +0.000180,42 +0.000204,42 +0.000298,42 +0.000289,42 +0.000190,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000201,42 +0.000314,42 +0.000307,42 +0.000314,42 +0.000338,42 +0.000333,42 +0.000327,42 +0.000317,42 +0.000329,42 +0.000328,42 +0.000363,42 +0.000331,42 +0.000323,42 +0.000311,42 +0.000269,42 +0.000233,42 +0.000212,42 +0.000217,42 +0.000272,42 +0.000322,42 +0.000341,42 +0.000225,42 +0.000195,42 +0.000182,42 +0.000182,42 +0.000207,42 +0.000273,42 +0.000187,42 +0.000187,42 +0.000187,42 +0.000187,42 +0.000193,42 +0.000182,42 +0.000182,42 +0.000182,42 +0.000215,42 +0.000220,42 +0.000202,42 +0.000191,42 +0.000208,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000180,42 +0.000209,44 +0.000207,44 +0.000207,44 +0.000285,44 +0.000239,44 +0.000239,44 +0.000247,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000253,44 +0.000235,44 +0.000246,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000221,44 +0.000212,44 +0.000212,44 +0.000263,44 +0.000250,44 +0.000227,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000226,44 +0.000207,44 +0.000207,44 +0.000257,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000246,44 +0.000249,44 +0.000217,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000244,44 +0.000239,44 +0.000207,44 +0.000207,44 +0.000231,44 +0.000240,44 +0.000247,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000273,44 +0.000237,44 +0.000216,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000224,44 +0.000245,44 +0.000262,44 +0.000227,44 +0.000207,44 +0.000207,44 +0.000212,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000226,44 +0.000271,44 +0.000272,44 +0.000212,44 +0.000217,44 +0.000212,44 +0.000212,44 +0.000212,44 +0.000212,44 +0.000212,44 +0.000245,44 +0.000227,44 +0.000207,44 +0.000207,44 +0.000210,44 +0.000249,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000207,44 +0.000237,46 +0.000261,46 +0.000249,46 +0.000236,46 +0.000236,46 +0.000255,46 +0.000240,46 +0.000281,46 +0.000263,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000235,46 +0.000236,46 +0.000274,46 +0.000241,46 +0.000274,46 +0.000230,46 +0.000229,46 +0.000230,46 +0.000259,46 +0.000357,46 +0.000296,46 +0.000256,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000255,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000255,46 +0.000248,46 +0.000269,46 +0.000253,46 +0.000229,46 +0.000324,46 +0.000286,46 +0.000245,46 +0.000240,46 +0.000282,46 +0.000265,46 +0.000230,46 +0.000230,46 +0.000230,46 +0.000230,46 +0.000283,46 +0.000302,46 +0.000239,46 +0.000230,46 +0.000230,46 +0.000230,46 +0.000229,46 +0.000230,46 +0.000229,46 +0.000230,46 +0.000229,46 +0.000230,46 +0.000229,46 +0.000230,46 +0.000230,46 +0.000230,46 +0.000229,46 +0.000230,46 +0.000280,46 +0.000230,46 +0.000230,46 +0.000229,46 +0.000229,46 +0.000322,46 +0.000386,46 +0.000279,46 +0.000242,46 +0.000242,46 +0.000242,46 +0.000267,46 +0.000236,46 +0.000236,46 +0.000235,46 +0.000236,46 +0.000260,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000235,46 +0.000236,46 +0.000236,46 +0.000236,46 +0.000242,46 +0.000265,46 +0.000372,46 +0.000339,48 +0.000281,48 +0.000438,48 +0.000286,48 +0.000281,48 +0.000260,48 +0.000276,48 +0.000333,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000293,48 +0.000363,48 +0.000319,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000299,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000371,48 +0.000476,48 +0.000272,48 +0.000263,48 +0.000304,48 +0.000263,48 +0.000309,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000300,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000352,48 +0.000466,48 +0.000337,48 +0.000263,48 +0.000263,48 +0.000263,48 +0.000378,48 +0.000471,48 +0.000335,48 +0.000260,48 +0.000260,48 +0.000260,48 +0.000358,48 +0.000337,48 +0.000293,48 +0.000260,48 +0.000274,48 +0.000271,48 +0.000274,48 +0.000271,48 +0.000273,48 +0.000271,48 +0.000282,48 +0.000283,48 +0.000260,48 +0.000260,48 +0.000285,48 +0.000260,48 +0.000284,48 +0.000260,48 +0.000272,48 +0.000272,48 +0.000260,48 +0.000331,48 +0.000461,48 +0.000328,48 +0.000291,48 +0.000325,48 +0.000402,48 +0.000333,48 +0.000284,48 +0.000300,50 +0.000316,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000533,50 +0.000402,50 +0.000340,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000400,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000301,50 +0.000506,50 +0.000445,50 +0.000294,50 +0.000309,50 +0.000424,50 +0.000302,50 +0.000304,50 +0.000304,50 +0.000310,50 +0.000294,50 +0.000294,50 +0.000344,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000355,50 +0.000308,50 +0.000333,50 +0.000294,50 +0.000333,50 +0.000465,50 +0.000440,50 +0.000349,50 +0.000508,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000341,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000313,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000374,50 +0.000299,50 +0.000294,50 +0.000344,50 +0.000294,50 +0.000300,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000572,50 +0.000427,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000332,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000297,50 +0.000461,50 +0.000454,50 +0.000376,50 +0.000313,50 +0.000294,50 +0.000294,50 +0.000294,50 +0.000354,50 +0.000294,50 +0.000588,52 +0.000370,52 +0.000333,52 +0.000333,52 +0.000378,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000415,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000655,52 +0.000353,52 +0.000591,52 +0.000396,52 +0.000367,52 +0.000341,52 +0.000375,52 +0.000330,52 +0.000330,52 +0.000378,52 +0.000591,52 +0.000334,52 +0.000333,52 +0.000333,52 +0.000333,52 +0.000333,52 +0.000333,52 +0.000375,52 +0.000330,52 +0.000369,52 +0.000330,52 +0.000330,52 +0.000336,52 +0.000493,52 +0.000479,52 +0.000333,52 +0.000333,52 +0.000333,52 +0.000378,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000494,52 +0.000468,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000376,52 +0.000408,52 +0.000376,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000575,52 +0.000368,52 +0.000330,52 +0.000340,52 +0.000405,52 +0.000378,52 +0.000339,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000600,52 +0.000340,52 +0.000330,52 +0.000330,52 +0.000345,52 +0.000349,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000390,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000382,52 +0.000589,52 +0.000369,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000329,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000330,52 +0.000372,54 +0.000369,54 +0.000369,54 +0.000579,54 +0.000500,54 +0.000471,54 +0.000378,54 +0.000369,54 +0.000379,54 +0.000378,54 +0.000443,54 +0.000369,54 +0.000410,54 +0.000515,54 +0.000437,54 +0.000546,54 +0.000378,54 +0.000377,54 +0.000369,54 +0.000380,54 +0.000588,54 +0.000405,54 +0.000368,54 +0.000369,54 +0.000369,54 +0.000369,54 +0.000369,54 +0.000431,54 +0.000369,54 +0.000369,54 +0.000369,54 +0.000410,54 +0.000413,54 +0.000369,54 +0.000369,54 +0.000651,54 +0.000382,54 +0.000373,54 +0.000373,54 +0.000373,54 +0.000373,54 +0.000373,54 +0.000416,54 +0.000369,54 +0.000369,54 +0.000369,54 +0.000400,54 +0.000459,54 +0.000369,54 +0.000369,54 +0.000381,54 +0.000378,54 +0.000402,54 +0.000379,54 +0.000411,54 +0.000527,54 +0.000369,54 +0.000379,54 +0.000408,54 +0.000369,54 +0.000369,54 +0.000369,54 +0.000404,54 +0.000369,54 +0.000409,54 +0.000369,54 +0.000369,54 +0.000389,54 +0.000369,54 +0.000459,54 +0.000376,54 +0.000438,54 +0.000442,54 +0.000378,54 +0.000369,54 +0.000369,54 +0.000541,54 +0.000588,54 +0.000392,54 +0.000389,54 +0.000389,54 +0.000403,54 +0.000378,54 +0.000378,54 +0.000378,54 +0.000379,54 +0.000378,54 +0.000378,54 +0.000434,54 +0.000369,54 +0.000369,54 +0.000369,54 +0.000406,54 +0.000368,54 +0.000369,54 +0.000369,54 +0.000454,54 +0.000443,54 +0.000395,54 +0.000369,54 +0.000412,56 +0.000410,56 +0.000452,56 +0.000410,56 +0.000411,56 +0.000410,56 +0.000411,56 +0.000411,56 +0.000410,56 +0.000411,56 +0.000451,56 +0.000455,56 +0.000490,56 +0.000466,56 +0.000411,56 +0.000410,56 +0.000411,56 +0.000411,56 +0.000410,56 +0.000410,56 +0.000411,56 +0.000447,56 +0.000410,56 +0.000410,56 +0.000411,56 +0.000411,56 +0.000411,56 +0.000430,56 +0.000486,56 +0.000467,56 +0.000448,56 +0.000411,56 +0.000410,56 +0.000498,56 +0.000450,56 +0.000491,56 +0.000471,56 +0.000411,56 +0.000410,56 +0.000443,56 +0.000410,56 +0.000410,56 +0.000411,56 +0.000411,56 +0.000410,56 +0.000410,56 +0.000411,56 +0.000410,56 +0.000412,56 +0.000528,56 +0.000454,56 +0.000411,56 +0.000451,56 +0.000411,56 +0.000410,56 +0.000410,56 +0.000517,56 +0.000489,56 +0.000410,56 +0.000410,56 +0.000498,56 +0.000450,56 +0.000410,56 +0.000410,56 +0.000411,56 +0.000431,56 +0.000437,56 +0.000479,56 +0.000411,56 +0.000411,56 +0.000430,56 +0.000442,56 +0.000662,56 +0.000483,56 +0.000445,56 +0.000454,56 +0.000410,56 +0.000410,56 +0.000410,56 +0.000410,56 +0.000597,56 +0.000603,56 +0.000460,56 +0.000458,56 +0.000709,56 +0.000501,56 +0.000462,56 +0.000453,56 +0.000433,56 +0.000421,56 +0.000421,56 +0.000421,56 +0.000449,56 +0.000411,56 +0.000411,56 +0.000679,56 +0.000441,56 +0.000421,56 +0.000421,56 +0.000421,56 +0.000469,58 +0.000832,58 +0.000624,58 +0.000507,58 +0.000506,58 +0.000455,58 +0.000455,58 +0.000538,58 +0.000739,58 +0.000536,58 +0.000467,58 +0.000467,58 +0.000468,58 +0.000487,58 +0.000554,58 +0.000495,58 +0.000467,58 +0.000467,58 +0.000559,58 +0.000508,58 +0.000480,58 +0.000480,58 +0.000582,58 +0.000483,58 +0.000480,58 +0.000480,58 +0.000480,58 +0.000480,58 +0.000506,58 +0.000477,58 +0.000467,58 +0.000467,58 +0.000499,58 +0.000455,58 +0.000697,58 +0.000636,58 +0.000502,58 +0.000472,58 +0.000514,58 +0.000506,58 +0.000566,58 +0.000465,58 +0.000455,58 +0.000515,58 +0.000707,58 +0.000478,58 +0.000487,58 +0.000519,58 +0.000490,58 +0.000467,58 +0.000467,58 +0.000522,58 +0.000483,58 +0.000467,58 +0.000488,58 +0.000477,58 +0.000467,58 +0.000467,58 +0.000467,58 +0.000478,58 +0.000642,58 +0.000498,58 +0.000483,58 +0.000472,58 +0.000467,58 +0.000467,58 +0.000467,58 +0.000502,58 +0.000533,58 +0.000473,58 +0.000467,58 +0.000480,58 +0.000455,58 +0.000498,58 +0.000544,58 +0.000455,58 +0.000632,58 +0.000488,58 +0.000500,58 +0.000507,58 +0.000468,58 +0.000486,58 +0.000499,58 +0.000455,58 +0.000480,58 +0.000493,58 +0.000467,58 +0.000530,58 +0.000557,58 +0.000495,58 +0.000518,58 +0.000539,58 +0.000572,58 +0.000487,58 +0.000467,58 +0.000495,58 +0.000467,58 +0.000498,58 +0.000613,58 +0.000513,58 +0.000605,60 +0.000517,60 +0.000526,60 +0.000540,60 +0.000503,60 +0.000504,60 +0.000648,60 +0.000701,60 +0.000610,60 +0.000554,60 +0.000532,60 +0.000517,60 +0.000645,60 +0.000517,60 +0.000516,60 +0.000517,60 +0.000531,60 +0.000638,60 +0.000557,60 +0.000517,60 +0.000517,60 +0.000517,60 +0.000517,60 +0.000517,60 +0.000563,60 +0.000653,60 +0.000517,60 +0.000517,60 +0.000565,60 +0.000560,60 +0.000555,60 +0.000548,60 +0.000517,60 +0.000525,60 +0.000650,60 +0.000613,60 +0.000596,60 +0.000517,60 +0.000547,60 +0.000614,60 +0.000526,60 +0.000517,60 +0.000556,60 +0.000551,60 +0.000517,60 +0.000517,60 +0.000670,60 +0.000537,60 +0.000517,60 +0.000531,60 +0.000517,60 +0.000517,60 +0.000613,60 +0.000547,60 +0.000517,60 +0.000585,60 +0.000543,60 +0.000517,60 +0.000517,60 +0.000552,60 +0.000550,60 +0.000553,60 +0.000528,60 +0.000559,60 +0.000517,60 +0.000517,60 +0.000684,60 +0.000583,60 +0.000526,60 +0.000517,60 +0.000604,60 +0.000517,60 +0.000517,60 +0.000517,60 +0.000517,60 +0.000588,60 +0.000538,60 +0.000610,60 +0.000534,60 +0.000622,60 +0.000517,60 +0.000517,60 +0.000596,60 +0.000558,60 +0.000544,60 +0.000564,60 +0.000545,60 +0.000537,60 +0.000517,60 +0.000542,60 +0.000586,60 +0.000582,60 +0.000579,60 +0.000522,60 +0.000517,60 +0.000554,60 +0.000558,60 +0.000604,60 +0.000526,60 +0.000563,60 +0.000599,62 +0.000611,62 +0.000569,62 +0.000601,62 +0.000648,62 +0.000579,62 +0.000605,62 +0.000607,62 +0.000613,62 +0.000570,62 +0.000654,62 +0.000610,62 +0.000637,62 +0.000569,62 +0.000569,62 +0.000596,62 +0.000611,62 +0.000664,62 +0.000569,62 +0.000598,62 +0.000570,62 +0.000575,62 +0.000639,62 +0.000654,62 +0.000661,62 +0.000570,62 +0.000569,62 +0.000671,62 +0.000625,62 +0.000630,62 +0.000595,62 +0.000580,62 +0.000695,62 +0.000584,62 +0.000569,62 +0.000719,62 +0.000616,62 +0.000569,62 +0.000644,62 +0.000610,62 +0.000615,62 +0.000605,62 +0.000626,62 +0.000580,62 +0.000580,62 +0.000659,62 +0.000601,62 +0.000570,62 +0.000675,62 +0.000597,62 +0.000570,62 +0.000735,62 +0.000596,62 +0.000570,62 +0.000569,62 +0.000609,62 +0.000749,62 +0.000793,62 +0.000687,62 +0.000570,62 +0.000785,62 +0.000754,62 +0.000608,62 +0.000626,62 +0.000628,62 +0.000734,62 +0.000564,62 +0.000593,62 +0.000564,62 +0.000598,62 +0.000848,62 +0.000569,62 +0.000602,62 +0.000569,62 +0.000781,62 +0.000628,62 +0.000621,62 +0.000570,62 +0.000569,62 +0.000689,62 +0.000595,62 +0.000598,62 +0.000650,62 +0.000576,62 +0.000569,62 +0.000627,62 +0.000617,62 +0.000649,62 +0.000590,62 +0.000579,62 +0.000569,62 +0.000569,62 +0.000569,62 +0.000587,62 +0.000582,62 +0.000569,62 +0.000570,62 +0.000570,62 +0.000555,62 +0.000779,62 +0.000785,64 +0.000667,64 +0.000626,64 +0.000672,64 +0.000706,64 +0.000632,64 +0.000670,64 +0.000610,64 +0.000609,64 +0.000704,64 +0.000675,64 +0.000625,64 +0.000799,64 +0.000684,64 +0.000636,64 +0.000636,64 +0.000610,64 +0.000610,64 +0.000652,64 +0.000610,64 +0.000609,64 +0.000621,64 +0.000832,64 +0.000626,64 +0.000740,64 +0.000707,64 +0.000636,64 +0.000626,64 +0.000626,64 +0.000677,64 +0.000675,64 +0.000680,64 +0.000849,64 +0.000617,64 +0.000616,64 +0.000617,64 +0.000655,64 +0.000617,64 +0.000894,64 +0.000675,64 +0.000660,64 +0.000877,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000630,64 +0.000630,64 +0.000610,64 +0.000822,64 +0.000718,64 +0.000626,64 +0.000816,64 +0.000610,64 +0.000732,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000803,64 +0.000667,64 +0.000646,64 +0.000626,64 +0.000640,64 +0.000626,64 +0.000650,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000646,64 +0.000610,64 +0.000610,64 +0.000755,64 +0.000610,64 +0.000610,64 +0.000630,64 +0.000767,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000653,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000650,64 +0.000610,64 +0.000658,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000610,64 +0.000643,64 +0.000610,64 +0.000701,66 +0.000736,66 +0.000701,66 +0.000695,66 +0.000757,66 +0.000892,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000794,66 +0.000719,66 +0.000730,66 +0.000720,66 +0.000768,66 +0.000752,66 +0.000803,66 +0.000695,66 +0.000803,66 +0.000817,66 +0.000695,66 +0.000730,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000730,66 +0.000695,66 +0.000695,66 +0.000714,66 +0.000695,66 +0.000695,66 +0.000733,66 +0.000735,66 +0.000877,66 +0.000695,66 +0.000695,66 +0.000788,66 +0.000696,66 +0.000707,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000736,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000696,66 +0.000695,66 +0.000730,66 +0.000830,66 +0.001033,66 +0.000793,66 +0.000776,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000695,66 +0.000734,66 +0.000734,66 +0.000695,66 +0.000705,66 +0.000695,66 +0.000695,66 +0.000723,66 +0.000735,66 +0.000887,66 +0.000839,66 +0.001128,66 +0.000973,66 +0.000763,66 +0.000749,66 +0.000970,66 +0.000838,66 +0.000749,66 +0.000845,66 +0.000848,66 +0.000736,66 +0.001027,66 +0.001168,66 +0.001270,66 +0.000751,66 +0.000812,66 +0.000766,66 +0.000714,66 +0.000796,66 +0.000723,66 +0.000749,66 +0.000777,66 +0.000744,66 +0.000703,66 +0.000795,66 +0.000938,66 +0.000951,66 +0.001383,66 +0.000888,66 +0.000774,66 +0.000845,66 +0.001012,66 +0.000972,66 +0.000907,68 +0.001312,68 +0.001344,68 +0.001450,68 +0.001564,68 +0.001454,68 +0.001484,68 +0.001321,68 +0.001172,68 +0.000795,68 +0.000780,68 +0.000896,68 +0.000932,68 +0.000758,68 +0.000793,68 +0.000760,68 +0.000781,68 +0.000796,68 +0.000750,68 +0.000798,68 +0.000770,68 +0.000750,68 +0.000815,68 +0.000750,68 +0.000768,68 +0.000752,68 +0.000890,68 +0.000791,68 +0.000766,68 +0.000730,68 +0.000794,68 +0.000783,68 +0.000771,68 +0.000731,68 +0.000795,68 +0.000825,68 +0.000740,68 +0.000731,68 +0.000730,68 +0.000730,68 +0.000773,68 +0.000730,68 +0.000749,68 +0.000730,68 +0.000829,68 +0.000801,68 +0.000730,68 +0.000872,68 +0.000770,68 +0.000843,68 +0.000796,68 +0.000978,68 +0.000765,68 +0.000857,68 +0.000780,68 +0.000829,68 +0.000744,68 +0.000778,68 +0.000767,68 +0.000777,68 +0.000798,68 +0.000741,68 +0.000730,68 +0.000799,68 +0.000816,68 +0.000816,68 +0.000731,68 +0.000730,68 +0.000800,68 +0.000808,68 +0.000837,68 +0.000731,68 +0.000770,68 +0.000770,68 +0.000832,68 +0.000751,68 +0.000831,68 +0.000730,68 +0.000792,68 +0.000730,68 +0.000751,68 +0.000774,68 +0.000730,68 +0.000730,68 +0.000730,68 +0.000730,68 +0.000830,68 +0.000773,68 +0.000881,68 +0.000797,68 +0.000875,68 +0.000819,68 +0.000830,68 +0.000844,68 +0.000806,68 +0.000879,68 +0.000793,68 +0.000781,68 +0.000763,68 +0.000952,68 +0.000825,70 +0.000867,70 +0.000921,70 +0.000877,70 +0.000817,70 +0.000908,70 +0.000816,70 +0.000816,70 +0.000816,70 +0.000817,70 +0.000928,70 +0.000842,70 +0.000823,70 +0.000836,70 +0.000795,70 +0.000836,70 +0.000795,70 +0.000834,70 +0.000795,70 +0.000835,70 +0.000830,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000841,70 +0.000815,70 +0.000795,70 +0.000795,70 +0.000889,70 +0.000954,70 +0.000795,70 +0.000795,70 +0.000820,70 +0.000839,70 +0.000795,70 +0.000795,70 +0.000835,70 +0.000795,70 +0.000842,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000818,70 +0.000795,70 +0.000795,70 +0.000796,70 +0.000795,70 +0.000822,70 +0.000835,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000840,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000835,70 +0.000804,70 +0.000835,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000797,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000797,70 +0.000795,70 +0.000835,70 +0.000795,70 +0.000795,70 +0.000842,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000819,70 +0.000835,70 +0.000795,70 +0.000795,70 +0.000795,70 +0.000801,70 +0.000795,70 +0.000819,70 +0.000814,70 +0.000795,70 +0.000797,70 +0.000984,70 +0.000963,70 +0.000832,70 +0.000852,70 +0.000813,70 +0.000854,70 +0.000875,70 +0.000834,70 +0.001028,70 +0.000839,70 +0.000928,72 +0.000914,72 +0.000922,72 +0.000943,72 +0.001004,72 +0.000911,72 +0.000916,72 +0.000949,72 +0.000974,72 +0.001009,72 +0.001021,72 +0.000943,72 +0.000939,72 +0.001050,72 +0.001369,72 +0.000906,72 +0.000931,72 +0.000939,72 +0.001310,72 +0.001418,72 +0.001016,72 +0.000865,72 +0.000924,72 +0.000993,72 +0.000865,72 +0.001087,72 +0.001341,72 +0.000912,72 +0.000969,72 +0.000912,72 +0.000910,72 +0.000887,72 +0.001002,72 +0.000927,72 +0.000911,72 +0.000972,72 +0.001009,72 +0.000945,72 +0.000917,72 +0.000887,72 +0.000948,72 +0.001074,72 +0.000913,72 +0.001173,72 +0.000888,72 +0.001074,72 +0.000951,72 +0.001027,72 +0.000887,72 +0.000908,72 +0.000988,72 +0.000917,72 +0.000887,72 +0.000888,72 +0.000888,72 +0.000912,72 +0.001002,72 +0.000969,72 +0.000928,72 +0.000915,72 +0.001005,72 +0.001022,72 +0.000888,72 +0.000914,72 +0.001134,72 +0.000888,72 +0.000888,72 +0.000908,72 +0.000944,72 +0.001175,72 +0.000911,72 +0.000897,72 +0.000915,72 +0.000887,72 +0.000887,72 +0.000951,72 +0.000912,72 +0.000887,72 +0.000907,72 +0.000887,72 +0.001062,72 +0.000899,72 +0.000865,72 +0.000865,72 +0.000865,72 +0.000925,72 +0.000875,72 +0.000894,72 +0.000865,72 +0.000900,72 +0.000865,72 +0.001257,72 +0.000972,72 +0.000991,72 +0.001001,72 +0.000906,72 +0.000978,72 +0.000865,72 +0.000907,72 +0.000898,72 +0.000985,74 +0.001021,74 +0.000988,74 +0.001000,74 +0.001000,74 +0.001176,74 +0.000992,74 +0.000938,74 +0.000938,74 +0.000938,74 +0.001051,74 +0.000978,74 +0.001045,74 +0.000988,74 +0.001011,74 +0.001138,74 +0.001130,74 +0.001041,74 +0.000939,74 +0.001171,74 +0.001081,74 +0.001145,74 +0.001003,74 +0.000959,74 +0.000938,74 +0.000974,74 +0.001038,74 +0.001237,74 +0.001027,74 +0.001068,74 +0.000938,74 +0.000938,74 +0.000938,74 +0.000975,74 +0.000938,74 +0.000978,74 +0.000965,74 +0.001030,74 +0.000938,74 +0.000938,74 +0.001065,74 +0.001153,74 +0.000963,74 +0.000998,74 +0.000958,74 +0.001040,74 +0.000952,74 +0.000938,74 +0.000999,74 +0.001004,74 +0.000938,74 +0.000938,74 +0.000977,74 +0.001011,74 +0.000938,74 +0.000978,74 +0.001126,74 +0.001096,74 +0.001035,74 +0.000964,74 +0.000978,74 +0.000970,74 +0.001084,74 +0.000958,74 +0.000958,74 +0.001020,74 +0.000938,74 +0.000938,74 +0.000939,74 +0.001004,74 +0.000978,74 +0.000938,74 +0.000938,74 +0.000938,74 +0.000961,74 +0.000938,74 +0.000938,74 +0.000958,74 +0.000963,74 +0.000938,74 +0.001061,74 +0.000938,74 +0.000966,74 +0.000938,74 +0.000938,74 +0.000938,74 +0.000988,74 +0.000938,74 +0.000978,74 +0.000938,74 +0.000961,74 +0.000938,74 +0.000938,74 +0.000938,74 +0.000943,74 +0.000938,74 +0.000938,74 +0.000959,74 +0.000938,74 +0.000963,74 +0.001054,76 +0.001051,76 +0.001090,76 +0.001150,76 +0.001072,76 +0.001172,76 +0.001086,76 +0.001111,76 +0.001071,76 +0.001152,76 +0.001089,76 +0.001051,76 +0.001051,76 +0.001086,76 +0.001061,76 +0.001051,76 +0.001051,76 +0.001075,76 +0.001051,76 +0.001091,76 +0.001112,76 +0.001086,76 +0.001051,76 +0.001071,76 +0.001051,76 +0.001055,76 +0.001051,76 +0.001051,76 +0.001055,76 +0.001051,76 +0.001051,76 +0.001051,76 +0.001053,76 +0.001051,76 +0.001091,76 +0.001051,76 +0.001094,76 +0.001051,76 +0.001051,76 +0.001090,76 +0.001055,76 +0.001052,76 +0.001051,76 +0.001051,76 +0.001118,76 +0.001051,76 +0.001051,76 +0.001183,76 +0.001303,76 +0.001051,76 +0.001112,76 +0.001124,76 +0.001051,76 +0.001051,76 +0.001075,76 +0.001051,76 +0.001553,76 +0.001176,76 +0.001095,76 +0.001416,76 +0.001071,76 +0.001087,76 +0.001051,76 +0.001051,76 +0.001091,76 +0.001083,76 +0.001102,76 +0.001051,76 +0.001092,76 +0.001051,76 +0.001051,76 +0.001071,76 +0.001075,76 +0.001051,76 +0.001216,76 +0.001051,76 +0.001080,76 +0.001051,76 +0.001051,76 +0.001051,76 +0.001114,76 +0.001090,76 +0.001051,76 +0.001053,76 +0.001051,76 +0.001051,76 +0.001051,76 +0.001055,76 +0.001052,76 +0.001094,76 +0.001051,76 +0.001053,76 +0.001051,76 +0.001051,76 +0.001051,76 +0.001115,76 +0.001051,76 +0.001091,76 +0.001053,76 +0.001051,76 +0.001100,78 +0.001097,78 +0.001101,78 +0.001097,78 +0.001097,78 +0.001097,78 +0.001099,78 +0.001097,78 +0.001097,78 +0.001122,78 +0.001097,78 +0.001136,78 +0.001156,78 +0.001120,78 +0.001097,78 +0.001097,78 +0.001125,78 +0.001097,78 +0.001097,78 +0.001097,78 +0.001099,78 +0.001097,78 +0.001097,78 +0.001097,78 +0.001101,78 +0.001097,78 +0.001136,78 +0.001138,78 +0.001097,78 +0.001097,78 +0.001097,78 +0.001101,78 +0.001097,78 +0.001097,78 +0.001097,78 +0.001119,78 +0.001147,78 +0.001097,78 +0.001167,78 +0.001097,78 +0.001097,78 +0.001136,78 +0.001140,78 +0.001097,78 +0.001097,78 +0.001099,78 +0.001097,78 +0.001097,78 +0.001141,78 +0.001167,78 +0.001148,78 +0.001130,78 +0.001170,78 +0.001122,78 +0.001332,78 +0.001157,78 +0.001139,78 +0.001136,78 +0.001097,78 +0.001121,78 +0.001196,78 +0.001097,78 +0.001096,78 +0.001127,78 +0.001097,78 +0.001097,78 +0.001119,78 +0.001097,78 +0.001097,78 +0.001097,78 +0.001160,78 +0.001117,78 +0.001116,78 +0.001097,78 +0.001125,78 +0.001097,78 +0.001097,78 +0.001119,78 +0.001097,78 +0.001097,78 +0.001096,78 +0.001122,78 +0.001097,78 +0.001097,78 +0.001121,78 +0.001136,78 +0.001097,78 +0.001136,78 +0.001128,78 +0.001097,78 +0.001171,78 +0.001097,78 +0.001103,78 +0.001097,78 +0.001117,78 +0.001106,78 +0.001097,78 +0.001097,78 +0.001097,78 +0.001100,78 +0.001264,80 +0.001262,80 +0.001225,80 +0.001223,80 +0.001223,80 +0.001227,80 +0.001223,80 +0.001223,80 +0.001223,80 +0.001225,80 +0.001223,80 +0.001223,80 +0.001227,80 +0.001223,80 +0.001262,80 +0.001283,80 +0.001223,80 +0.001223,80 +0.001227,80 +0.001223,80 +0.001223,80 +0.001223,80 +0.001225,80 +0.001282,80 +0.001223,80 +0.001227,80 +0.001223,80 +0.001712,80 +0.001329,80 +0.001264,80 +0.001255,80 +0.001251,80 +0.001223,80 +0.001599,80 +0.001299,80 +0.001271,80 +0.001335,80 +0.001309,80 +0.001575,80 +0.001408,80 +0.001299,80 +0.001467,80 +0.001480,80 +0.001317,80 +0.001264,80 +0.001394,80 +0.001587,80 +0.001334,80 +0.001425,80 +0.001378,80 +0.001411,80 +0.001429,80 +0.001355,80 +0.001371,80 +0.001385,80 +0.001368,80 +0.001379,80 +0.001418,80 +0.001370,80 +0.001374,80 +0.001350,80 +0.001364,80 +0.001342,80 +0.001407,80 +0.001450,80 +0.001360,80 +0.001466,80 +0.001275,80 +0.001433,80 +0.001438,80 +0.001355,80 +0.001501,80 +0.001334,80 +0.001378,80 +0.001397,80 +0.001461,80 +0.001453,80 +0.001389,80 +0.001323,80 +0.001326,80 +0.001358,80 +0.001449,80 +0.001381,80 +0.001467,80 +0.001347,80 +0.001351,80 +0.001440,80 +0.001414,80 +0.001330,80 +0.001410,80 +0.001383,80 +0.001459,80 +0.001375,80 +0.001542,80 +0.001452,80 +0.001452,80 +0.001384,80 +0.001366,80 +0.001429,80 +0.001353,80 +0.001473,82 +0.001418,82 +0.001347,82 +0.001387,82 +0.001345,82 +0.001437,82 +0.001763,82 +0.001388,82 +0.001389,82 +0.001345,82 +0.001426,82 +0.001455,82 +0.001466,82 +0.001407,82 +0.001468,82 +0.001408,82 +0.001475,82 +0.001458,82 +0.001405,82 +0.001397,82 +0.001423,82 +0.001519,82 +0.001587,82 +0.001440,82 +0.001367,82 +0.001421,82 +0.001491,82 +0.001387,82 +0.002170,82 +0.001483,82 +0.001421,82 +0.001546,82 +0.001426,82 +0.001630,82 +0.001557,82 +0.001396,82 +0.001408,82 +0.001490,82 +0.001365,82 +0.001479,82 +0.001402,82 +0.001574,82 +0.001383,82 +0.001400,82 +0.001366,82 +0.001451,82 +0.001437,82 +0.001522,82 +0.001670,82 +0.001963,82 +0.002133,82 +0.001533,82 +0.001973,82 +0.001660,82 +0.001853,82 +0.001586,82 +0.001375,82 +0.001368,82 +0.001519,82 +0.001350,82 +0.001552,82 +0.001479,82 +0.001522,82 +0.001393,82 +0.001417,82 +0.001377,82 +0.001486,82 +0.001379,82 +0.001348,82 +0.001396,82 +0.001349,82 +0.001388,82 +0.001407,82 +0.001410,82 +0.001679,82 +0.001334,82 +0.001647,82 +0.001530,82 +0.001803,82 +0.001343,82 +0.001370,82 +0.001336,82 +0.001697,82 +0.001429,82 +0.001737,82 +0.001503,82 +0.001345,82 +0.001364,82 +0.001308,82 +0.001612,82 +0.001366,82 +0.001341,82 +0.001347,82 +0.001424,82 +0.001590,82 +0.001366,82 +0.001375,82 +0.001321,82 +0.001353,82 +0.001294,82 +0.001669,84 +0.001526,84 +0.001538,84 +0.001411,84 +0.001462,84 +0.001597,84 +0.001472,84 +0.001640,84 +0.001412,84 +0.001575,84 +0.001458,84 +0.001693,84 +0.001625,84 +0.001592,84 +0.001543,84 +0.001544,84 +0.001556,84 +0.001714,84 +0.001522,84 +0.001623,84 +0.001591,84 +0.001423,84 +0.001478,84 +0.001554,84 +0.001472,84 +0.001471,84 +0.001495,84 +0.001573,84 +0.001593,84 +0.001494,84 +0.001552,84 +0.001578,84 +0.001505,84 +0.001621,84 +0.001543,84 +0.001499,84 +0.001560,84 +0.001557,84 +0.001518,84 +0.001988,84 +0.001971,84 +0.001965,84 +0.001966,84 +0.001569,84 +0.001649,84 +0.001778,84 +0.001657,84 +0.001753,84 +0.001536,84 +0.001505,84 +0.001472,84 +0.001468,84 +0.001448,84 +0.001509,84 +0.001477,84 +0.001544,84 +0.001528,84 +0.001538,84 +0.001554,84 +0.001537,84 +0.001515,84 +0.001594,84 +0.001543,84 +0.001528,84 +0.001484,84 +0.001527,84 +0.001571,84 +0.001508,84 +0.001607,84 +0.001540,84 +0.001538,84 +0.001628,84 +0.001552,84 +0.001569,84 +0.001489,84 +0.001556,84 +0.001618,84 +0.001560,84 +0.001519,84 +0.001590,84 +0.001533,84 +0.001639,84 +0.001880,84 +0.001776,84 +0.001651,84 +0.001795,84 +0.001832,84 +0.001781,84 +0.001668,84 +0.001819,84 +0.001829,84 +0.001789,84 +0.001550,84 +0.001519,84 +0.001526,84 +0.001636,84 +0.001549,84 +0.001489,84 +0.001573,84 +0.001508,84 +0.001689,86 +0.001727,86 +0.001814,86 +0.001746,86 +0.001651,86 +0.001581,86 +0.002784,86 +0.002020,86 +0.001751,86 +0.001838,86 +0.001704,86 +0.001713,86 +0.002233,86 +0.001671,86 +0.001552,86 +0.001590,86 +0.001488,86 +0.001489,86 +0.001621,86 +0.001542,86 +0.001672,86 +0.002154,86 +0.001683,86 +0.001518,86 +0.001719,86 +0.001589,86 +0.001469,86 +0.001469,86 +0.001507,86 +0.001609,86 +0.001761,86 +0.001685,86 +0.001559,86 +0.001546,86 +0.001493,86 +0.001549,86 +0.001502,86 +0.001508,86 +0.001536,86 +0.001624,86 +0.001597,86 +0.001576,86 +0.001566,86 +0.001572,86 +0.001469,86 +0.001510,86 +0.001543,86 +0.001469,86 +0.001513,86 +0.001469,86 +0.001572,86 +0.001678,86 +0.001723,86 +0.001591,86 +0.001565,86 +0.001511,86 +0.001586,86 +0.001469,86 +0.001469,86 +0.001552,86 +0.001868,86 +0.002483,86 +0.002891,86 +0.002797,86 +0.002861,86 +0.002462,86 +0.001964,86 +0.001836,86 +0.001599,86 +0.001622,86 +0.001578,86 +0.001706,86 +0.001705,86 +0.001788,86 +0.001986,86 +0.001600,86 +0.001528,86 +0.001697,86 +0.001970,86 +0.002888,86 +0.002401,86 +0.001572,86 +0.001520,86 +0.001580,86 +0.001508,86 +0.001532,86 +0.001548,86 +0.001624,86 +0.001765,86 +0.001488,86 +0.001627,86 +0.001469,86 +0.001530,86 +0.001525,86 +0.001469,86 +0.001469,86 +0.001512,86 +0.001666,86 +0.001702,86 +0.001659,86 +0.001687,88 +0.001593,88 +0.001635,88 +0.001608,88 +0.001574,88 +0.001612,88 +0.001613,88 +0.001802,88 +0.001868,88 +0.001818,88 +0.001712,88 +0.001593,88 +0.001653,88 +0.001897,88 +0.001593,88 +0.001613,88 +0.001574,88 +0.001771,88 +0.001871,88 +0.001981,88 +0.001962,88 +0.001625,88 +0.001635,88 +0.002564,88 +0.002989,88 +0.002923,88 +0.002775,88 +0.001774,88 +0.001841,88 +0.001674,88 +0.001592,88 +0.001612,88 +0.001573,88 +0.001729,88 +0.001627,88 +0.001949,88 +0.001631,88 +0.001706,88 +0.001599,88 +0.001656,88 +0.001611,88 +0.001573,88 +0.001574,88 +0.001757,88 +0.001927,88 +0.001673,88 +0.001680,88 +0.001703,88 +0.001627,88 +0.001689,88 +0.001610,88 +0.001880,88 +0.001652,88 +0.001959,88 +0.001833,88 +0.001758,88 +0.001791,88 +0.001764,88 +0.001767,88 +0.001668,88 +0.001744,88 +0.001651,88 +0.001574,88 +0.002012,88 +0.001927,88 +0.001750,88 +0.001866,88 +0.001627,88 +0.001799,88 +0.001638,88 +0.001658,88 +0.001789,88 +0.001902,88 +0.001845,88 +0.001852,88 +0.001896,88 +0.001632,88 +0.001619,88 +0.001929,88 +0.002279,88 +0.001912,88 +0.001828,88 +0.001703,88 +0.001683,88 +0.001792,88 +0.001699,88 +0.001671,88 +0.001785,88 +0.001695,88 +0.001674,88 +0.001746,88 +0.001835,88 +0.001816,88 +0.002181,88 +0.002106,88 +0.001822,88 +0.002063,88 +0.001751,88 +0.002060,88 +0.001953,88 +0.002506,90 +0.002729,90 +0.002557,90 +0.002289,90 +0.002198,90 +0.002215,90 +0.002222,90 +0.002952,90 +0.002940,90 +0.002199,90 +0.002351,90 +0.002141,90 +0.001943,90 +0.002165,90 +0.002890,90 +0.002427,90 +0.002257,90 +0.002644,90 +0.002190,90 +0.002735,90 +0.002083,90 +0.002364,90 +0.002731,90 +0.003146,90 +0.002302,90 +0.002487,90 +0.002181,90 +0.002008,90 +0.002087,90 +0.001829,90 +0.001937,90 +0.002182,90 +0.002111,90 +0.002008,90 +0.001927,90 +0.001947,90 +0.002299,90 +0.002398,90 +0.001884,90 +0.001889,90 +0.002031,90 +0.001808,90 +0.001882,90 +0.001899,90 +0.002200,90 +0.002058,90 +0.001909,90 +0.001916,90 +0.001905,90 +0.001876,90 +0.001885,90 +0.001819,90 +0.002004,90 +0.002309,90 +0.002066,90 +0.001904,90 +0.001882,90 +0.001827,90 +0.001815,90 +0.001880,90 +0.001880,90 +0.002356,90 +0.002548,90 +0.001877,90 +0.001901,90 +0.001806,90 +0.001802,90 +0.001874,90 +0.001893,90 +0.002230,90 +0.002034,90 +0.002065,90 +0.001932,90 +0.001997,90 +0.001898,90 +0.002424,90 +0.003206,90 +0.003277,90 +0.003128,90 +0.002408,90 +0.002066,90 +0.002048,90 +0.002269,90 +0.002389,90 +0.002295,90 +0.002206,90 +0.002143,90 +0.002052,90 +0.002010,90 +0.001989,90 +0.002045,90 +0.002232,90 +0.002216,90 +0.002354,90 +0.002202,90 +0.002418,90 +0.002099,90 +0.002110,90 +0.002142,90 +0.002166,90 +0.002204,92 +0.002298,92 +0.002207,92 +0.002173,92 +0.002178,92 +0.002327,92 +0.002337,92 +0.002156,92 +0.002237,92 +0.002421,92 +0.002156,92 +0.002213,92 +0.002182,92 +0.002491,92 +0.002323,92 +0.002225,92 +0.002425,92 +0.002284,92 +0.002338,92 +0.003061,92 +0.003377,92 +0.003534,92 +0.003016,92 +0.002268,92 +0.002223,92 +0.002220,92 +0.002490,92 +0.002097,92 +0.002016,92 +0.002111,92 +0.002131,92 +0.002017,92 +0.001990,92 +0.002122,92 +0.001988,92 +0.001986,92 +0.002012,92 +0.002017,92 +0.001991,92 +0.002005,92 +0.001974,92 +0.002031,92 +0.002031,92 +0.002045,92 +0.002075,92 +0.002085,92 +0.002380,92 +0.002281,92 +0.002188,92 +0.002187,92 +0.002204,92 +0.002148,92 +0.002144,92 +0.002126,92 +0.002146,92 +0.002135,92 +0.002182,92 +0.002274,92 +0.002168,92 +0.002217,92 +0.002235,92 +0.002338,92 +0.002226,92 +0.002195,92 +0.003377,92 +0.003636,92 +0.003556,92 +0.002944,92 +0.002353,92 +0.002290,92 +0.002484,92 +0.002277,92 +0.002147,92 +0.002483,92 +0.002218,92 +0.002122,92 +0.002113,92 +0.002255,92 +0.002275,92 +0.002155,92 +0.002152,92 +0.002163,92 +0.002218,92 +0.002204,92 +0.002177,92 +0.002174,92 +0.002196,92 +0.002190,92 +0.002202,92 +0.002230,92 +0.002163,92 +0.002154,92 +0.002150,92 +0.002293,92 +0.002182,92 +0.002219,92 +0.002143,92 +0.002209,92 +0.002253,92 +0.002173,92 +0.002319,94 +0.002370,94 +0.002364,94 +0.002271,94 +0.002365,94 +0.002355,94 +0.002271,94 +0.003291,94 +0.003712,94 +0.003714,94 +0.003034,94 +0.002388,94 +0.002673,94 +0.002384,94 +0.002423,94 +0.002168,94 +0.002159,94 +0.002336,94 +0.002190,94 +0.002172,94 +0.002268,94 +0.002195,94 +0.002355,94 +0.002301,94 +0.002343,94 +0.002207,94 +0.002375,94 +0.002346,94 +0.002500,94 +0.002342,94 +0.002345,94 +0.002385,94 +0.002242,94 +0.002254,94 +0.002465,94 +0.002337,94 +0.002118,94 +0.002088,94 +0.002141,94 +0.002053,94 +0.002127,94 +0.002154,94 +0.002742,94 +0.002204,94 +0.002145,94 +0.002119,94 +0.002109,94 +0.002133,94 +0.002150,94 +0.002110,94 +0.002025,94 +0.002053,94 +0.002768,94 +0.002178,94 +0.002147,94 +0.002126,94 +0.002086,94 +0.002378,94 +0.002387,94 +0.002090,94 +0.002102,94 +0.002120,94 +0.002158,94 +0.002133,94 +0.002197,94 +0.002690,94 +0.002092,94 +0.002132,94 +0.002095,94 +0.002105,94 +0.002079,94 +0.002148,94 +0.002127,94 +0.002543,94 +0.002073,94 +0.002065,94 +0.002016,94 +0.002084,94 +0.002091,94 +0.001971,94 +0.002219,94 +0.002043,94 +0.002093,94 +0.002011,94 +0.002007,94 +0.001957,94 +0.001953,94 +0.001918,94 +0.002061,94 +0.002174,94 +0.001999,94 +0.001918,94 +0.002002,94 +0.001957,94 +0.001952,94 +0.001918,94 +0.001996,94 +0.002121,94 +0.002045,94 +0.001991,94 +0.002271,96 +0.002186,96 +0.002124,96 +0.002056,96 +0.002083,96 +0.002061,96 +0.002075,96 +0.002041,96 +0.002082,96 +0.002100,96 +0.002065,96 +0.002071,96 +0.002041,96 +0.002045,96 +0.002042,96 +0.002046,96 +0.002042,96 +0.002122,96 +0.002041,96 +0.002087,96 +0.002101,96 +0.002043,96 +0.002041,96 +0.002043,96 +0.002041,96 +0.002128,96 +0.002041,96 +0.002063,96 +0.002041,96 +0.002045,96 +0.002372,96 +0.002088,96 +0.002136,96 +0.002389,96 +0.002162,96 +0.002095,96 +0.002505,96 +0.002663,96 +0.002072,96 +0.002533,96 +0.002530,96 +0.002976,96 +0.003597,96 +0.002478,96 +0.002308,96 +0.002326,96 +0.002289,96 +0.002277,96 +0.002227,96 +0.002305,96 +0.002198,96 +0.002152,96 +0.002522,96 +0.002326,96 +0.002328,96 +0.002126,96 +0.002330,96 +0.002453,96 +0.002437,96 +0.002298,96 +0.002287,96 +0.002595,96 +0.002550,96 +0.002598,96 +0.002488,96 +0.002446,96 +0.002734,96 +0.002717,96 +0.002524,96 +0.002335,96 +0.002321,96 +0.002189,96 +0.002176,96 +0.002150,96 +0.002250,96 +0.002277,96 +0.002221,96 +0.002236,96 +0.002231,96 +0.002248,96 +0.002288,96 +0.002260,96 +0.002340,96 +0.002302,96 +0.002257,96 +0.002349,96 +0.002321,96 +0.002243,96 +0.002259,96 +0.002285,96 +0.002158,96 +0.002152,96 +0.002160,96 +0.002265,96 +0.002317,96 +0.002278,96 +0.002304,96 +0.002213,96 +0.002157,96 +0.002183,96 +0.002445,98 +0.002454,98 +0.002461,98 +0.002463,98 +0.002556,98 +0.002383,98 +0.002484,98 +0.002539,98 +0.002351,98 +0.002377,98 +0.002374,98 +0.002373,98 +0.002304,98 +0.002409,98 +0.002439,98 +0.002416,98 +0.002296,98 +0.002313,98 +0.002352,98 +0.002399,98 +0.002295,98 +0.002355,98 +0.002379,98 +0.002352,98 +0.002363,98 +0.002364,98 +0.002298,98 +0.002357,98 +0.002371,98 +0.002279,98 +0.002246,98 +0.002735,98 +0.002591,98 +0.002416,98 +0.002642,98 +0.002502,98 +0.002411,98 +0.002420,98 +0.002512,98 +0.002377,98 +0.002522,98 +0.002426,98 +0.002718,98 +0.002724,98 +0.002641,98 +0.002545,98 +0.002366,98 +0.002431,98 +0.002570,98 +0.002433,98 +0.002428,98 +0.002452,98 +0.002455,98 +0.002421,98 +0.002828,98 +0.002920,98 +0.003138,98 +0.003385,98 +0.003285,98 +0.002902,98 +0.003023,98 +0.002947,98 +0.002916,98 +0.002957,98 +0.002793,98 +0.003201,98 +0.002843,98 +0.002986,98 +0.002336,98 +0.003146,98 +0.002695,98 +0.002431,98 +0.002494,98 +0.002348,98 +0.002304,98 +0.002355,98 +0.002373,98 +0.002362,98 +0.002358,98 +0.002454,98 +0.002325,98 +0.002288,98 +0.002278,98 +0.002257,98 +0.002223,98 +0.002179,98 +0.002391,98 +0.002197,98 +0.002214,98 +0.002179,98 +0.002314,98 +0.002227,98 +0.002189,98 +0.002274,98 +0.002424,98 +0.002317,98 +0.002325,98 +0.002287,98 +0.002440,98 +0.002235,98 +0.002631,100 +0.003587,100 +0.003203,100 +0.002856,100 +0.002599,100 +0.002795,100 +0.003222,100 +0.002630,100 +0.002563,100 +0.002547,100 +0.002723,100 +0.002813,100 +0.002615,100 +0.002694,100 +0.002470,100 +0.002390,100 +0.002378,100 +0.002357,100 +0.002366,100 +0.002859,100 +0.002374,100 +0.002423,100 +0.002399,100 +0.002359,100 +0.002351,100 +0.002440,100 +0.002509,100 +0.002368,100 +0.002309,100 +0.002358,100 +0.002390,100 +0.002361,100 +0.002445,100 +0.002447,100 +0.002343,100 +0.002413,100 +0.002403,100 +0.002494,100 +0.002308,100 +0.002389,100 +0.002390,100 +0.002425,100 +0.002337,100 +0.002404,100 +0.002424,100 +0.002375,100 +0.002355,100 +0.003358,100 +0.004333,100 +0.004395,100 +0.002452,100 +0.002391,100 +0.002436,100 +0.002365,100 +0.002428,100 +0.002455,100 +0.002320,100 +0.002347,100 +0.002438,100 +0.002372,100 +0.002368,100 +0.002329,100 +0.002793,100 +0.002615,100 +0.002933,100 +0.003123,100 +0.002914,100 +0.002838,100 +0.003154,100 +0.002967,100 +0.003166,100 +0.003947,100 +0.003279,100 +0.003344,100 +0.002560,100 +0.002644,100 +0.003361,100 +0.002568,100 +0.002543,100 +0.002499,100 +0.002502,100 +0.002419,100 +0.002838,100 +0.004438,100 +0.004333,100 +0.003139,100 +0.002395,100 +0.002680,100 +0.002382,100 +0.002357,100 +0.002347,100 +0.002398,100 +0.002343,100 +0.002342,100 +0.002576,100 +0.002307,100 +0.002332,100 +0.002468,100 +0.002346,100 +0.002337,100 +0.002496,102 +0.002542,102 +0.002490,102 +0.002453,102 +0.002558,102 +0.002461,102 +0.002476,102 +0.002542,102 +0.002453,102 +0.002459,102 +0.002561,102 +0.002531,102 +0.002735,102 +0.002487,102 +0.002580,102 +0.002558,102 +0.002536,102 +0.002528,102 +0.002747,102 +0.002652,102 +0.002880,102 +0.002657,102 +0.002634,102 +0.002690,102 +0.002908,102 +0.002496,102 +0.002894,102 +0.002579,102 +0.002784,102 +0.002583,102 +0.002614,102 +0.002550,102 +0.002555,102 +0.002724,102 +0.002518,102 +0.002594,102 +0.002585,102 +0.002763,102 +0.002479,102 +0.002635,102 +0.002453,102 +0.002732,102 +0.002579,102 +0.002501,102 +0.002537,102 +0.002552,102 +0.002534,102 +0.002491,102 +0.002521,102 +0.002630,102 +0.002478,102 +0.002453,102 +0.002599,102 +0.002474,102 +0.002485,102 +0.002490,102 +0.002544,102 +0.002462,102 +0.002457,102 +0.002535,102 +0.002597,102 +0.002591,102 +0.002620,102 +0.002619,102 +0.002475,102 +0.002493,102 +0.002487,102 +0.002495,102 +0.002473,102 +0.002588,102 +0.002487,102 +0.002486,102 +0.002559,102 +0.002453,102 +0.002496,102 +0.002492,102 +0.002496,102 +0.002455,102 +0.002453,102 +0.002457,102 +0.002455,102 +0.002454,102 +0.002496,102 +0.002492,102 +0.002455,102 +0.002457,102 +0.002452,102 +0.002455,102 +0.002617,102 +0.002530,102 +0.002455,102 +0.002492,102 +0.002455,102 +0.002458,102 +0.002453,102 +0.002455,102 +0.002530,102 +0.002486,102 +0.002476,102 +0.002453,102 +0.002644,104 +0.002914,104 +0.002769,104 +0.002818,104 +0.003162,104 +0.002768,104 +0.002623,104 +0.002629,104 +0.002696,104 +0.002602,104 +0.002633,104 +0.002769,104 +0.002594,104 +0.002641,104 +0.002669,104 +0.002631,104 +0.002635,104 +0.002638,104 +0.002594,104 +0.002596,104 +0.002593,104 +0.002675,104 +0.002601,104 +0.002594,104 +0.002599,104 +0.002614,104 +0.002682,104 +0.002697,104 +0.002606,104 +0.002593,104 +0.002598,104 +0.002596,104 +0.002827,104 +0.002739,104 +0.002733,104 +0.002605,104 +0.002660,104 +0.002610,104 +0.002770,104 +0.002754,104 +0.002903,104 +0.002616,104 +0.002653,104 +0.002636,104 +0.002594,104 +0.002617,104 +0.002683,104 +0.002593,104 +0.002621,104 +0.002694,104 +0.002593,104 +0.002931,104 +0.002687,104 +0.002611,104 +0.002615,104 +0.002731,104 +0.002594,104 +0.002599,104 +0.002743,104 +0.002827,104 +0.002593,104 +0.002853,104 +0.002641,104 +0.002677,104 +0.002846,104 +0.002660,104 +0.002593,104 +0.002880,104 +0.002618,104 +0.002593,104 +0.002888,104 +0.002700,104 +0.002593,104 +0.002697,104 +0.002763,104 +0.002742,104 +0.002744,104 +0.002944,104 +0.002612,104 +0.002875,104 +0.002688,104 +0.002594,104 +0.002825,104 +0.002811,104 +0.002790,104 +0.002676,104 +0.002923,104 +0.002650,104 +0.002593,104 +0.002882,104 +0.002773,104 +0.002749,104 +0.002754,104 +0.002698,104 +0.002613,104 +0.002846,104 +0.002832,104 +0.002777,104 +0.002671,104 +0.002618,104 +0.002861,106 +0.002804,106 +0.002767,106 +0.002771,106 +0.002765,106 +0.002768,106 +0.002816,106 +0.003076,106 +0.002747,106 +0.002774,106 +0.002827,106 +0.002822,106 +0.002887,106 +0.003106,106 +0.002937,106 +0.002827,106 +0.002802,106 +0.002752,106 +0.002786,106 +0.002772,106 +0.002751,106 +0.002766,106 +0.002749,106 +0.002751,106 +0.002757,106 +0.002778,106 +0.002750,106 +0.002749,106 +0.002746,106 +0.002751,106 +0.002749,106 +0.002808,106 +0.002755,106 +0.002766,106 +0.002747,106 +0.002748,106 +0.002812,106 +0.003042,106 +0.002754,106 +0.002816,106 +0.002796,106 +0.002796,106 +0.002974,106 +0.002886,106 +0.002746,106 +0.002830,106 +0.002770,106 +0.002814,106 +0.002845,106 +0.002852,106 +0.002921,106 +0.002764,106 +0.002799,106 +0.002937,106 +0.002828,106 +0.002919,106 +0.002782,106 +0.002887,106 +0.002747,106 +0.002781,106 +0.002797,106 +0.002784,106 +0.002768,106 +0.002771,106 +0.002777,106 +0.002746,106 +0.002824,106 +0.002789,106 +0.002930,106 +0.003093,106 +0.002806,106 +0.002859,106 +0.002835,106 +0.002773,106 +0.003069,106 +0.002904,106 +0.002781,106 +0.002778,106 +0.003197,106 +0.002853,106 +0.002909,106 +0.002748,106 +0.003053,106 +0.003029,106 +0.002944,106 +0.003028,106 +0.002922,106 +0.002943,106 +0.002805,106 +0.002842,106 +0.003043,106 +0.002790,106 +0.002891,106 +0.003061,106 +0.002766,106 +0.002845,106 +0.003088,106 +0.002893,106 +0.002975,106 +0.002841,106 +0.003258,108 +0.003219,108 +0.003353,108 +0.003234,108 +0.003371,108 +0.003265,108 +0.003275,108 +0.003025,108 +0.003320,108 +0.003132,108 +0.003040,108 +0.003275,108 +0.003107,108 +0.003192,108 +0.002982,108 +0.002944,108 +0.003102,108 +0.003042,108 +0.003119,108 +0.003389,108 +0.002972,108 +0.002947,108 +0.002959,108 +0.002946,108 +0.003023,108 +0.003080,108 +0.002959,108 +0.003009,108 +0.002963,108 +0.002908,108 +0.003800,108 +0.002959,108 +0.002980,108 +0.002962,108 +0.002907,108 +0.003076,108 +0.003053,108 +0.003043,108 +0.002974,108 +0.002942,108 +0.002948,108 +0.003255,108 +0.003202,108 +0.002996,108 +0.002961,108 +0.002941,108 +0.003798,108 +0.003248,108 +0.003472,108 +0.003765,108 +0.003114,108 +0.003797,108 +0.003137,108 +0.002941,108 +0.003015,108 +0.002948,108 +0.003830,108 +0.003539,108 +0.003319,108 +0.003370,108 +0.003390,108 +0.003863,108 +0.003414,108 +0.003166,108 +0.003177,108 +0.002997,108 +0.004755,108 +0.003511,108 +0.003067,108 +0.003015,108 +0.003014,108 +0.004106,108 +0.003278,108 +0.002963,108 +0.003018,108 +0.003021,108 +0.003756,108 +0.003218,108 +0.004016,108 +0.003551,108 +0.003735,108 +0.003652,108 +0.002973,108 +0.003049,108 +0.003021,108 +0.003233,108 +0.003566,108 +0.003014,108 +0.002982,108 +0.003015,108 +0.002909,108 +0.003506,108 +0.003099,108 +0.003016,108 +0.002987,108 +0.003012,108 +0.003344,108 +0.003108,108 +0.003036,108 +0.002986,108 +0.003121,110 +0.003308,110 +0.003645,110 +0.003130,110 +0.003139,110 +0.003119,110 +0.003193,110 +0.003599,110 +0.003218,110 +0.003943,110 +0.003833,110 +0.004163,110 +0.003342,110 +0.003072,110 +0.003193,110 +0.003109,110 +0.003806,110 +0.003317,110 +0.003172,110 +0.003261,110 +0.003104,110 +0.004003,110 +0.003298,110 +0.003116,110 +0.003148,110 +0.003104,110 +0.003832,110 +0.003439,110 +0.003874,110 +0.003440,110 +0.005118,110 +0.004115,110 +0.003377,110 +0.003371,110 +0.003585,110 +0.004081,110 +0.003263,110 +0.003363,110 +0.005218,110 +0.004327,110 +0.003541,110 +0.003458,110 +0.003406,110 +0.003481,110 +0.004168,110 +0.003612,110 +0.004007,110 +0.003247,110 +0.003406,110 +0.003569,110 +0.003616,110 +0.003771,110 +0.003692,110 +0.003914,110 +0.004257,110 +0.003764,110 +0.003408,110 +0.003849,110 +0.004592,110 +0.003795,110 +0.003294,110 +0.004595,110 +0.005149,110 +0.004321,110 +0.003406,110 +0.004178,110 +0.005475,110 +0.005511,110 +0.003782,110 +0.003560,110 +0.004343,110 +0.003608,110 +0.003263,110 +0.004953,110 +0.004977,110 +0.006301,110 +0.005646,110 +0.004369,110 +0.004527,110 +0.005416,110 +0.004751,110 +0.003676,110 +0.003736,110 +0.003644,110 +0.005144,110 +0.004847,110 +0.005405,110 +0.003992,110 +0.003676,110 +0.004584,110 +0.003187,110 +0.003931,110 +0.004963,110 +0.004742,110 +0.004872,110 +0.003628,110 +0.003541,110 +0.003228,110 +0.003850,110 +0.005009,110 +0.005836,112 +0.006242,112 +0.006106,112 +0.003673,112 +0.003781,112 +0.003425,112 +0.003692,112 +0.004829,112 +0.003334,112 +0.004316,112 +0.004068,112 +0.006432,112 +0.004738,112 +0.003701,112 +0.003584,112 +0.003472,112 +0.003439,112 +0.004773,112 +0.004372,112 +0.004500,112 +0.003843,112 +0.003317,112 +0.004180,112 +0.003587,112 +0.004891,112 +0.003355,112 +0.004367,112 +0.005543,112 +0.004212,112 +0.003753,112 +0.005279,112 +0.006208,112 +0.006200,112 +0.005718,112 +0.004388,112 +0.003853,112 +0.004592,112 +0.005675,112 +0.005520,112 +0.004401,112 +0.004859,112 +0.006026,112 +0.005075,112 +0.004250,112 +0.004091,112 +0.003717,112 +0.003554,112 +0.003785,112 +0.003421,112 +0.003694,112 +0.003385,112 +0.003369,112 +0.003600,112 +0.003460,112 +0.003418,112 +0.005473,112 +0.006749,112 +0.004214,112 +0.003674,112 +0.004082,112 +0.003621,112 +0.003577,112 +0.003567,112 +0.003612,112 +0.004367,112 +0.003855,112 +0.004755,112 +0.004980,112 +0.004530,112 +0.004115,112 +0.004447,112 +0.003744,112 +0.003871,112 +0.003347,112 +0.003526,112 +0.004476,112 +0.005915,112 +0.006213,112 +0.005642,112 +0.003939,112 +0.004915,112 +0.003862,112 +0.003666,112 +0.005661,112 +0.004728,112 +0.004609,112 +0.004075,112 +0.003584,112 +0.003461,112 +0.003718,112 +0.003806,112 +0.004843,112 +0.003594,112 +0.003614,112 +0.003549,112 +0.004039,112 +0.003723,112 +0.003414,112 +0.003796,112 +0.003973,112 +0.004787,114 +0.004136,114 +0.003698,114 +0.003936,114 +0.004186,114 +0.003469,114 +0.003586,114 +0.003563,114 +0.004120,114 +0.003981,114 +0.003613,114 +0.003603,114 +0.004202,114 +0.003610,114 +0.003615,114 +0.003970,114 +0.003713,114 +0.004594,114 +0.003967,114 +0.003705,114 +0.003533,114 +0.005343,114 +0.003616,114 +0.003937,114 +0.003666,114 +0.004701,114 +0.004117,114 +0.003791,114 +0.003927,114 +0.004133,114 +0.003919,114 +0.003650,114 +0.003989,114 +0.005745,114 +0.004907,114 +0.004419,114 +0.006310,114 +0.004878,114 +0.005730,114 +0.004555,114 +0.004293,114 +0.004167,114 +0.003760,114 +0.003707,114 +0.004708,114 +0.004830,114 +0.004394,114 +0.004506,114 +0.004576,114 +0.003709,114 +0.003710,114 +0.003735,114 +0.003963,114 +0.003603,114 +0.003639,114 +0.003622,114 +0.003918,114 +0.003500,114 +0.003536,114 +0.003496,114 +0.003747,114 +0.004614,114 +0.003626,114 +0.003560,114 +0.004132,114 +0.003929,114 +0.003513,114 +0.003639,114 +0.003501,114 +0.004693,114 +0.003638,114 +0.003510,114 +0.003523,114 +0.005249,114 +0.003929,114 +0.003533,114 +0.003540,114 +0.003679,114 +0.004028,114 +0.003837,114 +0.004211,114 +0.004641,114 +0.003909,114 +0.003980,114 +0.003944,114 +0.003978,114 +0.003950,114 +0.003711,114 +0.004290,114 +0.004783,114 +0.003931,114 +0.003651,114 +0.003681,114 +0.003937,114 +0.004409,114 +0.004043,114 +0.004928,114 +0.004647,114 +0.004604,114 +0.004061,114 +0.003837,116 +0.003813,116 +0.003887,116 +0.004217,116 +0.003743,116 +0.003736,116 +0.004412,116 +0.003754,116 +0.003727,116 +0.003773,116 +0.004102,116 +0.004182,116 +0.003631,116 +0.003809,116 +0.003794,116 +0.004108,116 +0.003639,116 +0.003756,116 +0.003689,116 +0.004026,116 +0.003754,116 +0.003671,116 +0.003682,116 +0.003978,116 +0.003798,116 +0.003636,116 +0.003711,116 +0.004586,116 +0.004441,116 +0.004037,116 +0.003830,116 +0.003782,116 +0.004104,116 +0.003632,116 +0.003748,116 +0.003665,116 +0.004122,116 +0.003719,116 +0.003682,116 +0.003697,116 +0.003930,116 +0.003940,116 +0.003639,116 +0.003774,116 +0.003674,116 +0.004208,116 +0.003627,116 +0.003687,116 +0.003675,116 +0.004086,116 +0.003825,116 +0.003594,116 +0.003723,116 +0.004457,116 +0.004397,116 +0.003899,116 +0.003694,116 +0.003790,116 +0.004091,116 +0.003629,116 +0.004212,116 +0.003711,116 +0.004105,116 +0.003695,116 +0.003939,116 +0.003718,116 +0.004045,116 +0.004201,116 +0.003629,116 +0.003789,116 +0.003828,116 +0.004067,116 +0.003635,116 +0.003762,116 +0.003638,116 +0.004158,116 +0.003709,116 +0.003672,116 +0.003669,116 +0.003834,116 +0.003983,116 +0.004511,116 +0.003747,116 +0.003918,116 +0.003984,116 +0.003632,116 +0.003687,116 +0.003700,116 +0.004324,116 +0.003912,116 +0.004117,116 +0.004163,116 +0.004294,116 +0.003923,116 +0.003681,116 +0.003711,116 +0.004289,116 +0.004412,116 +0.003677,116 +0.003650,116 +0.004346,118 +0.003991,118 +0.003824,118 +0.003865,118 +0.003964,118 +0.004073,118 +0.004120,118 +0.003890,118 +0.003943,118 +0.004015,118 +0.003822,118 +0.003899,118 +0.003838,118 +0.004025,118 +0.003836,118 +0.003853,118 +0.003892,118 +0.003903,118 +0.003821,118 +0.003811,118 +0.003981,118 +0.003875,118 +0.003817,118 +0.003806,118 +0.003877,118 +0.003795,118 +0.003856,118 +0.003790,118 +0.003831,118 +0.003843,118 +0.004057,118 +0.004039,118 +0.003847,118 +0.003866,118 +0.003882,118 +0.003810,118 +0.003817,118 +0.003938,118 +0.003862,118 +0.003835,118 +0.003787,118 +0.003868,118 +0.003877,118 +0.003898,118 +0.003814,118 +0.003827,118 +0.003906,118 +0.003855,118 +0.003836,118 +0.003836,118 +0.003881,118 +0.003875,118 +0.003795,118 +0.003789,118 +0.003846,118 +0.003810,118 +0.004143,118 +0.004031,118 +0.003871,118 +0.003842,118 +0.003850,118 +0.003794,118 +0.003790,118 +0.003881,118 +0.003891,118 +0.003850,118 +0.003791,118 +0.003886,118 +0.004017,118 +0.003790,118 +0.003787,118 +0.003825,118 +0.003930,118 +0.003822,118 +0.003789,118 +0.003793,118 +0.003874,118 +0.003793,118 +0.003789,118 +0.003789,118 +0.003855,118 +0.003809,118 +0.004019,118 +0.004125,118 +0.003866,118 +0.003863,118 +0.003847,118 +0.003883,118 +0.003818,118 +0.003886,118 +0.003990,118 +0.003835,118 +0.003814,118 +0.003876,118 +0.003837,118 +0.003814,118 +0.003791,118 +0.003847,118 +0.003900,118 +0.003798,118 +0.004000,120 +0.004003,120 +0.004077,120 +0.003994,120 +0.003974,120 +0.003978,120 +0.004037,120 +0.003980,120 +0.004235,120 +0.004179,120 +0.004089,120 +0.003979,120 +0.003974,120 +0.004010,120 +0.004069,120 +0.003998,120 +0.003995,120 +0.003976,120 +0.004063,120 +0.004007,120 +0.004009,120 +0.003985,120 +0.004014,120 +0.004230,120 +0.003977,120 +0.003984,120 +0.004036,120 +0.004071,120 +0.003974,120 +0.004011,120 +0.004010,120 +0.004069,120 +0.003974,120 +0.004183,120 +0.004231,120 +0.004194,120 +0.003994,120 +0.004074,120 +0.004010,120 +0.004118,120 +0.004167,120 +0.004004,120 +0.003977,120 +0.004067,120 +0.003977,120 +0.003979,120 +0.003978,120 +0.004116,120 +0.004197,120 +0.003985,120 +0.003974,120 +0.004189,120 +0.004266,120 +0.004054,120 +0.004065,120 +0.004118,120 +0.004036,120 +0.004116,120 +0.004106,120 +0.004314,120 +0.003997,120 +0.004074,120 +0.004018,120 +0.004176,120 +0.004099,120 +0.004020,120 +0.004015,120 +0.004070,120 +0.004088,120 +0.004059,120 +0.003995,120 +0.004057,120 +0.004145,120 +0.004015,120 +0.003982,120 +0.004031,120 +0.004070,120 +0.004034,120 +0.003996,120 +0.003981,120 +0.004161,120 +0.004040,120 +0.004191,120 +0.004170,120 +0.004290,120 +0.004079,120 +0.004132,120 +0.004137,120 +0.004106,120 +0.004235,120 +0.004068,120 +0.004007,120 +0.004126,120 +0.004024,120 +0.004011,120 +0.003998,120 +0.004253,120 +0.004004,120 +0.003992,120 +0.003978,120 +0.004298,122 +0.004239,122 +0.004193,122 +0.004273,122 +0.004511,122 +0.004250,122 +0.004320,122 +0.004322,122 +0.004460,122 +0.004300,122 +0.004190,122 +0.004215,122 +0.004357,122 +0.004246,122 +0.004205,122 +0.004235,122 +0.004389,122 +0.004201,122 +0.004194,122 +0.004306,122 +0.004595,122 +0.004326,122 +0.004256,122 +0.004449,122 +0.004713,122 +0.004423,122 +0.004446,122 +0.006128,122 +0.004411,122 +0.004457,122 +0.004512,122 +0.004526,122 +0.004402,122 +0.004343,122 +0.004366,122 +0.004230,122 +0.004355,122 +0.004229,122 +0.004364,122 +0.004227,122 +0.004440,122 +0.004216,122 +0.004329,122 +0.004527,122 +0.004341,122 +0.004345,122 +0.004381,122 +0.004347,122 +0.004344,122 +0.004340,122 +0.004348,122 +0.004345,122 +0.004357,122 +0.004451,122 +0.004466,122 +0.004447,122 +0.004343,122 +0.004389,122 +0.004335,122 +0.004316,122 +0.004315,122 +0.004398,122 +0.004329,122 +0.004331,122 +0.004306,122 +0.004485,122 +0.004364,122 +0.004366,122 +0.004397,122 +0.004434,122 +0.004343,122 +0.004308,122 +0.004346,122 +0.004389,122 +0.004326,122 +0.004366,122 +0.004459,122 +0.004491,122 +0.004347,122 +0.004341,122 +0.004427,122 +0.004351,122 +0.004329,122 +0.004334,122 +0.004406,122 +0.004350,122 +0.004357,122 +0.004361,122 +0.004495,122 +0.004339,122 +0.004342,122 +0.004354,122 +0.004483,122 +0.004325,122 +0.004302,122 +0.004377,122 +0.004309,122 +0.004324,122 +0.004372,122 +0.004457,122 +0.004703,124 +0.004598,124 +0.004443,124 +0.004476,124 +0.004466,124 +0.004408,124 +0.004476,124 +0.004529,124 +0.004481,124 +0.004412,124 +0.004553,124 +0.004512,124 +0.004408,124 +0.004450,124 +0.004573,124 +0.004461,124 +0.007765,124 +0.005173,124 +0.004744,124 +0.004438,124 +0.004704,124 +0.004726,124 +0.004482,124 +0.004423,124 +0.004644,124 +0.004437,124 +0.004417,124 +0.004424,124 +0.004531,124 +0.004459,124 +0.004431,124 +0.004436,124 +0.004615,124 +0.004449,124 +0.004406,124 +0.004666,124 +0.004435,124 +0.004412,124 +0.004413,124 +0.004490,124 +0.004397,124 +0.004397,124 +0.004487,124 +0.004666,124 +0.004561,124 +0.004433,124 +0.004493,124 +0.004520,124 +0.004441,124 +0.004409,124 +0.004517,124 +0.004419,124 +0.004487,124 +0.004420,124 +0.004562,124 +0.004588,124 +0.004433,124 +0.004631,124 +0.004484,124 +0.004458,124 +0.004426,124 +0.004541,124 +0.004425,124 +0.004432,124 +0.004439,124 +0.004638,124 +0.004596,124 +0.004526,124 +0.004487,124 +0.004598,124 +0.004609,124 +0.004424,124 +0.004537,124 +0.004436,124 +0.004412,124 +0.004425,124 +0.004503,124 +0.004560,124 +0.004420,124 +0.004558,124 +0.004533,124 +0.004439,124 +0.004428,124 +0.004719,124 +0.004512,124 +0.004412,124 +0.004443,124 +0.004649,124 +0.004616,124 +0.004498,124 +0.004453,124 +0.004595,124 +0.004456,124 +0.004447,124 +0.004518,124 +0.004489,124 +0.004441,124 +0.004410,124 +0.004513,124 +0.004580,124 +0.004662,126 +0.004719,126 +0.004843,126 +0.004653,126 +0.004644,126 +0.004688,126 +0.004709,126 +0.004654,126 +0.004646,126 +0.004866,126 +0.004883,126 +0.004728,126 +0.004737,126 +0.004719,126 +0.004731,126 +0.004628,126 +0.004735,126 +0.004633,126 +0.004650,126 +0.004696,126 +0.004805,126 +0.004666,126 +0.004765,126 +0.004727,126 +0.004697,126 +0.004747,126 +0.004852,126 +0.004697,126 +0.004709,126 +0.004681,126 +0.004790,126 +0.004838,126 +0.004740,126 +0.004898,126 +0.004784,126 +0.004648,126 +0.004651,126 +0.004750,126 +0.004659,126 +0.004632,126 +0.004671,126 +0.004750,126 +0.004914,126 +0.004887,126 +0.004847,126 +0.004825,126 +0.004675,126 +0.004664,126 +0.004737,126 +0.004657,126 +0.004647,126 +0.004924,126 +0.004950,126 +0.004737,126 +0.004776,126 +0.004728,126 +0.004695,126 +0.004665,126 +0.004781,126 +0.004666,126 +0.004647,126 +0.004690,126 +0.004912,126 +0.004696,126 +0.004686,126 +0.004803,126 +0.004740,126 +0.004676,126 +0.004654,126 +0.004776,126 +0.004657,126 +0.004629,126 +0.004816,126 +0.005045,126 +0.004844,126 +0.004628,126 +0.004776,126 +0.004704,126 +0.004647,126 +0.004736,126 +0.004655,126 +0.004628,126 +0.004640,126 +0.004790,126 +0.004961,126 +0.004783,126 +0.004804,126 +0.004800,126 +0.004720,126 +0.004644,126 +0.004755,126 +0.004661,126 +0.004621,126 +0.004692,126 +0.005043,126 +0.004882,126 +0.004638,126 +0.004839,126 +0.004672,126 +0.004690,126 +0.005225,128 +0.005116,128 +0.005117,128 +0.005175,128 +0.005454,128 +0.005123,128 +0.005107,128 +0.005244,128 +0.005112,128 +0.005123,128 +0.005198,128 +0.005114,128 +0.005077,128 +0.005257,128 +0.005528,128 +0.005315,128 +0.005355,128 +0.005147,128 +0.005106,128 +0.005195,128 +0.005178,128 +0.005105,128 +0.005101,128 +0.005230,128 +0.005409,128 +0.005327,128 +0.005247,128 +0.005288,128 +0.005124,128 +0.005236,128 +0.005127,128 +0.005086,128 +0.005232,128 +0.005578,128 +0.005388,128 +0.005298,128 +0.005190,128 +0.005099,128 +0.005194,128 +0.005261,128 +0.005117,128 +0.005080,128 +0.005250,128 +0.005435,128 +0.005136,128 +0.005334,128 +0.005132,128 +0.005104,128 +0.005230,128 +0.005121,128 +0.005105,128 +0.005130,128 +0.005415,128 +0.005546,128 +0.005168,128 +0.005223,128 +0.005133,128 +0.005122,128 +0.005209,128 +0.005182,128 +0.005085,128 +0.005205,128 +0.005457,128 +0.005141,128 +0.005219,128 +0.005170,128 +0.005112,128 +0.005161,128 +0.005167,128 +0.005112,128 +0.005090,128 +0.005313,128 +0.005500,128 +0.005229,128 +0.005250,128 +0.005178,128 +0.005094,128 +0.005220,128 +0.005137,128 +0.005098,128 +0.005203,128 +0.005323,128 +0.005221,128 +0.005148,128 +0.005209,128 +0.005150,128 +0.005138,128 +0.005215,128 +0.005138,128 +0.005098,128 +0.005285,128 +0.005508,128 +0.005329,128 +0.005309,128 +0.005242,128 +0.005208,128 +0.005242,128 +0.005098,128 +0.005136,128 +0.005154,128 +0.005345,130 +0.005109,130 +0.005101,130 +0.005213,130 +0.005168,130 +0.005101,130 +0.005221,130 +0.005093,130 +0.005125,130 +0.005204,130 +0.005441,130 +0.005309,130 +0.005259,130 +0.005137,130 +0.005116,130 +0.005168,130 +0.005155,130 +0.005108,130 +0.005112,130 +0.005368,130 +0.005092,130 +0.005176,130 +0.005233,130 +0.005154,130 +0.005104,130 +0.005250,130 +0.005092,130 +0.005104,130 +0.005175,130 +0.005286,130 +0.005459,130 +0.005212,130 +0.005176,130 +0.005118,130 +0.005108,130 +0.005281,130 +0.005082,130 +0.005103,130 +0.005340,130 +0.005336,130 +0.005093,130 +0.005294,130 +0.005209,130 +0.005164,130 +0.005152,130 +0.005189,130 +0.005329,130 +0.005140,130 +0.005263,130 +0.005501,130 +0.005242,130 +0.005252,130 +0.005155,130 +0.005076,130 +0.005336,130 +0.005101,130 +0.005096,130 +0.005204,130 +0.005323,130 +0.005099,130 +0.005217,130 +0.005142,130 +0.005118,130 +0.005215,130 +0.005208,130 +0.005089,130 +0.005125,130 +0.005244,130 +0.005430,130 +0.005506,130 +0.005299,130 +0.005211,130 +0.005093,130 +0.005205,130 +0.005145,130 +0.005165,130 +0.005192,130 +0.005181,130 +0.005061,130 +0.005089,130 +0.005094,130 +0.005067,130 +0.005056,130 +0.005117,130 +0.005075,130 +0.005056,130 +0.005119,130 +0.005140,130 +0.005332,130 +0.005271,130 +0.005136,130 +0.005077,130 +0.005105,130 +0.005112,130 +0.005063,130 +0.005056,130 +0.005156,130 +0.005151,130 +0.005054,130 +0.005122,130 +0.005310,132 +0.005291,132 +0.005352,132 +0.005298,132 +0.005291,132 +0.005321,132 +0.005322,132 +0.005535,132 +0.005626,132 +0.005791,132 +0.005476,132 +0.005464,132 +0.005361,132 +0.005298,132 +0.005315,132 +0.005324,132 +0.005383,132 +0.005287,132 +0.005357,132 +0.005293,132 +0.005288,132 +0.005351,132 +0.005338,132 +0.005285,132 +0.005348,132 +0.005316,132 +0.005635,132 +0.005557,132 +0.005343,132 +0.005305,132 +0.005344,132 +0.005322,132 +0.005313,132 +0.005343,132 +0.005423,132 +0.005314,132 +0.005394,132 +0.005388,132 +0.005292,132 +0.005315,132 +0.005354,132 +0.005294,132 +0.005286,132 +0.005360,132 +0.005639,132 +0.005569,132 +0.006009,132 +0.005312,132 +0.005299,132 +0.005374,132 +0.005315,132 +0.005288,132 +0.005413,132 +0.005389,132 +0.005398,132 +0.005396,132 +0.005329,132 +0.005370,132 +0.005364,132 +0.005331,132 +0.005289,132 +0.005350,132 +0.005295,132 +0.005458,132 +0.005831,132 +0.005349,132 +0.005310,132 +0.005362,132 +0.005319,132 +0.005291,132 +0.005315,132 +0.005331,132 +0.005644,132 +0.005542,132 +0.005394,132 +0.005322,132 +0.005315,132 +0.005354,132 +0.005291,132 +0.005286,132 +0.005589,132 +0.005461,132 +0.005522,132 +0.005612,132 +0.005323,132 +0.005350,132 +0.005379,132 +0.005328,132 +0.005358,132 +0.005373,132 +0.005383,132 +0.005312,132 +0.005371,132 +0.005300,132 +0.005297,132 +0.005343,132 +0.005318,132 +0.005354,132 +0.005344,132 +0.005297,132 +0.005727,134 +0.006001,134 +0.005604,134 +0.005544,134 +0.005591,134 +0.005575,134 +0.005543,134 +0.005602,134 +0.005628,134 +0.005538,134 +0.005601,134 +0.005582,134 +0.005604,134 +0.005593,134 +0.005555,134 +0.005542,134 +0.005612,134 +0.005551,134 +0.005696,134 +0.005928,134 +0.005598,134 +0.005536,134 +0.005602,134 +0.005548,134 +0.005540,134 +0.005598,134 +0.005626,134 +0.005551,134 +0.005602,134 +0.005581,134 +0.005547,134 +0.005591,134 +0.005553,134 +0.005532,134 +0.005735,134 +0.006111,134 +0.006117,134 +0.006362,134 +0.006082,134 +0.006000,134 +0.006281,134 +0.006361,134 +0.006285,134 +0.006281,134 +0.005964,134 +0.006317,134 +0.005929,134 +0.006001,134 +0.006070,134 +0.006045,134 +0.006063,134 +0.006067,134 +0.006021,134 +0.006119,134 +0.006383,134 +0.006022,134 +0.006130,134 +0.006054,134 +0.006025,134 +0.006338,134 +0.006325,134 +0.006297,134 +0.006315,134 +0.005940,134 +0.006068,134 +0.006203,134 +0.006115,134 +0.006111,134 +0.006095,134 +0.006063,134 +0.006335,134 +0.006279,134 +0.006346,134 +0.006127,134 +0.006091,134 +0.006185,134 +0.006060,134 +0.005912,134 +0.006329,134 +0.006379,134 +0.006502,134 +0.006095,134 +0.005933,134 +0.006228,134 +0.005815,134 +0.005759,134 +0.005961,134 +0.005614,134 +0.005607,134 +0.005765,134 +0.005981,134 +0.005591,134 +0.005644,134 +0.005614,134 +0.005600,134 +0.005722,134 +0.005538,134 +0.005589,134 +0.005558,134 +0.005544,134 +0.005834,136 +0.005784,136 +0.005778,136 +0.006098,136 +0.006070,136 +0.005775,136 +0.005948,136 +0.006690,136 +0.005806,136 +0.006403,136 +0.006005,136 +0.006340,136 +0.006973,136 +0.006158,136 +0.006490,136 +0.006354,136 +0.005946,136 +0.006281,136 +0.006280,136 +0.006033,136 +0.006958,136 +0.005882,136 +0.006158,136 +0.006321,136 +0.005967,136 +0.006395,136 +0.006145,136 +0.005931,136 +0.006476,136 +0.006284,136 +0.006077,136 +0.006248,136 +0.006011,136 +0.006106,136 +0.006188,136 +0.005986,136 +0.006076,136 +0.006000,136 +0.005937,136 +0.005843,136 +0.005895,136 +0.005877,136 +0.005874,136 +0.005772,136 +0.005883,136 +0.005784,136 +0.005777,136 +0.005908,136 +0.005777,136 +0.005814,136 +0.005822,136 +0.005816,136 +0.005897,136 +0.006165,136 +0.005819,136 +0.005870,136 +0.005808,136 +0.005839,136 +0.005863,136 +0.005844,136 +0.005773,136 +0.005864,136 +0.005783,136 +0.005776,136 +0.005863,136 +0.005780,136 +0.005784,136 +0.005877,136 +0.005782,136 +0.005913,136 +0.006143,136 +0.005873,136 +0.005858,136 +0.005805,136 +0.005825,136 +0.005900,136 +0.005794,136 +0.005851,136 +0.005868,136 +0.005780,136 +0.005806,136 +0.005853,136 +0.005777,136 +0.005772,136 +0.005847,136 +0.005780,136 +0.005777,136 +0.006138,136 +0.005983,136 +0.005805,136 +0.005818,136 +0.005781,136 +0.005883,136 +0.005782,136 +0.005879,136 +0.005866,136 +0.005825,136 +0.005798,136 +0.005845,136 +0.005789,136 +0.006144,138 +0.006206,138 +0.006050,138 +0.006082,138 +0.006384,138 +0.006272,138 +0.006127,138 +0.006058,138 +0.006054,138 +0.006137,138 +0.006182,138 +0.006050,138 +0.006651,138 +0.006438,138 +0.006146,138 +0.006533,138 +0.006085,138 +0.006288,138 +0.006086,138 +0.006083,138 +0.006998,138 +0.006314,138 +0.006406,138 +0.006107,138 +0.006110,138 +0.006393,138 +0.006200,138 +0.006092,138 +0.006353,138 +0.006054,138 +0.006401,138 +0.006207,138 +0.006265,138 +0.006150,138 +0.006073,138 +0.006086,138 +0.006353,138 +0.006384,138 +0.006190,138 +0.006075,138 +0.006109,138 +0.006160,138 +0.006171,138 +0.006062,138 +0.006181,138 +0.006079,138 +0.006195,138 +0.006082,138 +0.006056,138 +0.006119,138 +0.006057,138 +0.006043,138 +0.006311,138 +0.006433,138 +0.006132,138 +0.006261,138 +0.006091,138 +0.006167,138 +0.006054,138 +0.006126,138 +0.006143,138 +0.006052,138 +0.006045,138 +0.006127,138 +0.006047,138 +0.006085,138 +0.006126,138 +0.006050,138 +0.006128,138 +0.006386,138 +0.006225,138 +0.006126,138 +0.006080,138 +0.006061,138 +0.006171,138 +0.006165,138 +0.006168,138 +0.006123,138 +0.006081,138 +0.006128,138 +0.006048,138 +0.006047,138 +0.006126,138 +0.006076,138 +0.006082,138 +0.006268,138 +0.006333,138 +0.006179,138 +0.006075,138 +0.006054,138 +0.006144,138 +0.006149,138 +0.006059,138 +0.006157,138 +0.006082,138 +0.006094,138 +0.006091,138 +0.006047,138 +0.006129,138 +0.006050,138 +0.006337,140 +0.006400,140 +0.006574,140 +0.006676,140 +0.006315,140 +0.006319,140 +0.006404,140 +0.006336,140 +0.006425,140 +0.006379,140 +0.006310,140 +0.006384,140 +0.006309,140 +0.006344,140 +0.006387,140 +0.006314,140 +0.006349,140 +0.006525,140 +0.006626,140 +0.006451,140 +0.006317,140 +0.006307,140 +0.006405,140 +0.006402,140 +0.006386,140 +0.006310,140 +0.006303,140 +0.006385,140 +0.006305,140 +0.006345,140 +0.006347,140 +0.006308,140 +0.006397,140 +0.006469,140 +0.006585,140 +0.006423,140 +0.006313,140 +0.006412,140 +0.006308,140 +0.006395,140 +0.006382,140 +0.006307,140 +0.006343,140 +0.006368,140 +0.006309,140 +0.006386,140 +0.006307,140 +0.006304,140 +0.006382,140 +0.006535,140 +0.006571,140 +0.006345,140 +0.006319,140 +0.006407,140 +0.006317,140 +0.006471,140 +0.006446,140 +0.006339,140 +0.006411,140 +0.006311,140 +0.006303,140 +0.006465,140 +0.006307,140 +0.006342,140 +0.006347,140 +0.006552,140 +0.006571,140 +0.006321,140 +0.006361,140 +0.006429,140 +0.006384,140 +0.006402,140 +0.006311,140 +0.006303,140 +0.006386,140 +0.006306,140 +0.006354,140 +0.006357,140 +0.006309,140 +0.006384,140 +0.006307,140 +0.006558,140 +0.006513,140 +0.006311,140 +0.006354,140 +0.006346,140 +0.006407,140 +0.006385,140 +0.006308,140 +0.006305,140 +0.006381,140 +0.006309,140 +0.006383,140 +0.006312,140 +0.006313,140 +0.006383,140 +0.006480,140 +0.006622,140 +0.006399,140 +0.006320,140 +0.006685,142 +0.006591,142 +0.006702,142 +0.006625,142 +0.006589,142 +0.006665,142 +0.006586,142 +0.006584,142 +0.006666,142 +0.006587,142 +0.006679,142 +0.006590,142 +0.006811,142 +0.006806,142 +0.006596,142 +0.006669,142 +0.006599,142 +0.006663,142 +0.006728,142 +0.006585,142 +0.007004,142 +0.007236,142 +0.007073,142 +0.007474,142 +0.006630,142 +0.006928,142 +0.006732,142 +0.007071,142 +0.006601,142 +0.006587,142 +0.006673,142 +0.006685,142 +0.006709,142 +0.006656,142 +0.006584,142 +0.006663,142 +0.006588,142 +0.006665,142 +0.006650,142 +0.006594,142 +0.006675,142 +0.006671,142 +0.007029,142 +0.006622,142 +0.006624,142 +0.006750,142 +0.007873,142 +0.006733,142 +0.006849,142 +0.006880,142 +0.006839,142 +0.006767,142 +0.006828,142 +0.006757,142 +0.006806,142 +0.006630,142 +0.006778,142 +0.007067,142 +0.006704,142 +0.006746,142 +0.006644,142 +0.006692,142 +0.006747,142 +0.006707,142 +0.006716,142 +0.006660,142 +0.006632,142 +0.006743,142 +0.007173,142 +0.006932,142 +0.006678,142 +0.006988,142 +0.006903,142 +0.006596,142 +0.006914,142 +0.006590,142 +0.007036,142 +0.006830,142 +0.006713,142 +0.006756,142 +0.006656,142 +0.006650,142 +0.006702,142 +0.006673,142 +0.006853,142 +0.006643,142 +0.006941,142 +0.006973,142 +0.006675,142 +0.006820,142 +0.006726,142 +0.006739,142 +0.006694,142 +0.006696,142 +0.006955,142 +0.006669,142 +0.006780,142 +0.006669,142 +0.006774,142 +0.006784,142 +0.006946,144 +0.007180,144 +0.007175,144 +0.006981,144 +0.007011,144 +0.006981,144 +0.007058,144 +0.006979,144 +0.007020,144 +0.006891,144 +0.006974,144 +0.007013,144 +0.007064,144 +0.007010,144 +0.006935,144 +0.007171,144 +0.007264,144 +0.006881,144 +0.007101,144 +0.007048,144 +0.007135,144 +0.006928,144 +0.006969,144 +0.006954,144 +0.006935,144 +0.007018,144 +0.007033,144 +0.007058,144 +0.006911,144 +0.006959,144 +0.007164,144 +0.007034,144 +0.007004,144 +0.006925,144 +0.007048,144 +0.006911,144 +0.006925,144 +0.006982,144 +0.007009,144 +0.006980,144 +0.007044,144 +0.006942,144 +0.007042,144 +0.007044,144 +0.007140,144 +0.007128,144 +0.006992,144 +0.006979,144 +0.006992,144 +0.007026,144 +0.006894,144 +0.006992,144 +0.006908,144 +0.006913,144 +0.007092,144 +0.006903,144 +0.007016,144 +0.006961,144 +0.007095,144 +0.007097,144 +0.007115,144 +0.007031,144 +0.006934,144 +0.007039,144 +0.006954,144 +0.007028,144 +0.006887,144 +0.006999,144 +0.007085,144 +0.006888,144 +0.007021,144 +0.006992,144 +0.007038,144 +0.007296,144 +0.007040,144 +0.007109,144 +0.006944,144 +0.007045,144 +0.006961,144 +0.006940,144 +0.006953,144 +0.006940,144 +0.007063,144 +0.006913,144 +0.007011,144 +0.006932,144 +0.006881,144 +0.007184,144 +0.007128,144 +0.007072,144 +0.006937,144 +0.007065,144 +0.006980,144 +0.006957,144 +0.007054,144 +0.006988,144 +0.007102,144 +0.006926,144 +0.006940,144 +0.007007,144 +0.007310,146 +0.007503,146 +0.007518,146 +0.007639,146 +0.007285,146 +0.007494,146 +0.007291,146 +0.007312,146 +0.007408,146 +0.007292,146 +0.007390,146 +0.007326,146 +0.007384,146 +0.007387,146 +0.007313,146 +0.007532,146 +0.007562,146 +0.007357,146 +0.007306,146 +0.007373,146 +0.007276,146 +0.007394,146 +0.007270,146 +0.007294,146 +0.007332,146 +0.007257,146 +0.007375,146 +0.007292,146 +0.007418,146 +0.007439,146 +0.007513,146 +0.007323,146 +0.007384,146 +0.007416,146 +0.007336,146 +0.007373,146 +0.007230,146 +0.007855,146 +0.007391,146 +0.007525,146 +0.007321,146 +0.007766,146 +0.007705,146 +0.008125,146 +0.007839,146 +0.008005,146 +0.008066,146 +0.007611,146 +0.007603,146 +0.007924,146 +0.007917,146 +0.008697,146 +0.007902,146 +0.008156,146 +0.007777,146 +0.007991,146 +0.007792,146 +0.007690,146 +0.008070,146 +0.007532,146 +0.007425,146 +0.007711,146 +0.007342,146 +0.007745,146 +0.007388,146 +0.007762,146 +0.007380,146 +0.007572,146 +0.008872,146 +0.007442,146 +0.007244,146 +0.007486,146 +0.007478,146 +0.007317,146 +0.007404,146 +0.007255,146 +0.007393,146 +0.007261,146 +0.007373,146 +0.007560,146 +0.007425,146 +0.008690,146 +0.007781,146 +0.007627,146 +0.007529,146 +0.007442,146 +0.007458,146 +0.007404,146 +0.007270,146 +0.007425,146 +0.007276,146 +0.007546,146 +0.007440,146 +0.007283,146 +0.007965,146 +0.008321,146 +0.007419,146 +0.007291,146 +0.007481,146 +0.007402,146 +0.007778,148 +0.007615,148 +0.007758,148 +0.007670,148 +0.007914,148 +0.007726,148 +0.007688,148 +0.008380,148 +0.008756,148 +0.007832,148 +0.007708,148 +0.007808,148 +0.007701,148 +0.007684,148 +0.007601,148 +0.007729,148 +0.007646,148 +0.010019,148 +0.010566,148 +0.008456,148 +0.008756,148 +0.008002,148 +0.007720,148 +0.008182,148 +0.007676,148 +0.007769,148 +0.007617,148 +0.007762,148 +0.007616,148 +0.007896,148 +0.007661,148 +0.008434,148 +0.007774,148 +0.007898,148 +0.007938,148 +0.007794,148 +0.007770,148 +0.007682,148 +0.007740,148 +0.007658,148 +0.007811,148 +0.007639,148 +0.007765,148 +0.008333,148 +0.007766,148 +0.007792,148 +0.008049,148 +0.007656,148 +0.007810,148 +0.007844,148 +0.007735,148 +0.007690,148 +0.007637,148 +0.007724,148 +0.007651,148 +0.007805,148 +0.007719,148 +0.007757,148 +0.007824,148 +0.008019,148 +0.007648,148 +0.007793,148 +0.007652,148 +0.007700,148 +0.007683,148 +0.007605,148 +0.007735,148 +0.007639,148 +0.007750,148 +0.007703,148 +0.007735,148 +0.007821,148 +0.008072,148 +0.007652,148 +0.007801,148 +0.007742,148 +0.007765,148 +0.007639,148 +0.008044,148 +0.008433,148 +0.007989,148 +0.008329,148 +0.008245,148 +0.008221,148 +0.008322,148 +0.008063,148 +0.007857,148 +0.007852,148 +0.007735,148 +0.008152,148 +0.008043,148 +0.008220,148 +0.007921,148 +0.008088,148 +0.008168,148 +0.008056,148 +0.008000,148 +0.008362,148 +0.007909,148 +0.009064,148 +0.008346,150 +0.008128,150 +0.007978,150 +0.007981,150 +0.007997,150 +0.008024,150 +0.008138,150 +0.008056,150 +0.008012,150 +0.008554,150 +0.007982,150 +0.008079,150 +0.008173,150 +0.008247,150 +0.007963,150 +0.007973,150 +0.007973,150 +0.007978,150 +0.007963,150 +0.007982,150 +0.007996,150 +0.008331,150 +0.008317,150 +0.008052,150 +0.008038,150 +0.007984,150 +0.008001,150 +0.008107,150 +0.007991,150 +0.007992,150 +0.008025,150 +0.007979,150 +0.008018,150 +0.008062,150 +0.008459,150 +0.008003,150 +0.008107,150 +0.008063,150 +0.007981,150 +0.007958,150 +0.008063,150 +0.007984,150 +0.008013,150 +0.007974,150 +0.008009,150 +0.008056,150 +0.008926,150 +0.008235,150 +0.008700,150 +0.008811,150 +0.008310,150 +0.008023,150 +0.008036,150 +0.007984,150 +0.008003,150 +0.008007,150 +0.008060,150 +0.007973,150 +0.008231,150 +0.008441,150 +0.008058,150 +0.008011,150 +0.007978,150 +0.008027,150 +0.007937,150 +0.008053,150 +0.007993,150 +0.008003,150 +0.008118,150 +0.008002,150 +0.007976,150 +0.008652,150 +0.008004,150 +0.008149,150 +0.008675,150 +0.008305,150 +0.008023,150 +0.008031,150 +0.007990,150 +0.007980,150 +0.007962,150 +0.008021,150 +0.007980,150 +0.008286,150 +0.008263,150 +0.008098,150 +0.008096,150 +0.008071,150 +0.007968,150 +0.007976,150 +0.007980,150 +0.008035,150 +0.007977,150 +0.008001,150 +0.007974,150 +0.008073,150 +0.008516,150 +0.007981,150 +0.008411,150 +0.008241,150 +0.008650,152 +0.008546,152 +0.008398,152 +0.008301,152 +0.008325,152 +0.008319,152 +0.008371,152 +0.008372,152 +0.008826,152 +0.008335,152 +0.008408,152 +0.008364,152 +0.008326,152 +0.008344,152 +0.008336,152 +0.008302,152 +0.008316,152 +0.008305,152 +0.008350,152 +0.008368,152 +0.008856,152 +0.008355,152 +0.008551,152 +0.008376,152 +0.008291,152 +0.008303,152 +0.008329,152 +0.008321,152 +0.008396,152 +0.008476,152 +0.008333,152 +0.008421,152 +0.009212,152 +0.008451,152 +0.008314,152 +0.008375,152 +0.008240,152 +0.008306,152 +0.008367,152 +0.008485,152 +0.008341,152 +0.008528,152 +0.008268,152 +0.008497,152 +0.008824,152 +0.008429,152 +0.008309,152 +0.008354,152 +0.008250,152 +0.008309,152 +0.008308,152 +0.008352,152 +0.008268,152 +0.008575,152 +0.008266,152 +0.008708,152 +0.008738,152 +0.008758,152 +0.008415,152 +0.008447,152 +0.008256,152 +0.008588,152 +0.008314,152 +0.008504,152 +0.008304,152 +0.008422,152 +0.008275,152 +0.008529,152 +0.008792,152 +0.008401,152 +0.008369,152 +0.008584,152 +0.008314,152 +0.008303,152 +0.008326,152 +0.008382,152 +0.008319,152 +0.008334,152 +0.008260,152 +0.008533,152 +0.008883,152 +0.008571,152 +0.008472,152 +0.008538,152 +0.008479,152 +0.008707,152 +0.008450,152 +0.008625,152 +0.008442,152 +0.008723,152 +0.009167,152 +0.009004,152 +0.009271,152 +0.009005,152 +0.010127,152 +0.010188,152 +0.011063,152 +0.009559,152 +0.009838,152 +0.009961,152 +0.009792,154 +0.009499,154 +0.009653,154 +0.009494,154 +0.009772,154 +0.009646,154 +0.009619,154 +0.009178,154 +0.009863,154 +0.009757,154 +0.009511,154 +0.009677,154 +0.009544,154 +0.009983,154 +0.009500,154 +0.009243,154 +0.009506,154 +0.009279,154 +0.009287,154 +0.009049,154 +0.008765,154 +0.008746,154 +0.008860,154 +0.008931,154 +0.008970,154 +0.008748,154 +0.008955,154 +0.009060,154 +0.009114,154 +0.009070,154 +0.009268,154 +0.009261,154 +0.009288,154 +0.009213,154 +0.009292,154 +0.009037,154 +0.009542,154 +0.009994,154 +0.009146,154 +0.009390,154 +0.009094,154 +0.008783,154 +0.008926,154 +0.008703,154 +0.008679,154 +0.009198,154 +0.008700,154 +0.008618,154 +0.008616,154 +0.008538,154 +0.008603,154 +0.008568,154 +0.008587,154 +0.008565,154 +0.008594,154 +0.008616,154 +0.008779,154 +0.008935,154 +0.008574,154 +0.008673,154 +0.008572,154 +0.008687,154 +0.008556,154 +0.008651,154 +0.008531,154 +0.008601,154 +0.008538,154 +0.008599,154 +0.009100,154 +0.008690,154 +0.008595,154 +0.008651,154 +0.008587,154 +0.008598,154 +0.008538,154 +0.008612,154 +0.008553,154 +0.008637,154 +0.008539,154 +0.008770,154 +0.010257,154 +0.008723,154 +0.008869,154 +0.008579,154 +0.008621,154 +0.008552,154 +0.008607,154 +0.008537,154 +0.008603,154 +0.008534,154 +0.008603,154 +0.008690,154 +0.009026,154 +0.008675,154 +0.009593,154 +0.008742,154 +0.008727,154 +0.008825,154 +0.008665,154 +0.008692,154 +0.008984,156 +0.008931,156 +0.011467,156 +0.011223,156 +0.009128,156 +0.008904,156 +0.008958,156 +0.008882,156 +0.008937,156 +0.009507,156 +0.010447,156 +0.009244,156 +0.009419,156 +0.009403,156 +0.009228,156 +0.009477,156 +0.009392,156 +0.009371,156 +0.009207,156 +0.009178,156 +0.009348,156 +0.009250,156 +0.009315,156 +0.009246,156 +0.009537,156 +0.009041,156 +0.009492,156 +0.009271,156 +0.009272,156 +0.009327,156 +0.009955,156 +0.011658,156 +0.009964,156 +0.011695,156 +0.012714,156 +0.011539,156 +0.010104,156 +0.011475,156 +0.009902,156 +0.009919,156 +0.011891,156 +0.011584,156 +0.010316,156 +0.010424,156 +0.009976,156 +0.011155,156 +0.009782,156 +0.010686,156 +0.013995,156 +0.011084,156 +0.009411,156 +0.010324,156 +0.015872,156 +0.011228,156 +0.009864,156 +0.010520,156 +0.009239,156 +0.010670,156 +0.009977,156 +0.009525,156 +0.009844,156 +0.009151,156 +0.009747,156 +0.009790,156 +0.009815,156 +0.010218,156 +0.010520,156 +0.012190,156 +0.015521,156 +0.009509,156 +0.009140,156 +0.012884,156 +0.009942,156 +0.009681,156 +0.009923,156 +0.009139,156 +0.009531,156 +0.008975,156 +0.009821,156 +0.009291,156 +0.010210,156 +0.009505,156 +0.010075,156 +0.009369,156 +0.008945,156 +0.010025,156 +0.009424,156 +0.009071,156 +0.009673,156 +0.009162,156 +0.009764,156 +0.009041,156 +0.011949,156 +0.009617,156 +0.009074,156 +0.009598,156 +0.009052,156 +0.009570,156 +0.009098,156 +0.010041,156 +0.009708,158 +0.010064,158 +0.009928,158 +0.009806,158 +0.010372,158 +0.009740,158 +0.010422,158 +0.009990,158 +0.012470,158 +0.011446,158 +0.011016,158 +0.013338,158 +0.014195,158 +0.011668,158 +0.011490,158 +0.012130,158 +0.019081,158 +0.015487,158 +0.009681,158 +0.012794,158 +0.010850,158 +0.011093,158 +0.010817,158 +0.011067,158 +0.010525,158 +0.012347,158 +0.013523,158 +0.015113,158 +0.011413,158 +0.011253,158 +0.010759,158 +0.015331,158 +0.016442,158 +0.015369,158 +0.018370,158 +0.018265,158 +0.011872,158 +0.009907,158 +0.011238,158 +0.010150,158 +0.010105,158 +0.010182,158 +0.010156,158 +0.010646,158 +0.010022,158 +0.011163,158 +0.011613,158 +0.012204,158 +0.010184,158 +0.010941,158 +0.009729,158 +0.010241,158 +0.011784,158 +0.012669,158 +0.010926,158 +0.010744,158 +0.009868,158 +0.010450,158 +0.010083,158 +0.009632,158 +0.011187,158 +0.010271,158 +0.010291,158 +0.010722,158 +0.010145,158 +0.010388,158 +0.010175,158 +0.009634,158 +0.010690,158 +0.010194,158 +0.010933,158 +0.010413,158 +0.010111,158 +0.009954,158 +0.009935,158 +0.009513,158 +0.010208,158 +0.009461,158 +0.010033,158 +0.009768,158 +0.009675,158 +0.009992,158 +0.015378,158 +0.009805,158 +0.009962,158 +0.009615,158 +0.009814,158 +0.009782,158 +0.009562,158 +0.009641,158 +0.009396,158 +0.009651,158 +0.009703,158 +0.009545,158 +0.009404,158 +0.009308,158 +0.009399,158 +0.009599,158 +0.009542,158 +0.009624,158 +0.009764,160 +0.009766,160 +0.010419,160 +0.009815,160 +0.009659,160 +0.009766,160 +0.009896,160 +0.009800,160 +0.009621,160 +0.009634,160 +0.009769,160 +0.009709,160 +0.010182,160 +0.010103,160 +0.009729,160 +0.016327,160 +0.018110,160 +0.009952,160 +0.009734,160 +0.009748,160 +0.009848,160 +0.010281,160 +0.009908,160 +0.009824,160 +0.009719,160 +0.009832,160 +0.009633,160 +0.009759,160 +0.009556,160 +0.009787,160 +0.009659,160 +0.010176,160 +0.010140,160 +0.009638,160 +0.010102,160 +0.009776,160 +0.009687,160 +0.009705,160 +0.009597,160 +0.009634,160 +0.009557,160 +0.009941,160 +0.015949,160 +0.018097,160 +0.018372,160 +0.017274,160 +0.017383,160 +0.017845,160 +0.017787,160 +0.017123,160 +0.009852,160 +0.009752,160 +0.009764,160 +0.009808,160 +0.009696,160 +0.009943,160 +0.010198,160 +0.009885,160 +0.009826,160 +0.009636,160 +0.009895,160 +0.009603,160 +0.012460,160 +0.009786,160 +0.009703,160 +0.009974,160 +0.010484,160 +0.009772,160 +0.009750,160 +0.009698,160 +0.009840,160 +0.009727,160 +0.009810,160 +0.009745,160 +0.009768,160 +0.009757,160 +0.012811,160 +0.009725,160 +0.009802,160 +0.009732,160 +0.009781,160 +0.009819,160 +0.009776,160 +0.009768,160 +0.009759,160 +0.009821,160 +0.011373,160 +0.009787,160 +0.009738,160 +0.009744,160 +0.009732,160 +0.009770,160 +0.009758,160 +0.009691,160 +0.009695,160 +0.009737,160 +0.011340,160 +0.009818,160 +0.009742,160 +0.009665,160 +0.010148,162 +0.010251,162 +0.010111,162 +0.010181,162 +0.010023,162 +0.010160,162 +0.011832,162 +0.010147,162 +0.010344,162 +0.009981,162 +0.010106,162 +0.010133,162 +0.010074,162 +0.010133,162 +0.010118,162 +0.010709,162 +0.011354,162 +0.010097,162 +0.010123,162 +0.010064,162 +0.010051,162 +0.010191,162 +0.009993,162 +0.010145,162 +0.010079,162 +0.011254,162 +0.010817,162 +0.010116,162 +0.010152,162 +0.010225,162 +0.010111,162 +0.010227,162 +0.010041,162 +0.010084,162 +0.010101,162 +0.011673,162 +0.010321,162 +0.010229,162 +0.010453,162 +0.010441,162 +0.010382,162 +0.010084,162 +0.010164,162 +0.010015,162 +0.010080,162 +0.011790,162 +0.010053,162 +0.010139,162 +0.010015,162 +0.010101,162 +0.010225,162 +0.009966,162 +0.010188,162 +0.010130,162 +0.010811,162 +0.011149,162 +0.010074,162 +0.010151,162 +0.010192,162 +0.009983,162 +0.010172,162 +0.010086,162 +0.010313,162 +0.010065,162 +0.011288,162 +0.010595,162 +0.010108,162 +0.010117,162 +0.010081,162 +0.010025,162 +0.010051,162 +0.010062,162 +0.009960,162 +0.010127,162 +0.012434,162 +0.010552,162 +0.010108,162 +0.010048,162 +0.010067,162 +0.010161,162 +0.010022,162 +0.010066,162 +0.009953,162 +0.010138,162 +0.011683,162 +0.010006,162 +0.010122,162 +0.010041,162 +0.010038,162 +0.010052,162 +0.009980,162 +0.010051,162 +0.010021,162 +0.010381,162 +0.011370,162 +0.010045,162 +0.010075,162 +0.010103,162 +0.010161,162 +0.010138,162 +0.010413,164 +0.010478,164 +0.010468,164 +0.011700,164 +0.011035,164 +0.010514,164 +0.010441,164 +0.010456,164 +0.010483,164 +0.010397,164 +0.010585,164 +0.010424,164 +0.010495,164 +0.012097,164 +0.010512,164 +0.010464,164 +0.010491,164 +0.010400,164 +0.010487,164 +0.010544,164 +0.010423,164 +0.010437,164 +0.012053,164 +0.010544,164 +0.010522,164 +0.010433,164 +0.010460,164 +0.010495,164 +0.010396,164 +0.010457,164 +0.010480,164 +0.010995,164 +0.011689,164 +0.010565,164 +0.010388,164 +0.010465,164 +0.010401,164 +0.010423,164 +0.010470,164 +0.010378,164 +0.010484,164 +0.012143,164 +0.010831,164 +0.010480,164 +0.010462,164 +0.010407,164 +0.010435,164 +0.010439,164 +0.010430,164 +0.010510,164 +0.011330,164 +0.011362,164 +0.010723,164 +0.010432,164 +0.010464,164 +0.010741,164 +0.010533,164 +0.010585,164 +0.010826,164 +0.010397,164 +0.011904,164 +0.010379,164 +0.010397,164 +0.010446,164 +0.010295,164 +0.010390,164 +0.010363,164 +0.010311,164 +0.010359,164 +0.012203,164 +0.011248,164 +0.010458,164 +0.010732,164 +0.010783,164 +0.010587,164 +0.010392,164 +0.010336,164 +0.010346,164 +0.010453,164 +0.011919,164 +0.010390,164 +0.010326,164 +0.010369,164 +0.010723,164 +0.010331,164 +0.010576,164 +0.010334,164 +0.010446,164 +0.011779,164 +0.010543,164 +0.010437,164 +0.010399,164 +0.010404,164 +0.010340,164 +0.010328,164 +0.010594,164 +0.010360,164 +0.010354,164 +0.012024,164 +0.010405,164 +0.010744,166 +0.010745,166 +0.010723,166 +0.010712,166 +0.010866,166 +0.010727,166 +0.010759,166 +0.012288,166 +0.010952,166 +0.010841,166 +0.010858,166 +0.010729,166 +0.010668,166 +0.010714,166 +0.010732,166 +0.010707,166 +0.012446,166 +0.010702,166 +0.010806,166 +0.010861,166 +0.010752,166 +0.010744,166 +0.010715,166 +0.010670,166 +0.010739,166 +0.011991,166 +0.010997,166 +0.010792,166 +0.010768,166 +0.010704,166 +0.010760,166 +0.010717,166 +0.010701,166 +0.010783,166 +0.011691,166 +0.011293,166 +0.010739,166 +0.010756,166 +0.010708,166 +0.010774,166 +0.010693,166 +0.010799,166 +0.010777,166 +0.010820,166 +0.012218,166 +0.010780,166 +0.010711,166 +0.010703,166 +0.010750,166 +0.010693,166 +0.012657,166 +0.010827,166 +0.011021,166 +0.012073,166 +0.010826,166 +0.010750,166 +0.010721,166 +0.010735,166 +0.010689,166 +0.010798,166 +0.010740,166 +0.010746,166 +0.013313,166 +0.010825,166 +0.010754,166 +0.010796,166 +0.010818,166 +0.010668,166 +0.010738,166 +0.010805,166 +0.010845,166 +0.012153,166 +0.010795,166 +0.010743,166 +0.010758,166 +0.010742,166 +0.010670,166 +0.010774,166 +0.010884,166 +0.010697,166 +0.012186,166 +0.010813,166 +0.010782,166 +0.010716,166 +0.010772,166 +0.010932,166 +0.010732,166 +0.010799,166 +0.010905,166 +0.012334,166 +0.011287,166 +0.010728,166 +0.010781,166 +0.010719,166 +0.010703,166 +0.010891,166 +0.010675,166 +0.010746,166 +0.011915,166 +0.011197,166 +0.011188,168 +0.011176,168 +0.011134,168 +0.011091,168 +0.011122,168 +0.011091,168 +0.011333,168 +0.012676,168 +0.011323,168 +0.011132,168 +0.011158,168 +0.011182,168 +0.011040,168 +0.011103,168 +0.011119,168 +0.011032,168 +0.012494,168 +0.011247,168 +0.011090,168 +0.011127,168 +0.011116,168 +0.011033,168 +0.011132,168 +0.011111,168 +0.011323,168 +0.012560,168 +0.011198,168 +0.011052,168 +0.011112,168 +0.011170,168 +0.011056,168 +0.011182,168 +0.011106,168 +0.011096,168 +0.012608,168 +0.011202,168 +0.011168,168 +0.011096,168 +0.011665,168 +0.011273,168 +0.011239,168 +0.011162,168 +0.011810,168 +0.013018,168 +0.011296,168 +0.013346,168 +0.011301,168 +0.011328,168 +0.011371,168 +0.011118,168 +0.011642,168 +0.013363,168 +0.012294,168 +0.011239,168 +0.011365,168 +0.011286,168 +0.011206,168 +0.011182,168 +0.011193,168 +0.011358,168 +0.012980,168 +0.011323,168 +0.011290,168 +0.011096,168 +0.011324,168 +0.011231,168 +0.011120,168 +0.011345,168 +0.011328,168 +0.013012,168 +0.011295,168 +0.011217,168 +0.011203,168 +0.011287,168 +0.011296,168 +0.011253,168 +0.011104,168 +0.012233,168 +0.012366,168 +0.011131,168 +0.011286,168 +0.011339,168 +0.011209,168 +0.011334,168 +0.011235,168 +0.011186,168 +0.012163,168 +0.011562,168 +0.011245,168 +0.011236,168 +0.011327,168 +0.011180,168 +0.011227,168 +0.011246,168 +0.011389,168 +0.011467,168 +0.011451,168 +0.011252,168 +0.011184,168 +0.011440,168 +0.011803,170 +0.011633,170 +0.011754,170 +0.011733,170 +0.012118,170 +0.011671,170 +0.011704,170 +0.011708,170 +0.011543,170 +0.011757,170 +0.011879,170 +0.012707,170 +0.012234,170 +0.012154,170 +0.012029,170 +0.011819,170 +0.011794,170 +0.011707,170 +0.011739,170 +0.011616,170 +0.011782,170 +0.011894,170 +0.011620,170 +0.011676,170 +0.011737,170 +0.011665,170 +0.013483,170 +0.011864,170 +0.011862,170 +0.011783,170 +0.011887,170 +0.011690,170 +0.011598,170 +0.011614,170 +0.011786,170 +0.011668,170 +0.011574,170 +0.011753,170 +0.012154,170 +0.011741,170 +0.011661,170 +0.011731,170 +0.011587,170 +0.011728,170 +0.011885,170 +0.012014,170 +0.011749,170 +0.012165,170 +0.011731,170 +0.011691,170 +0.011632,170 +0.011787,170 +0.011654,170 +0.011534,170 +0.011671,170 +0.012229,170 +0.011720,170 +0.011710,170 +0.011681,170 +0.011628,170 +0.011850,170 +0.012076,170 +0.012006,170 +0.011998,170 +0.012166,170 +0.011650,170 +0.011619,170 +0.013339,170 +0.011921,170 +0.011944,170 +0.011613,170 +0.012039,170 +0.012333,170 +0.011874,170 +0.011528,170 +0.011718,170 +0.012276,170 +0.011680,170 +0.011720,170 +0.011750,170 +0.011871,170 +0.011891,170 +0.011765,170 +0.011748,170 +0.012251,170 +0.012336,170 +0.011824,170 +0.011639,170 +0.011552,170 +0.012302,170 +0.011869,170 +0.011699,170 +0.011653,170 +0.011691,170 +0.011702,170 +0.011613,170 +0.011693,170 +0.011867,170 +0.011884,170 +0.011810,170 +0.012074,172 +0.011974,172 +0.012033,172 +0.012139,172 +0.012091,172 +0.012195,172 +0.012515,172 +0.012144,172 +0.012095,172 +0.011989,172 +0.012052,172 +0.012197,172 +0.011944,172 +0.012017,172 +0.012634,172 +0.012185,172 +0.012032,172 +0.011984,172 +0.011944,172 +0.011948,172 +0.012013,172 +0.012059,172 +0.012414,172 +0.012556,172 +0.012083,172 +0.012123,172 +0.012035,172 +0.011958,172 +0.012100,172 +0.012146,172 +0.012187,172 +0.012415,172 +0.012021,172 +0.012361,172 +0.012271,172 +0.012159,172 +0.012322,172 +0.012592,172 +0.012602,172 +0.017974,172 +0.012685,172 +0.012590,172 +0.012584,172 +0.013232,172 +0.012474,172 +0.013220,172 +0.012502,172 +0.013119,172 +0.014392,172 +0.013448,172 +0.013295,172 +0.012219,172 +0.013097,172 +0.012303,172 +0.012687,172 +0.012114,172 +0.012033,172 +0.012130,172 +0.012114,172 +0.012187,172 +0.012298,172 +0.012147,172 +0.013105,172 +0.012013,172 +0.012057,172 +0.011979,172 +0.011942,172 +0.011856,172 +0.011861,172 +0.011924,172 +0.012072,172 +0.012259,172 +0.011844,172 +0.011881,172 +0.011843,172 +0.011926,172 +0.011862,172 +0.012586,172 +0.012893,172 +0.012599,172 +0.012343,172 +0.012339,172 +0.012494,172 +0.013816,172 +0.013387,172 +0.012774,172 +0.012310,172 +0.012798,172 +0.012672,172 +0.012516,172 +0.013154,172 +0.013189,172 +0.013596,172 +0.013207,172 +0.012189,172 +0.012599,172 +0.012129,172 +0.011997,172 +0.011920,172 +0.011909,172 +0.012384,174 +0.012414,174 +0.012323,174 +0.012920,174 +0.012416,174 +0.012512,174 +0.012308,174 +0.012340,174 +0.012355,174 +0.012403,174 +0.012300,174 +0.012744,174 +0.012276,174 +0.012355,174 +0.012279,174 +0.012386,174 +0.012333,174 +0.012360,174 +0.012270,174 +0.012730,174 +0.012328,174 +0.012354,174 +0.012453,174 +0.012383,174 +0.012623,174 +0.012689,174 +0.012315,174 +0.012723,174 +0.012302,174 +0.012564,174 +0.012282,174 +0.012302,174 +0.012277,174 +0.012412,174 +0.012272,174 +0.012768,174 +0.012377,174 +0.012371,174 +0.012361,174 +0.013034,174 +0.012987,174 +0.012628,174 +0.013998,174 +0.013698,174 +0.014008,174 +0.013889,174 +0.013980,174 +0.013791,174 +0.013426,174 +0.013223,174 +0.013151,174 +0.013028,174 +0.012541,174 +0.012331,174 +0.012293,174 +0.012333,174 +0.012407,174 +0.012313,174 +0.012564,174 +0.012576,174 +0.012471,174 +0.012335,174 +0.012304,174 +0.012388,174 +0.012524,174 +0.012404,174 +0.012559,174 +0.012668,174 +0.012388,174 +0.012343,174 +0.012292,174 +0.012377,174 +0.012352,174 +0.012424,174 +0.012519,174 +0.012774,174 +0.012341,174 +0.012310,174 +0.012281,174 +0.012314,174 +0.012306,174 +0.012409,174 +0.012421,174 +0.012911,174 +0.012366,174 +0.012398,174 +0.012284,174 +0.012317,174 +0.012333,174 +0.012430,174 +0.012790,174 +0.012808,174 +0.012425,174 +0.012461,174 +0.012323,174 +0.012311,174 +0.012329,174 +0.012341,174 +0.012318,174 +0.012892,174 +0.012960,176 +0.012683,176 +0.012958,176 +0.012756,176 +0.012903,176 +0.015272,176 +0.013608,176 +0.013179,176 +0.012783,176 +0.012762,176 +0.012756,176 +0.013141,176 +0.012996,176 +0.012790,176 +0.013298,176 +0.012712,176 +0.012703,176 +0.012714,176 +0.012706,176 +0.012737,176 +0.012772,176 +0.012755,176 +0.013546,176 +0.013366,176 +0.013516,176 +0.012994,176 +0.012751,176 +0.013049,176 +0.013413,176 +0.012935,176 +0.013297,176 +0.012956,176 +0.012993,176 +0.012823,176 +0.012865,176 +0.012933,176 +0.012857,176 +0.013186,176 +0.013147,176 +0.012913,176 +0.012906,176 +0.012921,176 +0.013084,176 +0.012999,176 +0.012901,176 +0.013274,176 +0.013093,176 +0.013013,176 +0.013214,176 +0.013072,176 +0.013100,176 +0.012980,176 +0.012936,176 +0.013306,176 +0.012931,176 +0.012915,176 +0.012792,176 +0.012953,176 +0.013011,176 +0.012916,176 +0.013064,176 +0.013292,176 +0.013001,176 +0.012893,176 +0.013025,176 +0.015394,176 +0.012886,176 +0.013035,176 +0.013505,176 +0.012926,176 +0.012864,176 +0.012822,176 +0.012955,176 +0.013117,176 +0.013025,176 +0.012799,176 +0.013449,176 +0.012980,176 +0.012970,176 +0.013047,176 +0.013065,176 +0.014701,176 +0.014472,176 +0.013191,176 +0.012983,176 +0.012964,176 +0.012861,176 +0.012866,176 +0.012829,176 +0.012984,176 +0.012747,176 +0.013213,176 +0.012899,176 +0.013713,176 +0.024383,176 +0.023947,176 +0.023787,176 +0.024533,176 +0.020622,176 +0.012850,176 +0.013423,178 +0.013214,178 +0.013369,178 +0.013415,178 +0.013215,178 +0.013210,178 +0.013217,178 +0.013262,178 +0.013397,178 +0.013134,178 +0.013471,178 +0.013426,178 +0.013207,178 +0.013239,178 +0.013152,178 +0.013520,178 +0.013238,178 +0.013340,178 +0.013517,178 +0.013335,178 +0.013132,178 +0.013216,178 +0.013238,178 +0.013494,178 +0.013076,178 +0.013547,178 +0.013249,178 +0.013361,178 +0.013213,178 +0.013097,178 +0.013363,178 +0.013336,178 +0.013284,178 +0.013659,178 +0.013276,178 +0.013364,178 +0.013297,178 +0.013291,178 +0.013249,178 +0.013256,178 +0.013445,178 +0.013561,178 +0.013437,178 +0.013181,178 +0.013125,178 +0.013279,178 +0.013336,178 +0.013215,178 +0.014821,178 +0.013188,178 +0.013328,178 +0.013293,178 +0.013606,178 +0.013379,178 +0.013260,178 +0.014431,178 +0.013638,178 +0.013395,178 +0.013212,178 +0.013191,178 +0.013361,178 +0.013519,178 +0.013701,178 +0.014332,178 +0.013212,178 +0.013294,178 +0.013222,178 +0.013290,178 +0.013266,178 +0.013418,178 +0.014835,178 +0.013408,178 +0.013361,178 +0.013201,178 +0.013219,178 +0.013530,178 +0.013478,178 +0.014482,178 +0.014100,178 +0.013266,178 +0.013233,178 +0.013167,178 +0.013363,178 +0.013241,178 +0.013262,178 +0.014768,178 +0.013224,178 +0.013219,178 +0.013202,178 +0.013827,178 +0.013347,178 +0.013195,178 +0.014322,178 +0.013850,178 +0.013280,178 +0.013235,178 +0.013249,178 +0.013219,178 +0.013212,178 +0.013230,178 +0.015233,180 +0.013626,180 +0.013766,180 +0.013514,180 +0.013690,180 +0.013639,180 +0.013634,180 +0.016223,180 +0.014035,180 +0.013553,180 +0.013603,180 +0.013822,180 +0.013851,180 +0.013732,180 +0.015221,180 +0.013563,180 +0.013429,180 +0.013443,180 +0.013436,180 +0.013512,180 +0.013390,180 +0.014203,180 +0.014348,180 +0.013512,180 +0.013476,180 +0.013443,180 +0.013712,180 +0.013452,180 +0.013452,180 +0.015234,180 +0.013533,180 +0.013496,180 +0.013369,180 +0.013502,180 +0.013443,180 +0.013460,180 +0.014897,180 +0.013679,180 +0.013442,180 +0.013460,180 +0.013442,180 +0.013522,180 +0.013461,180 +0.013933,180 +0.014692,180 +0.013510,180 +0.013534,180 +0.013457,180 +0.013455,180 +0.013410,180 +0.013439,180 +0.015126,180 +0.013476,180 +0.013476,180 +0.013371,180 +0.013891,180 +0.013455,180 +0.013458,180 +0.014949,180 +0.013609,180 +0.013448,180 +0.013444,180 +0.013600,180 +0.013514,180 +0.013525,180 +0.013936,180 +0.014586,180 +0.013585,180 +0.013459,180 +0.013418,180 +0.013584,180 +0.013392,180 +0.013459,180 +0.015049,180 +0.013426,180 +0.013406,180 +0.013403,180 +0.013465,180 +0.013494,180 +0.013467,180 +0.015478,180 +0.014293,180 +0.013425,180 +0.013365,180 +0.013495,180 +0.013476,180 +0.013442,180 +0.013944,180 +0.014480,180 +0.013447,180 +0.013480,180 +0.013425,180 +0.013722,180 +0.013414,180 +0.013474,180 +0.015276,180 +0.013472,180 +0.013435,180 +0.013424,180 +0.013643,180 +0.013902,182 +0.013907,182 +0.015443,182 +0.014029,182 +0.013959,182 +0.013974,182 +0.014015,182 +0.013872,182 +0.013870,182 +0.015263,182 +0.014036,182 +0.013872,182 +0.013946,182 +0.013903,182 +0.014017,182 +0.013900,182 +0.015056,182 +0.017820,182 +0.014901,182 +0.013865,182 +0.013997,182 +0.013866,182 +0.014549,182 +0.019217,182 +0.013981,182 +0.013916,182 +0.013907,182 +0.013986,182 +0.013927,182 +0.013883,182 +0.019150,182 +0.013907,182 +0.013926,182 +0.013915,182 +0.013980,182 +0.013910,182 +0.013977,182 +0.020017,182 +0.014346,182 +0.013972,182 +0.013997,182 +0.013899,182 +0.013899,182 +0.014963,182 +0.018291,182 +0.013958,182 +0.013986,182 +0.013974,182 +0.013918,182 +0.013935,182 +0.016002,182 +0.017890,182 +0.014267,182 +0.014013,182 +0.014023,182 +0.013904,182 +0.013822,182 +0.019177,182 +0.014132,182 +0.013980,182 +0.014011,182 +0.014188,182 +0.013923,182 +0.013921,182 +0.020269,182 +0.014097,182 +0.014227,182 +0.014711,182 +0.014058,182 +0.013927,182 +0.014158,182 +0.019033,182 +0.013974,182 +0.013980,182 +0.013983,182 +0.013825,182 +0.013902,182 +0.016214,182 +0.017030,182 +0.013948,182 +0.013924,182 +0.014053,182 +0.013955,182 +0.013969,182 +0.018330,182 +0.014625,182 +0.013950,182 +0.013899,182 +0.013992,182 +0.013903,182 +0.013896,182 +0.019139,182 +0.014123,182 +0.013892,182 +0.014028,182 +0.013953,182 +0.013911,182 +0.013905,182 +0.019032,182 +0.013962,182 +0.014479,184 +0.014455,184 +0.014369,184 +0.014412,184 +0.014929,184 +0.019210,184 +0.014443,184 +0.014334,184 +0.014386,184 +0.014356,184 +0.014315,184 +0.019437,184 +0.014461,184 +0.014292,184 +0.014367,184 +0.014483,184 +0.014369,184 +0.014329,184 +0.020059,184 +0.014497,184 +0.014341,184 +0.014386,184 +0.014289,184 +0.014306,184 +0.016362,184 +0.017521,184 +0.014389,184 +0.014344,184 +0.014387,184 +0.014368,184 +0.014352,184 +0.019472,184 +0.014474,184 +0.014347,184 +0.015075,184 +0.014360,184 +0.014348,184 +0.014399,184 +0.019423,184 +0.014507,184 +0.014438,184 +0.014416,184 +0.014332,184 +0.015185,184 +0.019410,184 +0.016408,184 +0.015864,184 +0.015536,184 +0.014972,184 +0.015582,184 +0.027270,184 +0.018104,184 +0.015220,184 +0.016124,184 +0.014965,184 +0.014821,184 +0.014793,184 +0.014504,184 +0.014466,184 +0.014458,184 +0.014914,184 +0.014509,184 +0.014484,184 +0.014877,184 +0.014463,184 +0.014389,184 +0.014486,184 +0.014340,184 +0.014570,184 +0.014492,184 +0.014879,184 +0.014335,184 +0.014371,184 +0.014412,184 +0.014258,184 +0.015139,184 +0.014796,184 +0.015086,184 +0.015209,184 +0.014670,184 +0.014514,184 +0.014402,184 +0.014345,184 +0.014389,184 +0.015136,184 +0.014319,184 +0.014330,184 +0.014358,184 +0.014303,184 +0.014298,184 +0.014372,184 +0.014798,184 +0.014356,184 +0.014343,184 +0.014388,184 +0.014325,184 +0.014326,184 +0.014415,184 +0.014743,184 +0.014389,184 +0.015259,186 +0.015109,186 +0.014963,186 +0.015024,186 +0.015551,186 +0.015172,186 +0.015104,186 +0.015000,186 +0.014967,186 +0.014994,186 +0.015068,186 +0.025382,186 +0.029037,186 +0.015744,186 +0.022137,186 +0.015311,186 +0.015295,186 +0.014945,186 +0.014972,186 +0.015185,186 +0.015195,186 +0.014981,186 +0.015459,186 +0.014972,186 +0.014958,186 +0.015054,186 +0.014974,186 +0.014953,186 +0.014940,186 +0.015495,186 +0.015012,186 +0.015054,186 +0.015140,186 +0.015008,186 +0.015085,186 +0.015402,186 +0.015411,186 +0.015059,186 +0.015014,186 +0.015397,186 +0.015012,186 +0.014989,186 +0.015490,186 +0.015117,186 +0.015029,186 +0.015152,186 +0.015804,186 +0.014965,186 +0.015016,186 +0.015574,186 +0.014951,186 +0.014957,186 +0.015062,186 +0.015000,186 +0.015073,186 +0.015221,186 +0.015300,186 +0.014961,186 +0.015027,186 +0.014961,186 +0.014952,186 +0.014975,186 +0.015491,186 +0.015028,186 +0.015032,186 +0.015069,186 +0.014967,186 +0.014969,186 +0.015113,186 +0.015516,186 +0.014974,186 +0.014906,186 +0.015022,186 +0.014984,186 +0.014992,186 +0.015205,186 +0.015358,186 +0.014973,186 +0.015069,186 +0.015046,186 +0.014976,186 +0.015026,186 +0.015461,186 +0.014995,186 +0.014958,186 +0.015029,186 +0.015035,186 +0.014989,186 +0.014946,186 +0.015537,186 +0.018234,186 +0.016711,186 +0.015068,186 +0.015017,186 +0.015000,186 +0.015504,186 +0.014981,186 +0.015016,186 +0.015108,186 +0.015070,186 +0.015702,188 +0.015573,188 +0.016011,188 +0.015475,188 +0.015665,188 +0.015472,188 +0.015559,188 +0.015475,188 +0.015965,188 +0.015482,188 +0.015496,188 +0.015608,188 +0.015600,188 +0.015478,188 +0.015600,188 +0.016119,188 +0.015570,188 +0.015585,188 +0.015472,188 +0.015473,188 +0.015478,188 +0.016057,188 +0.015521,188 +0.015449,188 +0.015591,188 +0.015474,188 +0.015849,188 +0.021293,188 +0.029933,188 +0.029273,188 +0.029209,188 +0.029517,188 +0.029054,188 +0.029225,188 +0.029937,188 +0.029164,188 +0.028743,188 +0.028933,188 +0.029663,188 +0.028790,188 +0.029312,188 +0.029178,188 +0.029934,188 +0.029684,188 +0.029071,188 +0.029666,188 +0.029133,188 +0.029237,188 +0.029800,188 +0.029108,188 +0.029052,188 +0.029270,188 +0.029256,188 +0.029173,188 +0.029406,188 +0.029462,188 +0.029302,188 +0.029582,188 +0.032099,188 +0.029381,188 +0.029352,188 +0.030201,188 +0.025227,188 +0.017845,188 +0.016191,188 +0.016249,188 +0.016641,188 +0.017521,188 +0.016085,188 +0.016326,188 +0.016309,188 +0.016209,188 +0.016283,188 +0.021234,188 +0.015879,188 +0.015915,188 +0.015630,188 +0.015712,188 +0.015935,188 +0.020878,188 +0.016506,188 +0.015879,188 +0.015805,188 +0.015917,188 +0.015749,188 +0.020783,188 +0.015975,188 +0.015752,188 +0.015739,188 +0.015889,188 +0.015739,188 +0.020795,188 +0.015937,188 +0.015899,188 +0.015682,188 +0.017630,188 +0.015786,188 +0.016189,188 +0.015989,188 +0.015832,188 +0.016330,190 +0.016433,190 +0.016326,190 +0.016356,190 +0.016731,190 +0.016684,190 +0.016410,190 +0.016675,190 +0.016609,190 +0.016545,190 +0.016663,190 +0.016281,190 +0.016178,190 +0.016171,190 +0.016348,190 +0.016273,190 +0.016541,190 +0.016366,190 +0.016309,190 +0.016257,190 +0.016565,190 +0.016389,190 +0.016721,190 +0.016352,190 +0.016311,190 +0.016366,190 +0.016356,190 +0.016395,190 +0.016891,190 +0.016458,190 +0.016458,190 +0.016651,190 +0.016730,190 +0.016754,190 +0.017093,190 +0.016874,190 +0.016853,190 +0.017064,190 +0.017028,190 +0.023721,190 +0.018242,190 +0.017103,190 +0.017085,190 +0.016747,190 +0.016366,190 +0.016701,190 +0.016568,190 +0.016367,190 +0.016247,190 +0.016355,190 +0.016363,190 +0.016749,190 +0.016560,190 +0.016463,190 +0.016335,190 +0.016366,190 +0.016223,190 +0.016496,190 +0.016825,190 +0.016327,190 +0.016257,190 +0.016236,190 +0.016298,190 +0.016230,190 +0.016841,190 +0.016357,190 +0.016425,190 +0.016208,190 +0.016314,190 +0.016231,190 +0.016985,190 +0.016357,190 +0.016317,190 +0.016216,190 +0.016243,190 +0.016221,190 +0.016878,190 +0.016325,190 +0.016272,190 +0.016287,190 +0.016271,190 +0.016204,190 +0.017171,190 +0.016317,190 +0.016377,190 +0.016395,190 +0.016442,190 +0.016784,190 +0.017779,190 +0.016077,190 +0.016126,190 +0.016031,190 +0.015989,190 +0.016613,190 +0.016412,190 +0.016562,190 +0.016252,190 +0.016061,190 +0.016037,190 +0.016055,190 +0.017758,192 +0.018130,192 +0.017835,192 +0.017625,192 +0.017569,192 +0.017560,192 +0.018093,192 +0.017590,192 +0.017646,192 +0.017595,192 +0.017589,192 +0.017593,192 +0.018053,192 +0.017857,192 +0.017576,192 +0.018595,192 +0.018000,192 +0.017856,192 +0.017902,192 +0.017668,192 +0.017556,192 +0.017600,192 +0.017589,192 +0.018096,192 +0.017726,192 +0.017848,192 +0.018263,192 +0.018465,192 +0.018469,192 +0.019493,192 +0.019087,192 +0.018881,192 +0.019300,192 +0.018882,192 +0.020475,192 +0.018907,192 +0.018425,192 +0.018675,192 +0.018796,192 +0.019180,192 +0.018455,192 +0.018796,192 +0.019406,192 +0.018863,192 +0.019209,192 +0.019241,192 +0.018335,192 +0.018386,192 +0.018598,192 +0.021133,192 +0.019768,192 +0.019792,192 +0.019381,192 +0.019887,192 +0.019157,192 +0.019405,192 +0.019352,192 +0.018494,192 +0.018213,192 +0.018221,192 +0.018205,192 +0.018568,192 +0.018134,192 +0.017751,192 +0.017784,192 +0.017656,192 +0.018212,192 +0.017853,192 +0.017730,192 +0.017663,192 +0.017586,192 +0.017701,192 +0.017985,192 +0.017648,192 +0.017545,192 +0.017614,192 +0.017532,192 +0.018059,192 +0.017754,192 +0.017547,192 +0.018010,192 +0.017615,192 +0.017596,192 +0.018172,192 +0.017703,192 +0.017613,192 +0.017505,192 +0.017577,192 +0.017640,192 +0.018077,192 +0.017675,192 +0.017876,192 +0.017800,192 +0.017545,192 +0.018172,192 +0.017663,192 +0.017645,192 +0.017551,192 +0.017570,192 +0.017639,192 +0.017723,194 +0.017201,194 +0.017217,194 +0.017284,194 +0.017187,194 +0.017117,194 +0.017673,194 +0.017179,194 +0.017058,194 +0.017121,194 +0.017032,194 +0.017173,194 +0.017470,194 +0.017173,194 +0.017038,194 +0.017035,194 +0.017031,194 +0.017312,194 +0.017448,194 +0.017117,194 +0.017095,194 +0.017161,194 +0.017030,194 +0.017458,194 +0.017410,194 +0.017029,194 +0.017090,194 +0.017150,194 +0.017056,194 +0.017628,194 +0.017249,194 +0.017056,194 +0.017107,194 +0.017040,194 +0.017043,194 +0.017798,194 +0.017358,194 +0.018198,194 +0.018354,194 +0.018124,194 +0.019318,194 +0.019823,194 +0.018403,194 +0.018274,194 +0.017861,194 +0.017662,194 +0.017762,194 +0.017314,194 +0.017294,194 +0.017188,194 +0.017390,194 +0.017211,194 +0.017584,194 +0.017199,194 +0.017207,194 +0.017087,194 +0.017136,194 +0.017488,194 +0.017390,194 +0.017213,194 +0.017064,194 +0.017075,194 +0.017029,194 +0.017756,194 +0.018961,194 +0.017272,194 +0.017127,194 +0.017087,194 +0.017077,194 +0.017945,194 +0.017222,194 +0.017054,194 +0.017034,194 +0.017032,194 +0.017027,194 +0.017971,194 +0.017141,194 +0.017032,194 +0.017031,194 +0.017031,194 +0.017108,194 +0.017596,194 +0.017183,194 +0.017266,194 +0.017126,194 +0.017049,194 +0.017203,194 +0.017470,194 +0.017219,194 +0.017033,194 +0.017059,194 +0.017057,194 +0.017218,194 +0.017503,194 +0.017104,194 +0.017073,194 +0.017095,194 +0.017032,194 +0.017256,194 +0.017648,194 +0.017649,196 +0.017528,196 +0.017527,196 +0.017525,196 +0.017969,196 +0.017686,196 +0.017538,196 +0.017524,196 +0.017531,196 +0.019247,196 +0.020003,196 +0.019093,196 +0.018780,196 +0.018794,196 +0.017793,196 +0.018126,196 +0.017694,196 +0.017561,196 +0.017558,196 +0.017488,196 +0.017509,196 +0.018199,196 +0.017556,196 +0.017535,196 +0.017544,196 +0.017471,196 +0.017794,196 +0.017866,196 +0.017479,196 +0.017464,196 +0.017628,196 +0.017493,196 +0.018101,196 +0.017621,196 +0.017466,196 +0.017535,196 +0.017462,196 +0.017503,196 +0.018121,196 +0.017712,196 +0.017655,196 +0.017517,196 +0.017495,196 +0.017710,196 +0.017903,196 +0.017532,196 +0.017483,196 +0.017467,196 +0.017495,196 +0.018009,196 +0.017698,196 +0.017549,196 +0.017547,196 +0.017500,196 +0.017464,196 +0.018189,196 +0.017632,196 +0.017809,196 +0.017598,196 +0.017607,196 +0.017754,196 +0.017993,196 +0.017522,196 +0.017505,196 +0.017483,196 +0.017663,196 +0.018069,196 +0.017601,196 +0.017471,196 +0.017477,196 +0.017527,196 +0.017463,196 +0.018090,196 +0.017821,196 +0.017606,196 +0.017499,196 +0.017503,196 +0.017560,196 +0.018135,196 +0.017621,196 +0.017612,196 +0.017501,196 +0.017469,196 +0.018569,196 +0.017776,196 +0.017502,196 +0.017464,196 +0.017463,196 +0.017467,196 +0.018028,196 +0.017664,196 +0.018535,196 +0.020325,196 +0.018020,196 +0.018523,196 +0.018185,196 +0.017650,196 +0.017807,196 +0.019012,196 +0.019560,196 +0.021297,198 +0.018879,198 +0.019415,198 +0.018237,198 +0.018151,198 +0.018833,198 +0.018286,198 +0.018125,198 +0.018174,198 +0.018090,198 +0.018107,198 +0.018952,198 +0.018206,198 +0.018143,198 +0.018094,198 +0.018124,198 +0.023542,198 +0.018220,198 +0.018218,198 +0.018148,198 +0.018384,198 +0.022983,198 +0.018703,198 +0.018196,198 +0.018158,198 +0.018113,198 +0.019203,198 +0.022723,198 +0.018422,198 +0.018436,198 +0.018288,198 +0.018514,198 +0.023999,198 +0.018266,198 +0.018654,198 +0.018360,198 +0.018278,198 +0.023968,198 +0.018381,198 +0.018400,198 +0.018328,198 +0.018368,198 +0.024078,198 +0.018356,198 +0.018515,198 +0.018419,198 +0.018498,198 +0.024293,198 +0.020207,198 +0.018954,198 +0.018380,198 +0.018465,198 +0.024021,198 +0.018793,198 +0.018296,198 +0.018294,198 +0.018455,198 +0.021622,198 +0.025022,198 +0.019093,198 +0.018406,198 +0.018466,198 +0.020783,198 +0.022209,198 +0.018543,198 +0.018451,198 +0.018320,198 +0.020868,198 +0.021467,198 +0.018890,198 +0.018451,198 +0.018416,198 +0.018991,198 +0.023501,198 +0.018466,198 +0.018396,198 +0.018622,198 +0.018818,198 +0.019036,198 +0.018999,198 +0.018954,198 +0.018368,198 +0.018850,198 +0.019231,198 +0.018180,198 +0.018262,198 +0.018089,198 +0.018069,198 +0.018296,198 +0.018660,198 +0.018183,198 +0.018072,198 +0.018069,198 +0.018087,198 +0.018824,198 +0.018486,198 +0.018444,198 +0.018565,198 +0.018482,198 +0.018686,198 +0.019614,200 +0.018985,200 +0.018951,200 +0.019013,200 +0.018900,200 +0.019752,200 +0.018977,200 +0.018916,200 +0.019042,200 +0.019185,200 +0.019620,200 +0.019126,200 +0.019041,200 +0.019046,200 +0.019005,200 +0.019648,200 +0.019398,200 +0.018984,200 +0.018921,200 +0.019097,200 +0.019108,200 +0.019361,200 +0.018982,200 +0.018946,200 +0.018984,200 +0.019093,200 +0.019620,200 +0.018948,200 +0.018868,200 +0.018854,200 +0.018931,200 +0.019449,200 +0.019022,200 +0.019014,200 +0.018844,200 +0.018885,200 +0.019446,200 +0.019151,200 +0.019011,200 +0.018906,200 +0.018898,200 +0.018926,200 +0.019673,200 +0.018902,200 +0.018821,200 +0.018833,200 +0.018963,200 +0.019687,200 +0.019112,200 +0.019051,200 +0.018897,200 +0.019042,200 +0.019607,200 +0.019062,200 +0.018903,200 +0.018925,200 +0.018920,200 +0.019317,200 +0.019451,200 +0.018919,200 +0.019014,200 +0.018887,200 +0.019028,200 +0.020660,200 +0.019032,200 +0.018857,200 +0.019030,200 +0.019124,200 +0.022260,200 +0.019522,200 +0.019082,200 +0.019479,200 +0.018689,200 +0.020167,200 +0.018665,200 +0.018714,200 +0.019436,200 +0.018740,200 +0.020238,200 +0.018807,200 +0.018606,200 +0.018601,200 +0.018634,200 +0.019663,200 +0.019381,200 +0.018664,200 +0.018644,200 +0.018625,200 +0.018611,200 +0.020134,200 +0.018772,200 +0.018611,200 +0.018597,200 +0.018606,200 +0.020143,200 +0.018630,200 +0.018587,200 +0.018580,200 +0.018601,200 +0.019625,200 +0.019955,202 +0.019270,202 +0.019276,202 +0.019466,202 +0.020023,202 +0.020513,202 +0.019293,202 +0.019209,202 +0.019191,202 +0.019206,202 +0.020959,202 +0.019258,202 +0.019271,202 +0.019220,202 +0.019201,202 +0.020855,202 +0.019424,202 +0.019376,202 +0.019329,202 +0.019204,202 +0.022095,202 +0.019331,202 +0.019276,202 +0.019260,202 +0.019274,202 +0.020895,202 +0.019298,202 +0.019362,202 +0.019265,202 +0.019339,202 +0.020935,202 +0.019314,202 +0.019344,202 +0.019257,202 +0.019289,202 +0.020819,202 +0.019280,202 +0.019256,202 +0.019269,202 +0.019241,202 +0.020638,202 +0.019632,202 +0.019357,202 +0.019642,202 +0.019539,202 +0.020262,202 +0.020131,202 +0.019248,202 +0.019233,202 +0.019343,202 +0.019285,202 +0.020917,202 +0.019276,202 +0.019215,202 +0.019297,202 +0.019431,202 +0.021968,202 +0.019440,202 +0.019328,202 +0.019243,202 +0.019206,202 +0.019737,202 +0.019363,202 +0.019230,202 +0.019292,202 +0.019199,202 +0.020305,202 +0.019640,202 +0.019347,202 +0.019220,202 +0.019197,202 +0.019628,202 +0.019511,202 +0.019280,202 +0.019240,202 +0.019250,202 +0.019447,202 +0.020550,202 +0.019445,202 +0.019274,202 +0.019406,202 +0.019407,202 +0.019588,202 +0.019275,202 +0.019281,202 +0.019254,202 +0.019371,202 +0.019940,202 +0.019374,202 +0.019312,202 +0.019333,202 +0.019288,202 +0.019764,202 +0.019403,202 +0.019297,202 +0.019224,202 +0.019246,202 +0.019714,202 +0.019373,202 +0.019290,202 +0.020346,204 +0.019918,204 +0.020338,204 +0.019947,204 +0.019849,204 +0.019833,204 +0.020035,204 +0.020295,204 +0.019921,204 +0.019865,204 +0.019769,204 +0.019774,204 +0.020104,204 +0.020178,204 +0.019959,204 +0.019820,204 +0.019834,204 +0.020111,204 +0.020052,204 +0.019878,204 +0.019775,204 +0.019783,204 +0.020072,204 +0.020188,204 +0.019887,204 +0.019811,204 +0.019828,204 +0.020040,204 +0.020067,204 +0.020056,204 +0.019794,204 +0.019855,204 +0.020051,204 +0.020079,204 +0.019893,204 +0.019762,204 +0.019778,204 +0.019882,204 +0.020157,204 +0.019869,204 +0.020606,204 +0.020034,204 +0.020459,204 +0.020252,204 +0.019838,204 +0.019776,204 +0.019760,204 +0.019930,204 +0.020156,204 +0.019840,204 +0.019778,204 +0.019795,204 +0.019914,204 +0.020118,204 +0.019836,204 +0.019809,204 +0.019894,204 +0.019863,204 +0.020166,204 +0.019825,204 +0.019781,204 +0.019731,204 +0.019851,204 +0.020210,204 +0.019788,204 +0.019774,204 +0.019908,204 +0.019780,204 +0.020163,204 +0.019885,204 +0.019818,204 +0.019725,204 +0.019835,204 +0.020265,204 +0.019733,204 +0.019779,204 +0.019784,204 +0.019784,204 +0.020236,204 +0.020084,204 +0.019783,204 +0.019811,204 +0.019831,204 +0.020212,204 +0.019767,204 +0.019805,204 +0.019774,204 +0.019814,204 +0.020358,204 +0.019773,204 +0.019830,204 +0.019771,204 +0.019804,204 +0.020233,204 +0.019854,204 +0.019767,204 +0.019772,204 +0.019890,204 +0.020138,204 +0.019739,204 +0.020474,206 +0.021390,206 +0.020503,206 +0.020879,206 +0.020554,206 +0.020528,206 +0.020522,206 +0.020726,206 +0.020909,206 +0.020593,206 +0.020475,206 +0.020340,206 +0.020749,206 +0.021044,206 +0.020424,206 +0.020461,206 +0.020456,206 +0.020496,206 +0.020875,206 +0.020437,206 +0.020355,206 +0.020425,206 +0.020503,206 +0.020988,206 +0.020476,206 +0.020374,206 +0.020402,206 +0.020521,206 +0.020866,206 +0.020498,206 +0.020491,206 +0.020461,206 +0.020494,206 +0.020731,206 +0.020377,206 +0.020408,206 +0.020478,206 +0.020558,206 +0.020627,206 +0.020435,206 +0.020376,206 +0.020436,206 +0.020589,206 +0.020674,206 +0.020367,206 +0.020386,206 +0.020430,206 +0.020825,206 +0.020477,206 +0.020425,206 +0.020371,206 +0.020455,206 +0.020832,206 +0.020454,206 +0.020433,206 +0.020450,206 +0.020546,206 +0.020845,206 +0.020509,206 +0.020404,206 +0.020361,206 +0.020545,206 +0.020790,206 +0.020547,206 +0.020483,206 +0.020445,206 +0.020497,206 +0.021000,206 +0.020620,206 +0.020432,206 +0.020507,206 +0.020377,206 +0.021019,206 +0.020574,206 +0.020587,206 +0.020427,206 +0.020517,206 +0.021153,206 +0.020512,206 +0.021221,206 +0.020608,206 +0.020599,206 +0.020907,206 +0.020395,206 +0.020442,206 +0.020490,206 +0.020755,206 +0.020848,206 +0.020516,206 +0.020425,206 +0.020515,206 +0.021067,206 +0.020579,206 +0.020578,206 +0.020460,206 +0.020519,206 +0.020952,206 +0.020452,206 +0.020415,206 +0.020555,206 +0.020937,208 +0.021447,208 +0.021110,208 +0.021063,208 +0.021080,208 +0.021059,208 +0.021476,208 +0.021106,208 +0.020988,208 +0.021031,208 +0.021058,208 +0.021473,208 +0.020970,208 +0.020922,208 +0.021063,208 +0.021414,208 +0.021251,208 +0.020921,208 +0.021078,208 +0.020971,208 +0.021575,208 +0.021036,208 +0.021007,208 +0.021015,208 +0.021137,208 +0.021794,208 +0.021007,208 +0.021026,208 +0.021033,208 +0.021063,208 +0.021563,208 +0.021013,208 +0.020908,208 +0.021028,208 +0.021103,208 +0.021375,208 +0.020978,208 +0.021054,208 +0.020989,208 +0.021518,208 +0.020965,208 +0.020957,208 +0.020970,208 +0.020899,208 +0.021561,208 +0.021345,208 +0.020959,208 +0.021026,208 +0.021020,208 +0.021515,208 +0.020916,208 +0.021116,208 +0.021035,208 +0.021011,208 +0.021544,208 +0.020938,208 +0.020971,208 +0.020993,208 +0.021331,208 +0.021146,208 +0.020975,208 +0.021000,208 +0.020880,208 +0.021581,208 +0.020919,208 +0.020933,208 +0.021065,208 +0.021079,208 +0.021627,208 +0.020984,208 +0.021031,208 +0.021143,208 +0.021434,208 +0.021466,208 +0.021069,208 +0.021036,208 +0.020908,208 +0.021261,208 +0.021241,208 +0.020960,208 +0.020993,208 +0.020928,208 +0.021676,208 +0.021072,208 +0.020921,208 +0.021194,208 +0.020953,208 +0.021478,208 +0.020900,208 +0.020952,208 +0.021031,208 +0.020963,208 +0.021564,208 +0.020987,208 +0.021018,208 +0.020997,208 +0.021287,208 +0.021463,208 +0.020961,208 +0.021010,208 +0.021837,210 +0.022359,210 +0.021703,210 +0.021722,210 +0.021748,210 +0.021800,210 +0.022293,210 +0.021726,210 +0.021681,210 +0.021713,210 +0.022189,210 +0.021968,210 +0.021695,210 +0.021828,210 +0.021751,210 +0.022327,210 +0.021710,210 +0.021823,210 +0.021882,210 +0.024530,210 +0.023167,210 +0.021845,210 +0.021955,210 +0.021629,210 +0.022300,210 +0.021750,210 +0.021700,210 +0.021613,210 +0.021707,210 +0.022299,210 +0.021728,210 +0.021733,210 +0.021715,210 +0.022258,210 +0.021667,210 +0.021689,210 +0.021675,210 +0.021617,210 +0.022322,210 +0.021623,210 +0.021723,210 +0.021755,210 +0.021899,210 +0.022125,210 +0.021792,210 +0.021803,210 +0.021650,210 +0.022226,210 +0.021704,210 +0.021738,210 +0.021623,210 +0.021700,210 +0.022291,210 +0.021647,210 +0.021842,210 +0.021684,210 +0.022042,210 +0.021837,210 +0.021654,210 +0.021712,210 +0.021604,210 +0.022472,210 +0.021726,210 +0.021741,210 +0.021754,210 +0.023545,210 +0.022155,210 +0.021975,210 +0.021686,210 +0.021615,210 +0.022360,210 +0.021625,210 +0.022446,210 +0.022446,210 +0.022270,210 +0.022792,210 +0.021866,210 +0.021678,210 +0.021673,210 +0.022255,210 +0.021645,210 +0.021740,210 +0.021689,210 +0.021647,210 +0.022128,210 +0.021689,210 +0.021829,210 +0.021827,210 +0.021905,210 +0.022211,210 +0.021896,210 +0.021644,210 +0.021800,210 +0.022196,210 +0.021754,210 +0.021831,210 +0.021608,210 +0.021701,210 +0.022241,210 +0.021665,210 +0.022333,212 +0.022289,212 +0.022824,212 +0.022219,212 +0.022375,212 +0.022238,212 +0.022223,212 +0.022961,212 +0.022227,212 +0.022258,212 +0.022534,212 +0.022837,212 +0.022326,212 +0.022341,212 +0.022220,212 +0.022228,212 +0.022974,212 +0.022232,212 +0.022573,212 +0.022355,212 +0.022848,212 +0.022325,212 +0.022381,212 +0.022277,212 +0.022785,212 +0.022947,212 +0.022319,212 +0.022236,212 +0.022260,212 +0.022802,212 +0.022282,212 +0.022393,212 +0.022251,212 +0.022384,212 +0.022750,212 +0.022347,212 +0.022354,212 +0.022219,212 +0.022789,212 +0.022340,212 +0.022302,212 +0.022216,212 +0.022453,212 +0.022677,212 +0.022374,212 +0.022228,212 +0.022263,212 +0.022823,212 +0.022218,212 +0.022228,212 +0.022198,212 +0.022395,212 +0.022869,212 +0.022323,212 +0.022361,212 +0.022268,212 +0.022801,212 +0.022334,212 +0.022253,212 +0.022175,212 +0.022361,212 +0.022652,212 +0.022286,212 +0.022231,212 +0.022339,212 +0.023049,212 +0.022210,212 +0.022239,212 +0.022321,212 +0.022345,212 +0.022578,212 +0.022393,212 +0.022224,212 +0.022156,212 +0.022832,212 +0.022247,212 +0.022352,212 +0.022454,212 +0.022399,212 +0.022739,212 +0.022451,212 +0.022183,212 +0.022177,212 +0.022833,212 +0.022297,212 +0.023886,212 +0.022259,212 +0.022521,212 +0.022645,212 +0.022403,212 +0.022249,212 +0.022298,212 +0.022748,212 +0.022594,212 +0.022305,212 +0.022199,212 +0.022525,212 +0.022699,212 +0.022429,212 +0.022883,212 +0.023026,214 +0.023601,214 +0.022894,214 +0.022924,214 +0.022801,214 +0.023424,214 +0.022784,214 +0.022958,214 +0.022937,214 +0.023036,214 +0.023292,214 +0.022977,214 +0.022910,214 +0.022914,214 +0.023308,214 +0.022945,214 +0.022868,214 +0.022820,214 +0.023361,214 +0.022903,214 +0.022967,214 +0.023011,214 +0.022831,214 +0.023594,214 +0.022994,214 +0.022835,214 +0.022873,214 +0.023355,214 +0.023009,214 +0.022910,214 +0.022801,214 +0.023142,214 +0.023126,214 +0.022873,214 +0.022995,214 +0.022831,214 +0.023499,214 +0.022909,214 +0.022804,214 +0.022903,214 +0.023405,214 +0.023121,214 +0.023190,214 +0.023021,214 +0.023059,214 +0.023475,214 +0.022920,214 +0.022871,214 +0.023039,214 +0.023400,214 +0.022957,214 +0.022797,214 +0.022976,214 +0.023346,214 +0.023228,214 +0.022894,214 +0.023023,214 +0.022950,214 +0.023304,214 +0.022880,214 +0.022979,214 +0.022820,214 +0.023251,214 +0.022990,214 +0.022892,214 +0.022999,214 +0.023206,214 +0.023043,214 +0.022884,214 +0.022835,214 +0.022819,214 +0.023492,214 +0.022915,214 +0.022874,214 +0.022853,214 +0.023394,214 +0.022965,214 +0.022915,214 +0.022892,214 +0.023037,214 +0.023072,214 +0.022953,214 +0.022892,214 +0.022866,214 +0.023559,214 +0.022908,214 +0.023742,214 +0.022807,214 +0.023526,214 +0.023016,214 +0.022789,214 +0.023650,214 +0.023282,214 +0.023171,214 +0.022981,214 +0.022893,214 +0.022843,214 +0.023337,214 +0.022931,214 +0.022935,214 +0.023484,216 +0.023960,216 +0.023784,216 +0.023437,216 +0.023560,216 +0.023767,216 +0.023759,216 +0.023548,216 +0.023554,216 +0.023648,216 +0.023907,216 +0.023504,216 +0.023411,216 +0.023361,216 +0.023976,216 +0.023612,216 +0.023527,216 +0.023568,216 +0.024065,216 +0.023642,216 +0.023505,216 +0.023500,216 +0.023761,216 +0.023708,216 +0.023398,216 +0.023390,216 +0.023527,216 +0.023995,216 +0.023649,216 +0.023565,216 +0.023520,216 +0.024105,216 +0.023535,216 +0.023515,216 +0.023435,216 +0.024056,216 +0.023549,216 +0.023436,216 +0.023527,216 +0.023797,216 +0.024015,216 +0.023496,216 +0.023743,216 +0.023574,216 +0.023869,216 +0.023564,216 +0.023412,216 +0.023448,216 +0.024012,216 +0.023638,216 +0.023633,216 +0.023510,216 +0.024206,216 +0.023510,216 +0.023539,216 +0.023430,216 +0.023712,216 +0.023728,216 +0.023420,216 +0.023466,216 +0.023403,216 +0.023832,216 +0.023598,216 +0.023477,216 +0.023488,216 +0.023875,216 +0.023622,216 +0.023453,216 +0.023399,216 +0.024021,216 +0.023578,216 +0.023585,216 +0.023475,216 +0.024381,216 +0.024930,216 +0.023957,216 +0.024402,216 +0.023838,216 +0.024771,216 +0.023503,216 +0.023520,216 +0.023429,216 +0.025026,216 +0.023553,216 +0.023468,216 +0.023556,216 +0.024949,216 +0.023713,216 +0.023406,216 +0.023559,216 +0.024893,216 +0.023608,216 +0.023511,216 +0.023548,216 +0.025018,216 +0.023749,216 +0.023568,216 +0.023493,216 +0.023500,216 +0.025098,216 +0.024321,218 +0.024253,218 +0.024154,218 +0.025959,218 +0.024192,218 +0.024190,218 +0.024139,218 +0.025750,218 +0.024191,218 +0.024242,218 +0.024402,218 +0.030602,218 +0.024774,218 +0.024360,218 +0.024410,218 +0.024888,218 +0.024177,218 +0.024285,218 +0.024374,218 +0.024681,218 +0.024682,218 +0.024262,218 +0.024223,218 +0.024665,218 +0.024532,218 +0.024227,218 +0.024309,218 +0.024826,218 +0.024397,218 +0.024196,218 +0.024256,218 +0.024776,218 +0.024537,218 +0.024244,218 +0.024336,218 +0.024614,218 +0.024646,218 +0.024301,218 +0.024200,218 +0.024366,218 +0.024733,218 +0.024201,218 +0.024230,218 +0.024197,218 +0.024804,218 +0.024310,218 +0.024180,218 +0.024274,218 +0.024824,218 +0.024214,218 +0.024201,218 +0.024154,218 +0.025116,218 +0.024334,218 +0.024319,218 +0.024365,218 +0.024794,218 +0.024186,218 +0.024323,218 +0.024177,218 +0.024657,218 +0.024300,218 +0.024207,218 +0.024112,218 +0.024419,218 +0.024600,218 +0.024227,218 +0.024217,218 +0.024233,218 +0.024734,218 +0.024214,218 +0.025253,218 +0.024190,218 +0.024788,218 +0.024715,218 +0.024626,218 +0.024456,218 +0.024755,218 +0.024196,218 +0.024166,218 +0.024235,218 +0.024681,218 +0.024260,218 +0.024331,218 +0.024221,218 +0.024686,218 +0.024356,218 +0.024330,218 +0.024253,218 +0.024664,218 +0.024319,218 +0.024420,218 +0.025809,218 +0.024817,218 +0.024451,218 +0.024223,218 +0.024401,218 +0.024759,218 +0.024375,218 +0.024219,218 +0.024873,220 +0.025108,220 +0.025061,220 +0.024885,220 +0.024765,220 +0.025074,220 +0.025367,220 +0.024839,220 +0.024765,220 +0.025052,220 +0.025111,220 +0.024817,220 +0.024792,220 +0.025239,220 +0.025257,220 +0.025068,220 +0.024841,220 +0.025115,220 +0.025180,220 +0.024913,220 +0.024890,220 +0.025050,220 +0.025184,220 +0.024911,220 +0.024798,220 +0.025013,220 +0.025192,220 +0.024926,220 +0.024795,220 +0.024976,220 +0.025252,220 +0.024912,220 +0.024793,220 +0.024958,220 +0.025602,220 +0.024894,220 +0.024824,220 +0.024999,220 +0.025398,220 +0.024906,220 +0.024775,220 +0.024963,220 +0.025427,220 +0.024907,220 +0.024832,220 +0.024869,220 +0.025427,220 +0.025238,220 +0.024822,220 +0.024873,220 +0.025321,220 +0.024911,220 +0.024858,220 +0.024902,220 +0.025402,220 +0.024943,220 +0.024956,220 +0.024943,220 +0.025503,220 +0.024872,220 +0.024849,220 +0.024872,220 +0.025515,220 +0.024940,220 +0.024794,220 +0.024854,220 +0.025468,220 +0.025027,220 +0.024804,220 +0.024812,220 +0.025526,220 +0.024885,220 +0.024797,220 +0.024926,220 +0.025620,220 +0.024928,220 +0.024839,220 +0.024926,220 +0.025429,220 +0.025009,220 +0.024797,220 +0.024856,220 +0.025474,220 +0.024913,220 +0.024784,220 +0.024895,220 +0.025441,220 +0.025252,220 +0.024798,220 +0.024784,220 +0.025461,220 +0.024823,220 +0.024757,220 +0.025039,220 +0.026051,220 +0.025156,220 +0.026092,220 +0.024877,220 +0.025423,220 +0.024875,220 +0.025803,222 +0.025612,222 +0.026133,222 +0.025814,222 +0.026533,222 +0.025811,222 +0.026799,222 +0.028307,222 +0.026128,222 +0.026274,222 +0.026490,222 +0.025989,222 +0.025987,222 +0.027747,222 +0.026207,222 +0.025834,222 +0.026027,222 +0.027656,222 +0.025946,222 +0.025867,222 +0.025983,222 +0.027567,222 +0.025950,222 +0.025924,222 +0.025934,222 +0.027547,222 +0.025963,222 +0.025842,222 +0.026992,222 +0.026363,222 +0.025988,222 +0.025937,222 +0.027749,222 +0.025962,222 +0.026520,222 +0.026097,222 +0.027628,222 +0.025700,222 +0.026003,222 +0.025730,222 +0.027521,222 +0.025729,222 +0.026208,222 +0.025815,222 +0.027381,222 +0.025782,222 +0.025681,222 +0.025890,222 +0.027240,222 +0.025703,222 +0.026188,222 +0.028180,222 +0.026576,222 +0.025724,222 +0.025760,222 +0.027488,222 +0.026379,222 +0.026555,222 +0.027810,222 +0.029167,222 +0.026614,222 +0.027743,222 +0.027495,222 +0.029081,222 +0.028671,222 +0.027525,222 +0.026388,222 +0.026126,222 +0.026361,222 +0.026159,222 +0.027152,222 +0.026343,222 +0.026092,222 +0.026325,222 +0.026569,222 +0.026080,222 +0.026654,222 +0.026354,222 +0.026697,222 +0.026229,222 +0.026825,222 +0.027730,222 +0.028674,222 +0.027830,222 +0.028155,222 +0.028284,222 +0.028044,222 +0.026559,222 +0.028011,222 +0.033725,222 +0.027623,222 +0.028418,222 +0.031350,222 +0.028729,222 +0.026083,222 +0.026010,222 +0.032434,222 +0.027779,222 +0.026996,222 +0.028396,222 +0.028949,224 +0.027685,224 +0.026853,224 +0.027342,224 +0.026836,224 +0.026846,224 +0.027353,224 +0.027514,224 +0.035273,224 +0.032047,224 +0.027517,224 +0.026843,224 +0.026461,224 +0.026823,224 +0.026482,224 +0.026429,224 +0.026592,224 +0.026880,224 +0.026321,224 +0.026325,224 +0.026351,224 +0.026876,224 +0.026249,224 +0.026443,224 +0.026446,224 +0.026957,224 +0.026337,224 +0.026385,224 +0.026553,224 +0.026630,224 +0.026286,224 +0.026370,224 +0.026752,224 +0.026410,224 +0.026253,224 +0.026425,224 +0.027212,224 +0.026683,224 +0.026352,224 +0.026306,224 +0.026796,224 +0.026319,224 +0.026409,224 +0.027414,224 +0.027239,224 +0.026580,224 +0.026598,224 +0.026857,224 +0.026380,224 +0.026298,224 +0.026425,224 +0.026794,224 +0.026301,224 +0.026350,224 +0.026489,224 +0.027160,224 +0.026314,224 +0.026349,224 +0.026421,224 +0.026793,224 +0.026374,224 +0.026456,224 +0.026503,224 +0.026953,224 +0.026346,224 +0.026434,224 +0.026791,224 +0.026370,224 +0.026421,224 +0.026372,224 +0.026847,224 +0.026371,224 +0.026353,224 +0.026352,224 +0.026915,224 +0.026435,224 +0.026356,224 +0.026417,224 +0.026870,224 +0.026376,224 +0.026433,224 +0.026624,224 +0.027409,224 +0.026897,224 +0.026468,224 +0.026801,224 +0.026327,224 +0.026391,224 +0.026394,224 +0.026912,224 +0.026554,224 +0.026577,224 +0.026535,224 +0.026772,224 +0.026386,224 +0.026433,224 +0.026597,224 +0.026615,224 +0.026654,224 +0.026921,224 +0.028603,226 +0.027266,226 +0.027135,226 +0.027072,226 +0.027474,226 +0.027131,226 +0.027086,226 +0.027116,226 +0.027478,226 +0.027045,226 +0.027091,226 +0.027592,226 +0.027407,226 +0.027063,226 +0.027063,226 +0.027425,226 +0.027157,226 +0.027344,226 +0.027210,226 +0.027718,226 +0.027114,226 +0.027143,226 +0.027466,226 +0.027005,226 +0.027020,226 +0.026995,226 +0.027437,226 +0.027026,226 +0.026995,226 +0.027142,226 +0.027541,226 +0.026967,226 +0.027073,226 +0.027470,226 +0.026976,226 +0.027179,226 +0.027682,226 +0.027688,226 +0.027113,226 +0.027033,226 +0.027071,226 +0.027531,226 +0.026931,226 +0.027160,226 +0.027355,226 +0.027081,226 +0.026994,226 +0.027038,226 +0.027578,226 +0.027147,226 +0.027222,226 +0.027132,226 +0.027484,226 +0.026990,226 +0.027118,226 +0.027287,226 +0.027333,226 +0.027106,226 +0.027130,226 +0.027430,226 +0.027058,226 +0.026931,226 +0.027072,226 +0.027519,226 +0.027034,226 +0.027094,226 +0.027110,226 +0.027528,226 +0.027124,226 +0.027042,226 +0.027476,226 +0.027152,226 +0.027089,226 +0.027805,226 +0.027947,226 +0.027093,226 +0.027021,226 +0.026933,226 +0.027671,226 +0.027016,226 +0.026995,226 +0.027477,226 +0.027034,226 +0.027993,226 +0.027066,226 +0.027560,226 +0.027294,226 +0.027060,226 +0.027045,226 +0.027400,226 +0.027050,226 +0.026985,226 +0.027514,226 +0.027799,226 +0.027884,226 +0.027555,226 +0.027529,226 +0.026994,226 +0.027625,226 +0.027030,226 +0.028396,228 +0.027789,228 +0.027706,228 +0.028292,228 +0.027713,228 +0.027641,228 +0.027753,228 +0.028166,228 +0.027764,228 +0.027839,228 +0.027917,228 +0.028371,228 +0.027708,228 +0.027819,228 +0.028142,228 +0.027675,228 +0.027806,228 +0.027774,228 +0.028090,228 +0.027691,228 +0.028016,228 +0.028347,228 +0.027715,228 +0.027710,228 +0.027669,228 +0.028135,228 +0.027709,228 +0.027739,228 +0.028289,228 +0.027917,228 +0.027731,228 +0.027709,228 +0.028199,228 +0.027688,228 +0.027750,228 +0.027957,228 +0.028081,228 +0.027754,228 +0.027762,228 +0.028137,228 +0.027730,228 +0.027760,228 +0.027624,228 +0.028232,228 +0.027763,228 +0.027841,228 +0.027998,228 +0.028292,228 +0.027739,228 +0.027804,228 +0.028145,228 +0.027705,228 +0.027735,228 +0.027768,228 +0.028157,228 +0.027802,228 +0.027793,228 +0.028159,228 +0.027800,228 +0.027955,228 +0.027726,228 +0.028202,228 +0.027815,228 +0.027765,228 +0.027927,228 +0.028082,228 +0.027911,228 +0.028507,228 +0.029761,228 +0.029541,228 +0.030357,228 +0.029105,228 +0.030264,228 +0.030174,228 +0.028764,228 +0.028345,228 +0.028749,228 +0.028297,228 +0.031972,228 +0.027970,228 +0.028245,228 +0.027927,228 +0.033471,228 +0.029183,228 +0.030954,228 +0.030335,228 +0.029571,228 +0.029664,228 +0.029525,228 +0.029456,228 +0.029034,228 +0.028302,228 +0.028582,228 +0.027869,228 +0.027958,228 +0.032860,228 +0.054217,228 +0.055905,228 +0.032124,228 +0.030037,228 +0.031212,230 +0.031446,230 +0.029493,230 +0.028981,230 +0.029714,230 +0.029217,230 +0.029330,230 +0.029472,230 +0.028810,230 +0.028966,230 +0.028912,230 +0.029368,230 +0.029060,230 +0.028714,230 +0.029201,230 +0.028925,230 +0.029145,230 +0.029026,230 +0.029022,230 +0.028966,230 +0.028870,230 +0.029391,230 +0.028822,230 +0.029057,230 +0.029450,230 +0.028822,230 +0.029209,230 +0.029746,230 +0.029454,230 +0.028988,230 +0.029127,230 +0.029064,230 +0.029241,230 +0.029435,230 +0.029081,230 +0.031390,230 +0.029498,230 +0.029355,230 +0.029553,230 +0.028982,230 +0.028996,230 +0.028980,230 +0.029188,230 +0.029060,230 +0.028818,230 +0.029422,230 +0.029067,230 +0.028992,230 +0.029280,230 +0.029486,230 +0.029258,230 +0.029168,230 +0.029584,230 +0.029309,230 +0.029174,230 +0.029294,230 +0.028859,230 +0.029155,230 +0.028960,230 +0.029254,230 +0.029074,230 +0.030576,230 +0.030232,230 +0.029177,230 +0.029131,230 +0.030245,230 +0.029385,230 +0.028945,230 +0.028784,230 +0.029233,230 +0.029134,230 +0.029420,230 +0.029514,230 +0.028832,230 +0.028563,230 +0.028667,230 +0.029067,230 +0.028526,230 +0.028438,230 +0.028899,230 +0.029096,230 +0.028589,230 +0.028424,230 +0.029054,230 +0.028619,230 +0.028536,230 +0.028929,230 +0.028593,230 +0.029794,230 +0.038274,230 +0.028631,230 +0.028745,230 +0.028442,230 +0.028873,230 +0.028448,230 +0.028783,230 +0.028461,230 +0.028953,230 +0.028479,230 +0.028411,230 +0.029688,232 +0.029182,232 +0.029007,232 +0.029212,232 +0.030177,232 +0.029792,232 +0.030598,232 +0.033744,232 +0.033655,232 +0.030829,232 +0.032066,232 +0.032223,232 +0.031038,232 +0.030659,232 +0.030033,232 +0.029460,232 +0.029567,232 +0.029924,232 +0.029216,232 +0.029134,232 +0.029829,232 +0.029198,232 +0.029112,232 +0.029550,232 +0.029096,232 +0.029180,232 +0.029056,232 +0.029627,232 +0.029195,232 +0.029088,232 +0.029468,232 +0.029486,232 +0.030023,232 +0.029728,232 +0.029768,232 +0.029106,232 +0.029068,232 +0.029595,232 +0.029140,232 +0.029497,232 +0.029585,232 +0.029460,232 +0.029183,232 +0.029034,232 +0.029641,232 +0.029115,232 +0.029208,232 +0.029817,232 +0.029447,232 +0.029239,232 +0.029114,232 +0.029866,232 +0.029166,232 +0.029146,232 +0.029593,232 +0.029066,232 +0.029145,232 +0.029049,232 +0.029621,232 +0.029042,232 +0.029041,232 +0.029647,232 +0.029164,232 +0.029283,232 +0.029343,232 +0.029674,232 +0.029265,232 +0.029332,232 +0.029687,232 +0.029218,232 +0.029087,232 +0.029494,232 +0.029337,232 +0.029189,232 +0.029091,232 +0.029642,232 +0.029189,232 +0.029207,232 +0.029540,232 +0.029594,232 +0.029035,232 +0.029327,232 +0.032385,232 +0.030660,232 +0.029237,232 +0.029852,232 +0.029299,232 +0.029156,232 +0.029341,232 +0.029562,232 +0.029221,232 +0.029107,232 +0.029742,232 +0.029237,232 +0.029049,232 +0.029655,232 +0.029219,232 +0.029072,232 +0.029165,232 +0.029762,232 +0.030358,234 +0.030127,234 +0.030604,234 +0.030153,234 +0.030130,234 +0.030406,234 +0.030486,234 +0.030233,234 +0.030003,234 +0.030490,234 +0.030202,234 +0.030074,234 +0.030438,234 +0.030215,234 +0.030018,234 +0.031065,234 +0.032074,234 +0.030253,234 +0.030099,234 +0.030677,234 +0.031515,234 +0.031204,234 +0.033240,234 +0.031116,234 +0.030199,234 +0.030712,234 +0.030225,234 +0.030108,234 +0.030597,234 +0.030284,234 +0.030132,234 +0.030359,234 +0.030782,234 +0.030082,234 +0.030109,234 +0.030729,234 +0.030159,234 +0.030105,234 +0.030472,234 +0.030409,234 +0.030108,234 +0.030038,234 +0.030701,234 +0.030097,234 +0.032153,234 +0.032187,234 +0.030610,234 +0.030178,234 +0.030790,234 +0.030180,234 +0.030011,234 +0.030187,234 +0.030570,234 +0.030096,234 +0.030133,234 +0.031568,234 +0.030319,234 +0.030084,234 +0.030822,234 +0.030645,234 +0.030130,234 +0.030539,234 +0.031045,234 +0.030107,234 +0.030286,234 +0.030675,234 +0.030380,234 +0.030718,234 +0.031886,234 +0.032856,234 +0.033020,234 +0.032307,234 +0.031610,234 +0.032002,234 +0.032058,234 +0.031528,234 +0.030505,234 +0.030506,234 +0.030780,234 +0.030169,234 +0.030483,234 +0.030792,234 +0.030206,234 +0.030239,234 +0.031256,234 +0.030443,234 +0.030501,234 +0.030984,234 +0.030521,234 +0.030428,234 +0.030373,234 +0.030966,234 +0.030462,234 +0.030669,234 +0.030869,234 +0.030494,234 +0.030628,234 +0.031014,234 +0.031166,234 +0.033034,234 +0.033777,236 +0.033994,236 +0.033944,236 +0.034148,236 +0.031757,236 +0.030948,236 +0.032556,236 +0.031320,236 +0.031032,236 +0.031013,236 +0.032891,236 +0.032434,236 +0.032233,236 +0.034586,236 +0.033126,236 +0.033744,236 +0.034739,236 +0.031994,236 +0.031318,236 +0.033039,236 +0.031272,236 +0.031136,236 +0.032828,236 +0.031334,236 +0.031468,236 +0.032985,236 +0.031576,236 +0.031285,236 +0.033451,236 +0.035104,236 +0.034135,236 +0.032739,236 +0.032981,236 +0.032480,236 +0.032441,236 +0.032488,236 +0.033266,236 +0.031990,236 +0.031856,236 +0.031373,236 +0.031471,236 +0.031751,236 +0.032149,236 +0.031541,236 +0.031784,236 +0.031390,236 +0.031234,236 +0.031803,236 +0.031537,236 +0.031533,236 +0.032068,236 +0.031771,236 +0.031798,236 +0.031953,236 +0.031569,236 +0.031234,236 +0.031939,236 +0.031545,236 +0.031601,236 +0.031578,236 +0.031932,236 +0.031237,236 +0.031325,236 +0.031721,236 +0.031366,236 +0.031220,236 +0.031750,236 +0.031240,236 +0.032455,236 +0.033766,236 +0.031280,236 +0.030793,236 +0.031328,236 +0.030853,236 +0.030771,236 +0.031968,236 +0.031074,236 +0.030757,236 +0.030916,236 +0.032139,236 +0.032433,236 +0.034592,236 +0.033978,236 +0.032397,236 +0.032334,236 +0.031628,236 +0.031247,236 +0.031339,236 +0.031525,236 +0.032272,236 +0.034320,236 +0.035302,236 +0.033631,236 +0.032443,236 +0.031868,236 +0.036478,236 +0.032029,236 +0.031947,236 +0.030840,236 +0.030834,236 +0.032290,238 +0.031663,238 +0.031577,238 +0.033485,238 +0.033872,238 +0.035361,238 +0.035761,238 +0.032871,238 +0.032131,238 +0.032473,238 +0.031940,238 +0.031745,238 +0.032728,238 +0.032135,238 +0.031720,238 +0.032094,238 +0.033397,238 +0.032657,238 +0.034607,238 +0.034474,238 +0.034204,238 +0.038265,238 +0.033422,238 +0.032119,238 +0.032749,238 +0.032330,238 +0.033634,238 +0.034926,238 +0.036489,238 +0.034506,238 +0.033690,238 +0.032542,238 +0.032052,238 +0.032223,238 +0.033186,238 +0.034131,238 +0.034831,238 +0.034710,238 +0.033838,238 +0.032466,238 +0.032274,238 +0.032050,238 +0.031949,238 +0.032542,238 +0.031693,238 +0.031649,238 +0.032263,238 +0.031716,238 +0.031614,238 +0.032194,238 +0.033197,238 +0.035426,238 +0.035452,238 +0.033799,238 +0.034757,238 +0.033376,238 +0.032357,238 +0.032370,238 +0.033924,238 +0.031932,238 +0.031730,238 +0.033355,238 +0.031602,238 +0.032070,238 +0.033182,238 +0.031728,238 +0.031650,238 +0.033281,238 +0.031678,238 +0.031882,238 +0.034564,238 +0.031760,238 +0.031552,238 +0.033319,238 +0.031600,238 +0.031533,238 +0.032823,238 +0.032028,238 +0.031525,238 +0.031993,238 +0.032756,238 +0.031828,238 +0.031746,238 +0.033238,238 +0.031641,238 +0.031616,238 +0.033137,238 +0.031554,238 +0.031585,238 +0.033085,238 +0.031562,238 +0.031473,238 +0.033401,238 +0.031639,238 +0.031512,238 +0.033092,238 +0.031949,238 +0.031735,238 +0.033181,238 +0.031755,238 +0.032343,240 +0.033862,240 +0.034092,240 +0.032217,240 +0.033336,240 +0.032581,240 +0.032189,240 +0.032208,240 +0.033655,240 +0.032166,240 +0.032460,240 +0.033617,240 +0.032209,240 +0.032333,240 +0.033738,240 +0.032283,240 +0.032250,240 +0.033561,240 +0.033114,240 +0.034166,240 +0.035387,240 +0.034878,240 +0.034778,240 +0.035309,240 +0.032956,240 +0.032670,240 +0.034152,240 +0.032453,240 +0.032523,240 +0.033747,240 +0.032219,240 +0.032256,240 +0.034852,240 +0.032188,240 +0.032216,240 +0.033476,240 +0.032083,240 +0.033007,240 +0.034557,240 +0.032568,240 +0.032249,240 +0.033585,240 +0.032223,240 +0.032403,240 +0.033472,240 +0.032224,240 +0.032070,240 +0.032631,240 +0.032187,240 +0.032076,240 +0.032691,240 +0.032156,240 +0.032070,240 +0.032641,240 +0.032126,240 +0.032065,240 +0.032322,240 +0.032443,240 +0.032428,240 +0.032233,240 +0.032845,240 +0.032217,240 +0.032185,240 +0.032981,240 +0.032174,240 +0.032270,240 +0.032766,240 +0.032613,240 +0.032274,240 +0.032744,240 +0.032155,240 +0.032178,240 +0.032682,240 +0.032216,240 +0.032185,240 +0.032755,240 +0.032373,240 +0.032354,240 +0.032655,240 +0.032702,240 +0.032727,240 +0.033254,240 +0.032606,240 +0.032792,240 +0.033288,240 +0.032707,240 +0.032698,240 +0.032970,240 +0.033131,240 +0.032702,240 +0.032809,240 +0.032904,240 +0.032723,240 +0.032811,240 +0.033252,240 +0.032700,240 +0.032779,240 +0.033331,240 +0.032580,240 +0.032634,240 +0.034677,242 +0.034333,242 +0.035353,242 +0.037132,242 +0.035416,242 +0.035410,242 +0.034834,242 +0.033790,242 +0.034383,242 +0.033788,242 +0.033457,242 +0.034437,242 +0.035468,242 +0.036031,242 +0.038102,242 +0.036129,242 +0.036671,242 +0.038472,242 +0.034601,242 +0.034189,242 +0.036864,242 +0.036533,242 +0.036482,242 +0.037213,242 +0.036504,242 +0.038268,242 +0.036324,242 +0.038244,242 +0.035677,242 +0.035634,242 +0.034792,242 +0.036135,242 +0.036817,242 +0.037817,242 +0.037462,242 +0.036281,242 +0.036753,242 +0.036863,242 +0.035234,242 +0.034721,242 +0.034226,242 +0.034461,242 +0.035540,242 +0.036877,242 +0.036143,242 +0.036095,242 +0.035628,242 +0.034672,242 +0.034271,242 +0.034081,242 +0.034506,242 +0.035000,242 +0.035985,242 +0.035727,242 +0.036704,242 +0.037648,242 +0.035403,242 +0.034006,242 +0.033905,242 +0.034223,242 +0.036224,242 +0.036299,242 +0.038138,242 +0.036845,242 +0.036640,242 +0.036335,242 +0.036843,242 +0.034545,242 +0.033487,242 +0.036115,242 +0.036344,242 +0.036293,242 +0.035307,242 +0.038131,242 +0.045884,242 +0.042915,242 +0.035826,242 +0.036449,242 +0.035700,242 +0.036295,242 +0.039672,242 +0.035614,242 +0.035382,242 +0.034891,242 +0.033864,242 +0.034920,242 +0.035236,242 +0.036033,242 +0.037853,242 +0.036326,242 +0.036606,242 +0.035340,242 +0.038935,242 +0.033753,242 +0.033520,242 +0.038138,242 +0.035472,242 +0.035660,242 +0.035369,242 +0.034935,242 +0.035351,244 +0.035871,244 +0.035230,244 +0.035925,244 +0.038724,244 +0.040129,244 +0.039379,244 +0.038537,244 +0.040497,244 +0.036633,244 +0.035343,244 +0.038747,244 +0.038757,244 +0.045130,244 +0.036858,244 +0.041927,244 +0.039854,244 +0.037641,244 +0.038082,244 +0.043394,244 +0.039307,244 +0.038785,244 +0.037869,244 +0.037780,244 +0.035217,244 +0.034456,244 +0.036203,244 +0.037800,244 +0.040150,244 +0.050008,244 +0.049812,244 +0.041325,244 +0.045832,244 +0.052610,244 +0.052008,244 +0.042045,244 +0.067749,244 +0.072703,244 +0.072166,244 +0.046886,244 +0.038491,244 +0.039296,244 +0.037777,244 +0.049037,244 +0.036943,244 +0.036475,244 +0.036480,244 +0.036279,244 +0.036979,244 +0.035601,244 +0.037431,244 +0.035981,244 +0.035024,244 +0.035396,244 +0.035535,244 +0.035078,244 +0.035980,244 +0.035874,244 +0.035106,244 +0.034888,244 +0.034206,244 +0.034227,244 +0.034895,244 +0.038662,244 +0.034279,244 +0.039300,244 +0.035010,244 +0.034118,244 +0.034979,244 +0.034239,244 +0.034100,244 +0.047447,244 +0.034204,244 +0.034705,244 +0.034445,244 +0.034354,244 +0.034837,244 +0.034082,244 +0.034278,244 +0.034973,244 +0.034284,244 +0.034085,244 +0.034760,244 +0.034259,244 +0.034188,244 +0.034593,244 +0.034133,244 +0.034105,244 +0.034614,244 +0.034142,244 +0.034141,244 +0.034646,244 +0.034292,244 +0.034239,244 +0.034943,244 +0.034119,244 +0.034072,244 +0.034719,244 +0.034357,244 +0.034145,244 +0.035788,246 +0.035212,246 +0.035194,246 +0.035476,246 +0.035298,246 +0.036709,246 +0.035462,246 +0.035223,246 +0.035805,246 +0.035209,246 +0.035165,246 +0.035768,246 +0.035274,246 +0.035219,246 +0.035662,246 +0.035250,246 +0.035914,246 +0.036826,246 +0.038206,246 +0.044112,246 +0.041421,246 +0.043092,246 +0.042983,246 +0.036796,246 +0.039207,246 +0.038178,246 +0.037697,246 +0.039172,246 +0.038369,246 +0.038217,246 +0.037788,246 +0.039724,246 +0.043731,246 +0.039567,246 +0.039280,246 +0.036046,246 +0.035558,246 +0.037500,246 +0.037027,246 +0.037366,246 +0.038814,246 +0.037329,246 +0.036223,246 +0.036504,246 +0.035596,246 +0.036479,246 +0.037131,246 +0.035821,246 +0.036483,246 +0.035860,246 +0.035607,246 +0.036814,246 +0.035801,246 +0.035939,246 +0.036605,246 +0.036062,246 +0.036307,246 +0.035925,246 +0.036517,246 +0.037065,246 +0.036557,246 +0.035529,246 +0.036068,246 +0.036164,246 +0.035511,246 +0.036099,246 +0.035529,246 +0.035457,246 +0.036358,246 +0.035706,246 +0.035986,246 +0.037572,246 +0.035684,246 +0.036861,246 +0.035794,246 +0.035796,246 +0.036792,246 +0.035434,246 +0.035464,246 +0.036024,246 +0.035524,246 +0.035594,246 +0.036032,246 +0.035576,246 +0.036133,246 +0.035656,246 +0.035641,246 +0.036242,246 +0.035668,246 +0.035511,246 +0.036249,246 +0.035679,246 +0.035835,246 +0.036350,246 +0.035769,246 +0.035779,246 +0.036081,246 +0.035742,246 +0.036305,246 +0.035666,246 +0.036538,248 +0.036950,248 +0.036891,248 +0.037282,248 +0.037122,248 +0.035963,248 +0.035966,248 +0.036533,248 +0.035865,248 +0.036491,248 +0.036088,248 +0.035918,248 +0.036324,248 +0.036204,248 +0.036010,248 +0.036408,248 +0.036022,248 +0.035875,248 +0.036484,248 +0.035847,248 +0.035988,248 +0.036638,248 +0.035939,248 +0.036479,248 +0.036101,248 +0.035841,248 +0.037387,248 +0.035967,248 +0.036096,248 +0.036605,248 +0.037319,248 +0.036080,248 +0.036739,248 +0.035905,248 +0.036373,248 +0.036001,248 +0.035857,248 +0.036426,248 +0.036060,248 +0.036116,248 +0.036435,248 +0.036006,248 +0.035934,248 +0.036601,248 +0.036661,248 +0.038456,248 +0.037034,248 +0.036383,248 +0.037245,248 +0.036645,248 +0.036301,248 +0.036790,248 +0.036420,248 +0.036386,248 +0.039304,248 +0.037737,248 +0.036706,248 +0.037622,248 +0.039952,248 +0.039045,248 +0.039536,248 +0.038979,248 +0.037102,248 +0.040524,248 +0.047871,248 +0.039514,248 +0.038784,248 +0.036877,248 +0.036276,248 +0.036576,248 +0.036445,248 +0.036307,248 +0.038011,248 +0.036560,248 +0.036393,248 +0.039587,248 +0.037070,248 +0.038024,248 +0.036550,248 +0.036464,248 +0.039896,248 +0.040696,248 +0.039671,248 +0.037722,248 +0.037045,248 +0.037030,248 +0.036760,248 +0.036654,248 +0.036918,248 +0.036292,248 +0.036506,248 +0.036907,248 +0.036397,248 +0.036666,248 +0.037172,248 +0.036737,248 +0.037231,248 +0.036764,248 +0.037268,248 +0.037170,248 +0.038086,250 +0.038827,250 +0.038990,250 +0.037656,250 +0.039527,250 +0.037633,250 +0.037549,250 +0.038221,250 +0.037844,250 +0.038290,250 +0.037835,250 +0.037638,250 +0.038288,250 +0.037639,250 +0.037595,250 +0.038418,250 +0.037800,250 +0.038053,250 +0.037847,250 +0.037909,250 +0.038100,250 +0.037897,250 +0.037869,250 +0.038147,250 +0.037684,250 +0.038149,250 +0.038995,250 +0.043489,250 +0.045378,250 +0.039512,250 +0.043945,250 +0.041917,250 +0.046253,250 +0.051930,250 +0.061852,250 +0.060873,250 +0.055203,250 +0.056209,250 +0.049196,250 +0.052504,250 +0.054557,250 +0.049361,250 +0.055008,250 +0.048738,250 +0.048519,250 +0.040005,250 +0.052799,250 +0.053327,250 +0.043411,250 +0.044696,250 +0.042284,250 +0.040053,250 +0.043783,250 +0.040671,250 +0.043014,250 +0.041375,250 +0.039464,250 +0.038793,250 +0.037435,250 +0.037281,250 +0.037981,250 +0.037245,250 +0.037327,250 +0.037564,250 +0.037241,250 +0.037451,250 +0.039258,250 +0.037382,250 +0.037922,250 +0.037268,250 +0.037188,250 +0.037485,250 +0.037387,250 +0.038525,250 +0.038325,250 +0.038383,250 +0.038073,250 +0.040982,250 +0.074718,250 +0.038744,250 +0.038323,250 +0.038145,250 +0.037754,250 +0.039391,250 +0.037818,250 +0.038091,250 +0.038323,250 +0.037743,250 +0.038526,250 +0.037601,250 +0.037652,250 +0.038597,250 +0.037943,250 +0.038059,250 +0.037976,250 +0.037702,250 +0.038592,250 +0.037895,250 +0.037840,250 +0.038815,250 +0.038699,252 +0.039045,252 +0.038515,252 +0.038525,252 +0.039196,252 +0.038629,252 +0.038606,252 +0.039003,252 +0.038791,252 +0.039151,252 +0.038370,252 +0.038741,252 +0.039158,252 +0.038488,252 +0.039305,252 +0.038434,252 +0.038216,252 +0.039576,252 +0.038537,252 +0.038717,252 +0.038729,252 +0.038565,252 +0.039139,252 +0.038482,252 +0.038509,252 +0.039110,252 +0.038557,252 +0.039360,252 +0.038386,252 +0.038276,252 +0.039334,252 +0.038254,252 +0.038748,252 +0.038706,252 +0.038297,252 +0.039110,252 +0.038381,252 +0.038306,252 +0.038858,252 +0.038423,252 +0.039294,252 +0.038163,252 +0.037901,252 +0.038654,252 +0.037990,252 +0.038164,252 +0.038542,252 +0.037878,252 +0.038594,252 +0.038343,252 +0.038125,252 +0.038493,252 +0.037896,252 +0.038614,252 +0.038042,252 +0.037831,252 +0.038678,252 +0.038131,252 +0.038024,252 +0.038536,252 +0.042861,252 +0.038422,252 +0.037953,252 +0.037943,252 +0.038348,252 +0.037991,252 +0.038721,252 +0.038117,252 +0.037917,252 +0.038919,252 +0.037938,252 +0.038027,252 +0.039191,252 +0.037861,252 +0.038955,252 +0.040984,252 +0.038092,252 +0.040819,252 +0.038052,252 +0.039542,252 +0.037981,252 +0.037802,252 +0.039468,252 +0.037887,252 +0.037890,252 +0.038429,252 +0.037804,252 +0.038395,252 +0.038648,252 +0.037949,252 +0.038276,252 +0.037851,252 +0.038169,252 +0.039792,252 +0.042231,252 +0.039571,252 +0.038210,252 +0.038467,252 +0.038717,252 +0.038249,252 +0.039936,254 +0.039465,254 +0.039334,254 +0.040065,254 +0.039383,254 +0.040090,254 +0.039435,254 +0.039177,254 +0.040657,254 +0.039187,254 +0.040312,254 +0.039448,254 +0.039488,254 +0.040645,254 +0.040085,254 +0.041609,254 +0.039331,254 +0.039357,254 +0.041614,254 +0.039211,254 +0.041913,254 +0.039449,254 +0.039495,254 +0.041637,254 +0.039478,254 +0.041623,254 +0.039509,254 +0.039517,254 +0.043351,254 +0.039365,254 +0.041827,254 +0.039644,254 +0.039558,254 +0.041600,254 +0.039541,254 +0.041388,254 +0.039354,254 +0.039592,254 +0.041203,254 +0.039634,254 +0.041391,254 +0.039556,254 +0.039549,254 +0.041227,254 +0.039462,254 +0.041692,254 +0.039581,254 +0.039455,254 +0.041425,254 +0.039442,254 +0.041406,254 +0.039491,254 +0.039306,254 +0.042753,254 +0.039219,254 +0.041637,254 +0.039697,254 +0.039207,254 +0.043401,254 +0.039485,254 +0.041004,254 +0.038971,254 +0.039117,254 +0.041379,254 +0.038966,254 +0.040863,254 +0.038944,254 +0.038962,254 +0.042000,254 +0.039254,254 +0.039711,254 +0.039101,254 +0.038850,254 +0.040741,254 +0.039132,254 +0.039386,254 +0.039018,254 +0.038897,254 +0.039604,254 +0.039720,254 +0.039484,254 +0.039226,254 +0.039947,254 +0.039878,254 +0.039104,254 +0.039400,254 +0.040058,254 +0.039104,254 +0.039540,254 +0.039171,254 +0.039434,254 +0.039560,254 +0.039144,254 +0.039675,254 +0.039228,254 +0.039316,254 +0.039891,254 +0.038911,254 +0.039681,254 +0.039048,254 +0.045297,256 +0.045849,256 +0.045395,256 +0.046163,256 +0.045344,256 +0.046896,256 +0.045613,256 +0.048069,256 +0.045930,256 +0.046376,256 +0.045710,256 +0.046088,256 +0.047383,256 +0.045935,256 +0.047501,256 +0.045963,256 +0.047293,256 +0.046090,256 +0.047512,256 +0.045820,256 +0.047847,256 +0.045723,256 +0.047504,256 +0.045714,256 +0.046280,256 +0.048077,256 +0.045847,256 +0.047505,256 +0.045955,256 +0.047295,256 +0.045545,256 +0.047311,256 +0.045926,256 +0.047432,256 +0.045836,256 +0.047683,256 +0.045752,256 +0.047709,256 +0.046274,256 +0.046592,256 +0.047855,256 +0.050953,256 +0.047916,256 +0.045931,256 +0.047817,256 +0.046053,256 +0.049004,256 +0.046315,256 +0.048031,256 +0.046460,256 +0.048593,256 +0.046224,256 +0.047719,256 +0.045832,256 +0.047828,256 +0.046105,256 +0.045767,256 +0.047757,256 +0.045915,256 +0.048175,256 +0.046601,256 +0.047080,256 +0.045218,256 +0.046985,256 +0.045308,256 +0.046867,256 +0.045136,256 +0.047985,256 +0.045647,256 +0.045707,256 +0.046499,256 +0.045497,256 +0.047160,256 +0.045219,256 +0.047095,256 +0.045170,256 +0.046713,256 +0.045684,256 +0.046960,256 +0.045355,256 +0.046547,256 +0.045593,256 +0.045185,256 +0.046832,256 +0.045076,256 +0.047068,256 +0.045091,256 +0.046798,256 +0.045298,256 +0.048013,256 +0.045422,256 +0.046954,256 +0.045552,256 +0.046425,256 +0.046089,256 +0.045377,256 +0.045881,256 +0.045229,256 +0.045887,256 +0.045230,256 +0.042081,258 +0.042614,258 +0.041833,258 +0.042086,258 +0.041492,258 +0.043070,258 +0.042303,258 +0.042069,258 +0.042106,258 +0.041970,258 +0.042518,258 +0.041982,258 +0.042699,258 +0.041835,258 +0.042066,258 +0.042568,258 +0.042002,258 +0.042405,258 +0.042074,258 +0.042611,258 +0.042106,258 +0.041835,258 +0.042608,258 +0.041898,258 +0.042480,258 +0.042001,258 +0.041909,258 +0.042463,258 +0.045149,258 +0.043737,258 +0.042288,258 +0.042411,258 +0.041625,258 +0.042247,258 +0.042165,258 +0.041585,258 +0.042754,258 +0.041842,258 +0.043590,258 +0.041990,258 +0.043031,258 +0.044013,258 +0.041785,258 +0.043605,258 +0.041802,258 +0.043916,258 +0.041727,258 +0.041861,258 +0.043481,258 +0.042282,258 +0.043696,258 +0.042073,258 +0.043473,258 +0.041695,258 +0.041836,258 +0.043509,258 +0.041741,258 +0.043380,258 +0.042463,258 +0.041709,258 +0.042632,258 +0.042106,258 +0.042620,258 +0.042544,258 +0.045255,258 +0.043871,258 +0.041508,258 +0.041967,258 +0.041501,258 +0.041899,258 +0.041971,258 +0.041960,258 +0.041676,258 +0.041295,258 +0.042285,258 +0.041558,258 +0.042110,258 +0.041293,258 +0.041305,258 +0.042215,258 +0.041494,258 +0.041830,258 +0.041343,258 +0.041394,258 +0.042209,258 +0.041295,258 +0.042063,258 +0.043349,258 +0.045494,258 +0.043548,258 +0.041453,258 +0.046725,258 +0.041732,258 +0.046617,258 +0.041177,258 +0.046633,258 +0.041518,258 +0.045840,258 +0.042901,258 +0.041345,258 +0.048255,260 +0.042324,260 +0.047944,260 +0.042678,260 +0.047935,260 +0.042694,260 +0.044666,260 +0.046949,260 +0.042397,260 +0.048135,260 +0.042603,260 +0.047941,260 +0.042574,260 +0.048251,260 +0.042447,260 +0.047803,260 +0.042785,260 +0.042291,260 +0.048307,260 +0.042330,260 +0.048392,260 +0.042397,260 +0.048226,260 +0.042667,260 +0.047873,260 +0.042525,260 +0.042523,260 +0.048155,260 +0.042379,260 +0.049098,260 +0.042286,260 +0.048006,260 +0.042583,260 +0.047957,260 +0.042498,260 +0.043690,260 +0.046701,260 +0.042336,260 +0.048451,260 +0.042400,260 +0.048644,260 +0.042495,260 +0.048564,260 +0.042649,260 +0.045546,260 +0.045037,260 +0.042463,260 +0.048389,260 +0.042364,260 +0.047973,260 +0.042311,260 +0.048661,260 +0.042668,260 +0.047775,260 +0.043000,260 +0.042421,260 +0.049528,260 +0.042978,260 +0.048586,260 +0.042669,260 +0.048119,260 +0.042438,260 +0.048009,260 +0.042556,260 +0.043498,260 +0.047218,260 +0.042378,260 +0.048384,260 +0.042388,260 +0.048305,260 +0.042455,260 +0.048446,260 +0.042351,260 +0.044113,260 +0.047139,260 +0.042322,260 +0.048408,260 +0.042434,260 +0.048234,260 +0.042494,260 +0.048293,260 +0.042480,260 +0.047994,260 +0.042675,260 +0.042313,260 +0.048334,260 +0.042412,260 +0.048358,260 +0.042306,260 +0.048182,260 +0.042543,260 +0.048056,260 +0.042424,260 +0.042349,260 +0.048096,260 +0.042478,260 +0.049024,260 +0.042525,260 +0.048152,260 +0.042303,260 +0.051544,262 +0.045612,262 +0.050535,262 +0.045288,262 +0.048709,262 +0.047252,262 +0.045144,262 +0.051457,262 +0.045062,262 +0.051046,262 +0.045063,262 +0.050513,262 +0.045180,262 +0.051306,262 +0.045181,262 +0.050392,262 +0.045029,262 +0.051435,262 +0.045635,262 +0.050680,262 +0.045062,262 +0.050670,262 +0.045119,262 +0.050427,262 +0.045001,262 +0.046788,262 +0.049032,262 +0.045134,262 +0.050543,262 +0.045412,262 +0.051262,262 +0.045004,262 +0.050438,262 +0.045083,262 +0.051226,262 +0.045002,262 +0.050308,262 +0.045029,262 +0.052155,262 +0.045088,262 +0.050504,262 +0.045078,262 +0.050475,262 +0.045118,262 +0.050361,262 +0.046407,262 +0.045584,262 +0.050035,262 +0.045313,262 +0.051202,262 +0.045060,262 +0.051355,262 +0.045182,262 +0.051282,262 +0.049080,262 +0.046642,262 +0.045015,262 +0.045746,262 +0.045166,262 +0.045918,262 +0.045070,262 +0.045495,262 +0.045338,262 +0.045044,262 +0.045700,262 +0.045056,262 +0.045916,262 +0.045165,262 +0.045669,262 +0.045212,262 +0.045766,262 +0.045216,262 +0.045616,262 +0.045724,262 +0.045022,262 +0.045808,262 +0.045308,262 +0.047476,262 +0.045366,262 +0.045937,262 +0.045114,262 +0.045810,262 +0.045430,262 +0.045258,262 +0.045845,262 +0.045254,262 +0.045789,262 +0.045173,262 +0.045872,262 +0.045020,262 +0.045713,262 +0.045355,262 +0.045629,262 +0.045504,262 +0.045357,262 +0.045746,262 +0.045122,262 +0.045805,262 +0.045116,262 +0.045932,262 +0.045572,264 +0.045377,264 +0.044911,264 +0.045498,264 +0.045480,264 +0.045013,264 +0.045361,264 +0.044835,264 +0.045345,264 +0.044850,264 +0.045363,264 +0.044819,264 +0.045119,264 +0.045038,264 +0.044929,264 +0.045277,264 +0.045018,264 +0.045337,264 +0.044766,264 +0.045071,264 +0.045004,264 +0.045191,264 +0.044777,264 +0.044833,264 +0.045091,264 +0.044788,264 +0.045319,264 +0.044897,264 +0.045363,264 +0.045009,264 +0.045403,264 +0.044783,264 +0.044908,264 +0.045218,264 +0.044848,264 +0.045603,264 +0.044800,264 +0.045850,264 +0.047181,264 +0.045717,264 +0.044871,264 +0.045471,264 +0.044947,264 +0.044940,264 +0.045371,264 +0.044852,264 +0.045318,264 +0.044823,264 +0.045581,264 +0.044927,264 +0.045449,264 +0.045173,264 +0.044880,264 +0.045276,264 +0.045357,264 +0.045468,264 +0.044777,264 +0.045276,264 +0.044682,264 +0.047804,264 +0.046794,264 +0.046725,264 +0.044823,264 +0.044911,264 +0.049118,264 +0.045572,264 +0.045130,264 +0.045017,264 +0.045110,264 +0.044772,264 +0.045407,264 +0.045054,264 +0.045183,264 +0.045040,264 +0.044867,264 +0.045725,264 +0.044958,264 +0.045318,264 +0.044947,264 +0.045226,264 +0.044847,264 +0.045403,264 +0.045587,264 +0.045449,264 +0.045266,264 +0.044929,264 +0.045318,264 +0.044923,264 +0.045372,264 +0.045250,264 +0.045429,264 +0.044795,264 +0.044988,264 +0.045278,264 +0.045132,264 +0.045579,264 +0.044765,264 +0.045500,264 +0.044827,264 +0.045411,264 +0.048093,266 +0.048554,266 +0.047857,266 +0.048832,266 +0.048130,266 +0.048065,266 +0.048130,266 +0.047908,266 +0.048489,266 +0.048060,266 +0.048360,266 +0.047964,266 +0.048440,266 +0.047902,266 +0.048555,266 +0.048409,266 +0.048603,266 +0.047875,266 +0.048451,266 +0.047899,266 +0.048415,266 +0.047878,266 +0.048513,266 +0.048003,266 +0.048460,266 +0.048109,266 +0.048418,266 +0.047827,266 +0.048355,266 +0.048271,266 +0.048101,266 +0.048250,266 +0.047861,266 +0.048418,266 +0.047947,266 +0.048736,266 +0.047898,266 +0.048680,266 +0.047957,266 +0.048521,266 +0.048046,266 +0.048546,266 +0.048040,266 +0.049049,266 +0.047991,266 +0.048726,266 +0.048007,266 +0.048397,266 +0.047939,266 +0.048432,266 +0.047919,266 +0.048511,266 +0.048066,266 +0.048158,266 +0.048293,266 +0.048010,266 +0.048770,266 +0.048032,266 +0.048726,266 +0.047981,266 +0.048417,266 +0.048049,266 +0.048393,266 +0.048031,266 +0.048320,266 +0.048281,266 +0.049239,266 +0.047884,266 +0.048425,266 +0.047931,266 +0.048400,266 +0.047844,266 +0.048448,266 +0.048015,266 +0.048546,266 +0.048001,266 +0.048574,266 +0.048322,266 +0.048336,266 +0.048125,266 +0.048212,266 +0.048421,266 +0.048035,266 +0.048492,266 +0.047906,266 +0.048542,266 +0.048039,266 +0.048647,266 +0.047852,266 +0.048421,266 +0.047796,266 +0.048576,266 +0.047807,266 +0.048873,266 +0.047809,266 +0.048401,266 +0.047913,266 +0.048670,266 +0.048133,266 +0.048864,266 +0.048275,268 +0.048696,268 +0.048144,268 +0.048465,268 +0.048125,268 +0.048255,268 +0.048431,268 +0.048170,268 +0.048705,268 +0.048052,268 +0.048540,268 +0.048015,268 +0.048595,268 +0.048046,268 +0.048586,268 +0.048002,268 +0.049067,268 +0.048110,268 +0.048884,268 +0.048117,268 +0.048584,268 +0.048039,268 +0.048778,268 +0.048048,268 +0.048461,268 +0.048128,268 +0.048589,268 +0.048218,268 +0.048745,268 +0.048078,268 +0.048564,268 +0.048037,268 +0.048153,268 +0.048413,268 +0.047985,268 +0.048706,268 +0.048094,268 +0.048498,268 +0.048325,268 +0.048784,268 +0.048145,268 +0.048614,268 +0.048069,268 +0.048603,268 +0.048081,268 +0.048666,268 +0.048397,268 +0.048522,268 +0.048516,268 +0.048846,268 +0.048086,268 +0.048523,268 +0.048044,268 +0.048577,268 +0.048127,268 +0.048515,268 +0.048060,268 +0.048525,268 +0.048301,268 +0.048229,268 +0.048670,268 +0.048532,268 +0.048557,268 +0.048008,268 +0.048688,268 +0.048004,268 +0.048554,268 +0.048121,268 +0.048588,268 +0.048915,268 +0.048832,268 +0.048046,268 +0.048471,268 +0.048041,268 +0.048648,268 +0.048166,268 +0.048498,268 +0.048032,268 +0.048534,268 +0.048124,268 +0.048592,268 +0.048203,268 +0.048449,268 +0.048046,268 +0.048568,268 +0.048168,268 +0.048328,268 +0.048358,268 +0.048142,268 +0.048514,268 +0.048489,268 +0.048674,268 +0.048018,268 +0.048568,268 +0.048246,268 +0.048617,268 +0.048178,268 +0.048707,268 +0.048113,268 +0.048557,268 +0.051342,270 +0.051541,270 +0.051119,270 +0.051441,270 +0.051187,270 +0.051469,270 +0.050958,270 +0.051311,270 +0.051083,270 +0.051505,270 +0.051255,270 +0.051646,270 +0.050894,270 +0.051497,270 +0.050975,270 +0.051511,270 +0.050891,270 +0.051461,270 +0.051058,270 +0.051288,270 +0.051191,270 +0.051547,270 +0.051195,270 +0.051279,270 +0.051556,270 +0.051011,270 +0.051468,270 +0.050985,270 +0.051403,270 +0.051001,270 +0.051945,270 +0.050997,270 +0.051442,270 +0.051165,270 +0.051447,270 +0.051047,270 +0.051476,270 +0.051056,270 +0.051486,270 +0.051006,270 +0.051561,270 +0.051181,270 +0.051743,270 +0.051012,270 +0.051433,270 +0.050948,270 +0.051489,270 +0.051084,270 +0.051561,270 +0.051276,270 +0.051648,270 +0.050909,270 +0.051372,270 +0.051003,270 +0.051535,270 +0.050986,270 +0.051464,270 +0.050818,270 +0.051522,270 +0.050939,270 +0.051597,270 +0.050956,270 +0.051504,270 +0.050854,270 +0.051526,270 +0.050830,270 +0.051485,270 +0.050898,270 +0.051404,270 +0.056755,270 +0.052415,270 +0.051187,270 +0.051174,270 +0.051398,270 +0.050898,270 +0.051421,270 +0.051019,270 +0.051525,270 +0.050984,270 +0.051634,270 +0.051033,270 +0.051498,270 +0.050999,270 +0.051528,270 +0.050991,270 +0.051460,270 +0.050919,270 +0.051540,270 +0.051221,270 +0.051615,270 +0.050929,270 +0.051637,270 +0.051243,270 +0.051707,270 +0.051443,270 +0.051519,270 +0.050925,270 +0.051655,270 +0.051174,270 +0.051755,270 +0.049435,272 +0.049712,272 +0.049166,272 +0.049631,272 +0.049171,272 +0.049689,272 +0.049117,272 +0.049701,272 +0.049306,272 +0.049876,272 +0.049086,272 +0.049662,272 +0.049139,272 +0.049734,272 +0.049166,272 +0.049868,272 +0.049411,272 +0.049673,272 +0.049128,272 +0.049832,272 +0.049201,272 +0.049724,272 +0.051215,272 +0.050721,272 +0.049178,272 +0.050670,272 +0.049205,272 +0.050658,272 +0.049243,272 +0.050589,272 +0.049139,272 +0.050582,272 +0.049158,272 +0.050957,272 +0.049261,272 +0.050503,272 +0.049055,272 +0.050749,272 +0.049715,272 +0.051716,272 +0.049319,272 +0.050582,272 +0.049194,272 +0.050733,272 +0.049297,272 +0.051079,272 +0.049202,272 +0.050302,272 +0.049431,272 +0.050735,272 +0.049148,272 +0.050486,272 +0.049299,272 +0.050421,272 +0.049318,272 +0.050266,272 +0.049265,272 +0.050209,272 +0.049803,272 +0.051081,272 +0.049932,272 +0.050271,272 +0.049587,272 +0.050158,272 +0.049592,272 +0.050020,272 +0.049635,272 +0.050008,272 +0.050422,272 +0.049948,272 +0.049773,272 +0.049773,272 +0.050027,272 +0.049700,272 +0.050082,272 +0.049474,272 +0.050181,272 +0.049382,272 +0.050677,272 +0.049202,272 +0.052091,272 +0.049543,272 +0.050200,272 +0.049158,272 +0.050576,272 +0.049119,272 +0.050529,272 +0.049232,272 +0.050573,272 +0.049112,272 +0.050611,272 +0.049247,272 +0.050781,272 +0.049196,272 +0.050974,272 +0.049342,272 +0.050484,272 +0.049243,272 +0.050431,272 +0.049244,272 +0.055936,274 +0.053476,274 +0.053482,274 +0.054314,274 +0.052765,274 +0.054135,274 +0.052769,274 +0.054386,274 +0.053011,274 +0.054183,274 +0.052823,274 +0.054154,274 +0.052873,274 +0.054188,274 +0.052746,274 +0.054069,274 +0.052887,274 +0.054350,274 +0.054909,274 +0.053474,274 +0.053989,274 +0.052878,274 +0.054203,274 +0.052980,274 +0.054277,274 +0.052768,274 +0.054341,274 +0.052917,274 +0.054331,274 +0.052932,274 +0.054125,274 +0.052855,274 +0.054084,274 +0.053899,274 +0.053103,274 +0.054212,274 +0.052839,274 +0.055637,274 +0.053230,274 +0.054193,274 +0.052798,274 +0.054121,274 +0.052883,274 +0.054491,274 +0.053176,274 +0.054155,274 +0.052861,274 +0.054216,274 +0.053711,274 +0.053177,274 +0.054143,274 +0.052794,274 +0.054244,274 +0.052822,274 +0.054396,274 +0.052789,274 +0.055424,274 +0.052788,274 +0.054105,274 +0.052730,274 +0.054005,274 +0.052820,274 +0.054166,274 +0.053538,274 +0.053382,274 +0.054193,274 +0.053835,274 +0.055035,274 +0.055093,274 +0.055100,274 +0.054008,274 +0.055025,274 +0.053819,274 +0.054744,274 +0.053556,274 +0.056024,274 +0.054414,274 +0.053970,274 +0.055162,274 +0.053304,274 +0.055780,274 +0.053383,274 +0.055202,274 +0.053354,274 +0.054638,274 +0.053250,274 +0.054771,274 +0.053860,274 +0.054538,274 +0.054270,274 +0.053734,274 +0.054906,274 +0.053493,274 +0.055184,274 +0.053665,274 +0.053948,274 +0.053557,274 +0.054322,274 +0.053787,274 +0.053672,274 +0.054128,276 +0.054896,276 +0.054354,276 +0.054290,276 +0.054894,276 +0.053618,276 +0.054930,276 +0.053730,276 +0.054892,276 +0.054017,276 +0.056243,276 +0.054117,276 +0.056417,276 +0.054062,276 +0.055307,276 +0.055088,276 +0.054532,276 +0.054670,276 +0.053246,276 +0.054359,276 +0.053118,276 +0.054349,276 +0.053165,276 +0.054354,276 +0.053115,276 +0.054216,276 +0.053150,276 +0.054336,276 +0.054530,276 +0.053243,276 +0.055437,276 +0.053164,276 +0.054328,276 +0.053144,276 +0.054764,276 +0.054260,276 +0.054312,276 +0.056166,276 +0.055131,276 +0.053252,276 +0.053969,276 +0.054267,276 +0.053053,276 +0.054094,276 +0.053045,276 +0.053980,276 +0.053225,276 +0.055082,276 +0.053120,276 +0.053623,276 +0.053141,276 +0.054539,276 +0.053074,276 +0.053560,276 +0.053681,276 +0.053762,276 +0.055634,276 +0.053254,276 +0.053405,276 +0.054822,276 +0.054325,276 +0.053122,276 +0.053438,276 +0.053207,276 +0.053634,276 +0.053511,276 +0.053607,276 +0.053119,276 +0.053694,276 +0.053250,276 +0.053541,276 +0.053725,276 +0.053152,276 +0.053525,276 +0.053539,276 +0.053485,276 +0.053115,276 +0.053708,276 +0.053342,276 +0.053600,276 +0.053844,276 +0.053480,276 +0.053116,276 +0.053744,276 +0.053231,276 +0.053467,276 +0.053083,276 +0.053788,276 +0.053221,276 +0.053674,276 +0.053589,276 +0.053146,276 +0.053575,276 +0.053412,276 +0.053608,276 +0.053061,276 +0.053592,276 +0.053129,276 +0.053909,276 +0.052992,276 +0.056686,278 +0.056121,278 +0.056500,278 +0.056478,278 +0.055945,278 +0.056477,278 +0.055941,278 +0.056564,278 +0.055995,278 +0.056528,278 +0.056414,278 +0.056325,278 +0.056512,278 +0.056066,278 +0.056793,278 +0.056123,278 +0.056582,278 +0.055945,278 +0.056602,278 +0.056426,278 +0.056327,278 +0.056475,278 +0.056034,278 +0.056723,278 +0.056029,278 +0.056717,278 +0.056075,278 +0.056660,278 +0.056743,278 +0.056300,278 +0.056511,278 +0.055932,278 +0.056550,278 +0.056184,278 +0.056580,278 +0.056058,278 +0.056266,278 +0.056487,278 +0.056185,278 +0.056611,278 +0.055784,278 +0.056613,278 +0.056066,278 +0.056499,278 +0.056814,278 +0.055931,278 +0.056476,278 +0.056853,278 +0.056435,278 +0.055918,278 +0.056794,278 +0.057376,278 +0.056570,278 +0.056438,278 +0.055998,278 +0.056864,278 +0.056111,278 +0.056630,278 +0.055871,278 +0.056763,278 +0.056253,278 +0.056417,278 +0.056558,278 +0.055982,278 +0.056670,278 +0.055937,278 +0.056469,278 +0.055934,278 +0.056489,278 +0.056263,278 +0.056659,278 +0.056447,278 +0.056029,278 +0.056709,278 +0.056107,278 +0.056422,278 +0.055829,278 +0.056632,278 +0.056431,278 +0.055938,278 +0.056483,278 +0.055816,278 +0.056627,278 +0.055849,278 +0.056359,278 +0.055843,278 +0.057168,278 +0.056457,278 +0.055904,278 +0.056399,278 +0.055899,278 +0.057277,278 +0.055828,278 +0.056306,278 +0.055929,278 +0.056550,278 +0.056387,278 +0.055821,278 +0.056925,278 +0.056030,278 +0.056039,280 +0.054997,280 +0.056157,280 +0.055203,280 +0.055545,280 +0.055597,280 +0.055629,280 +0.055476,280 +0.055143,280 +0.055797,280 +0.055150,280 +0.055650,280 +0.055104,280 +0.055887,280 +0.055714,280 +0.055130,280 +0.055771,280 +0.055378,280 +0.055863,280 +0.055104,280 +0.055756,280 +0.055104,280 +0.055971,280 +0.055739,280 +0.055151,280 +0.055592,280 +0.055293,280 +0.055854,280 +0.055124,280 +0.055650,280 +0.055182,280 +0.055857,280 +0.055306,280 +0.055486,280 +0.055568,280 +0.055182,280 +0.055911,280 +0.055098,280 +0.055473,280 +0.055237,280 +0.055612,280 +0.055152,280 +0.055658,280 +0.055459,280 +0.055312,280 +0.055762,280 +0.055169,280 +0.055615,280 +0.055152,280 +0.055908,280 +0.055204,280 +0.055705,280 +0.055386,280 +0.055221,280 +0.056019,280 +0.055110,280 +0.055731,280 +0.055292,280 +0.056103,280 +0.055521,280 +0.055667,280 +0.055302,280 +0.055408,280 +0.055828,280 +0.055129,280 +0.055558,280 +0.055119,280 +0.055847,280 +0.055210,280 +0.055756,280 +0.055195,280 +0.055800,280 +0.055859,280 +0.055122,280 +0.055436,280 +0.055093,280 +0.055607,280 +0.055062,280 +0.055480,280 +0.055228,280 +0.055440,280 +0.055857,280 +0.055213,280 +0.055463,280 +0.055038,280 +0.055800,280 +0.055128,280 +0.055669,280 +0.055285,280 +0.055366,280 +0.055615,280 +0.055130,280 +0.055400,280 +0.055457,280 +0.055801,280 +0.056098,280 +0.055713,280 +0.055297,280 +0.055464,280 +0.055897,280 +0.061178,282 +0.060940,282 +0.060385,282 +0.061193,282 +0.060907,282 +0.060585,282 +0.060973,282 +0.061083,282 +0.060710,282 +0.060792,282 +0.060495,282 +0.060994,282 +0.060557,282 +0.060853,282 +0.060833,282 +0.060674,282 +0.061016,282 +0.060525,282 +0.060771,282 +0.060985,282 +0.060689,282 +0.060932,282 +0.060415,282 +0.060865,282 +0.065272,282 +0.060795,282 +0.060861,282 +0.060535,282 +0.060739,282 +0.060891,282 +0.060540,282 +0.060519,282 +0.060961,282 +0.060622,282 +0.060677,282 +0.060447,282 +0.060994,282 +0.060663,282 +0.060750,282 +0.060640,282 +0.060824,282 +0.061117,282 +0.060853,282 +0.060488,282 +0.061053,282 +0.060691,282 +0.060881,282 +0.060800,282 +0.060519,282 +0.060955,282 +0.060484,282 +0.060771,282 +0.061039,282 +0.060620,282 +0.061179,282 +0.060412,282 +0.060860,282 +0.061263,282 +0.060412,282 +0.060798,282 +0.060409,282 +0.061082,282 +0.060783,282 +0.060369,282 +0.060791,282 +0.060680,282 +0.060823,282 +0.060749,282 +0.060454,282 +0.060993,282 +0.060702,282 +0.060723,282 +0.060732,282 +0.060771,282 +0.060674,282 +0.060352,282 +0.060997,282 +0.060970,282 +0.060575,282 +0.060690,282 +0.060320,282 +0.061755,282 +0.060964,282 +0.060513,282 +0.060540,282 +0.060371,282 +0.060994,282 +0.061590,282 +0.060600,282 +0.061419,282 +0.060636,282 +0.060621,282 +0.060998,282 +0.060314,282 +0.060860,282 +0.060558,282 +0.060567,282 +0.060689,282 +0.060647,282 +0.060750,282 +0.058921,284 +0.058936,284 +0.059176,284 +0.058603,284 +0.059371,284 +0.058771,284 +0.060202,284 +0.059112,284 +0.058822,284 +0.059130,284 +0.058993,284 +0.059290,284 +0.059066,284 +0.058856,284 +0.059348,284 +0.059093,284 +0.059185,284 +0.058805,284 +0.059290,284 +0.059479,284 +0.059320,284 +0.059182,284 +0.058853,284 +0.059464,284 +0.059027,284 +0.058661,284 +0.058992,284 +0.058628,284 +0.060052,284 +0.058768,284 +0.058889,284 +0.058936,284 +0.058981,284 +0.059222,284 +0.058769,284 +0.059221,284 +0.059170,284 +0.059063,284 +0.059002,284 +0.058687,284 +0.059421,284 +0.058926,284 +0.058686,284 +0.059023,284 +0.058684,284 +0.059015,284 +0.058624,284 +0.059053,284 +0.059106,284 +0.058753,284 +0.059009,284 +0.058660,284 +0.059045,284 +0.058886,284 +0.059208,284 +0.058953,284 +0.058749,284 +0.059335,284 +0.058585,284 +0.059025,284 +0.059127,284 +0.058718,284 +0.059328,284 +0.058785,284 +0.059074,284 +0.059040,284 +0.059038,284 +0.059060,284 +0.058690,284 +0.059024,284 +0.058809,284 +0.062781,284 +0.062612,284 +0.059017,284 +0.062422,284 +0.061937,284 +0.058787,284 +0.062778,284 +0.058929,284 +0.062076,284 +0.062005,284 +0.058849,284 +0.062248,284 +0.058850,284 +0.061965,284 +0.061794,284 +0.060139,284 +0.063142,284 +0.059049,284 +0.061887,284 +0.061915,284 +0.058789,284 +0.061870,284 +0.058607,284 +0.061869,284 +0.062020,284 +0.058899,284 +0.061880,284 +0.058643,284 +0.062002,284 +0.065981,286 +0.063085,286 +0.065705,286 +0.066395,286 +0.063186,286 +0.065908,286 +0.065949,286 +0.062979,286 +0.065761,286 +0.063785,286 +0.064798,286 +0.064375,286 +0.062746,286 +0.063914,286 +0.063989,286 +0.062908,286 +0.064041,286 +0.063173,286 +0.062956,286 +0.063980,286 +0.063076,286 +0.063271,286 +0.063561,286 +0.062711,286 +0.063212,286 +0.063110,286 +0.063045,286 +0.063386,286 +0.062728,286 +0.063221,286 +0.063484,286 +0.063042,286 +0.063231,286 +0.063095,286 +0.062986,286 +0.063989,286 +0.062867,286 +0.063241,286 +0.063624,286 +0.062800,286 +0.063251,286 +0.063172,286 +0.062871,286 +0.063358,286 +0.062740,286 +0.063326,286 +0.063316,286 +0.062790,286 +0.063419,286 +0.063193,286 +0.062935,286 +0.063784,286 +0.063122,286 +0.064094,286 +0.067483,286 +0.062756,286 +0.063161,286 +0.063158,286 +0.062857,286 +0.063157,286 +0.063145,286 +0.062850,286 +0.063292,286 +0.062744,286 +0.063340,286 +0.063324,286 +0.062920,286 +0.063674,286 +0.063221,286 +0.064689,286 +0.063610,286 +0.062748,286 +0.064264,286 +0.063843,286 +0.062842,286 +0.063239,286 +0.063366,286 +0.063586,286 +0.063319,286 +0.063017,286 +0.063736,286 +0.063332,286 +0.062838,286 +0.063847,286 +0.063231,286 +0.063415,286 +0.063301,286 +0.063123,286 +0.062875,286 +0.063330,286 +0.063156,286 +0.063569,286 +0.063378,286 +0.063101,286 +0.063237,286 +0.063325,286 +0.062859,286 +0.063421,286 +0.062976,286 +0.063373,286 +0.065231,288 +0.065049,288 +0.065202,288 +0.065060,288 +0.064777,288 +0.065043,288 +0.064091,288 +0.063515,288 +0.064231,288 +0.064605,288 +0.063848,288 +0.064219,288 +0.063622,288 +0.063975,288 +0.064850,288 +0.064732,288 +0.065307,288 +0.065324,288 +0.064693,288 +0.065179,288 +0.065310,288 +0.064844,288 +0.065290,288 +0.064943,288 +0.065224,288 +0.065342,288 +0.064823,288 +0.065187,288 +0.063950,288 +0.063716,288 +0.064065,288 +0.064224,288 +0.063697,288 +0.064055,288 +0.063800,288 +0.063614,288 +0.064130,288 +0.063993,288 +0.063986,288 +0.064079,288 +0.063585,288 +0.064072,288 +0.065238,288 +0.065154,288 +0.065189,288 +0.065756,288 +0.064803,288 +0.065795,288 +0.065136,288 +0.064741,288 +0.065112,288 +0.064663,288 +0.065022,288 +0.065250,288 +0.064910,288 +0.065307,288 +0.065144,288 +0.064645,288 +0.065135,288 +0.065097,288 +0.064721,288 +0.065196,288 +0.065120,288 +0.064938,288 +0.065088,288 +0.064598,288 +0.065139,288 +0.065346,288 +0.064673,288 +0.065012,288 +0.065111,288 +0.064899,288 +0.064962,288 +0.065290,288 +0.064877,288 +0.065087,288 +0.065402,288 +0.064656,288 +0.065058,288 +0.064950,288 +0.064708,288 +0.064946,288 +0.064646,288 +0.064967,288 +0.065059,288 +0.064819,288 +0.064989,288 +0.065037,288 +0.064656,288 +0.065418,288 +0.065141,288 +0.065037,288 +0.064033,288 +0.063644,288 +0.063892,288 +0.063866,288 +0.064388,288 +0.065006,288 +0.065188,288 +0.064741,288 +0.066894,290 +0.066439,290 +0.065936,290 +0.066189,290 +0.066283,290 +0.065873,290 +0.066252,290 +0.066334,290 +0.066409,290 +0.066338,290 +0.066291,290 +0.065812,290 +0.066247,290 +0.066345,290 +0.065786,290 +0.066483,290 +0.066503,290 +0.066027,290 +0.065965,290 +0.066054,290 +0.066133,290 +0.066230,290 +0.065766,290 +0.066377,290 +0.066257,290 +0.065813,290 +0.066228,290 +0.066223,290 +0.065864,290 +0.066141,290 +0.066147,290 +0.065878,290 +0.066227,290 +0.066032,290 +0.065745,290 +0.066243,290 +0.066123,290 +0.066314,290 +0.066257,290 +0.066300,290 +0.065877,290 +0.066223,290 +0.066203,290 +0.066044,290 +0.066232,290 +0.066328,290 +0.065944,290 +0.066421,290 +0.066077,290 +0.066266,290 +0.066172,290 +0.066210,290 +0.065911,290 +0.066374,290 +0.065973,290 +0.066060,290 +0.066242,290 +0.065823,290 +0.066221,290 +0.066933,290 +0.065836,290 +0.066934,290 +0.066470,290 +0.065773,290 +0.066684,290 +0.066227,290 +0.065889,290 +0.066280,290 +0.066238,290 +0.065969,290 +0.066354,290 +0.066274,290 +0.065947,290 +0.066260,290 +0.066301,290 +0.065937,290 +0.066530,290 +0.066418,290 +0.066328,290 +0.066159,290 +0.066282,290 +0.065979,290 +0.066425,290 +0.066258,290 +0.066737,290 +0.066388,290 +0.066281,290 +0.065948,290 +0.066293,290 +0.066228,290 +0.066327,290 +0.066376,290 +0.066135,290 +0.066085,290 +0.066672,290 +0.066038,290 +0.066262,290 +0.066243,290 +0.065868,290 +0.067703,290 +0.068319,292 +0.065282,292 +0.066127,292 +0.066207,292 +0.065202,292 +0.065459,292 +0.065341,292 +0.065483,292 +0.065563,292 +0.065269,292 +0.065137,292 +0.065553,292 +0.066180,292 +0.065189,292 +0.065532,292 +0.065671,292 +0.065080,292 +0.065441,292 +0.065277,292 +0.066142,292 +0.065382,292 +0.065143,292 +0.065610,292 +0.065445,292 +0.064946,292 +0.065470,292 +0.065479,292 +0.065502,292 +0.065399,292 +0.065523,292 +0.065342,292 +0.065557,292 +0.065380,292 +0.065116,292 +0.065437,292 +0.065276,292 +0.065088,292 +0.065440,292 +0.065563,292 +0.065113,292 +0.065422,292 +0.067850,292 +0.065228,292 +0.065730,292 +0.065117,292 +0.065829,292 +0.065496,292 +0.065036,292 +0.065513,292 +0.065588,292 +0.065061,292 +0.065361,292 +0.065541,292 +0.065403,292 +0.065816,292 +0.065784,292 +0.065190,292 +0.065547,292 +0.065565,292 +0.065511,292 +0.066175,292 +0.065516,292 +0.065099,292 +0.065469,292 +0.065223,292 +0.065155,292 +0.065435,292 +0.065118,292 +0.065490,292 +0.065777,292 +0.064977,292 +0.065431,292 +0.065489,292 +0.065406,292 +0.065351,292 +0.065495,292 +0.067420,292 +0.065514,292 +0.065273,292 +0.065096,292 +0.065467,292 +0.065280,292 +0.065053,292 +0.065718,292 +0.065420,292 +0.065287,292 +0.065960,292 +0.065394,292 +0.065229,292 +0.066330,292 +0.065249,292 +0.065580,292 +0.065533,292 +0.065008,292 +0.065597,292 +0.065550,292 +0.065213,292 +0.065404,292 +0.065527,292 +0.065221,292 +0.070272,294 +0.069894,294 +0.069447,294 +0.069989,294 +0.070190,294 +0.069640,294 +0.069925,294 +0.069958,294 +0.069810,294 +0.069592,294 +0.070002,294 +0.069833,294 +0.069407,294 +0.070111,294 +0.070008,294 +0.069346,294 +0.069899,294 +0.070334,294 +0.074104,294 +0.069582,294 +0.073152,294 +0.072409,294 +0.069674,294 +0.073156,294 +0.072663,294 +0.072446,294 +0.069788,294 +0.072631,294 +0.073153,294 +0.069503,294 +0.072394,294 +0.072529,294 +0.072809,294 +0.069747,294 +0.073212,294 +0.072429,294 +0.069558,294 +0.072261,294 +0.072765,294 +0.072226,294 +0.069624,294 +0.073477,294 +0.072357,294 +0.069487,294 +0.072482,294 +0.072561,294 +0.072795,294 +0.069543,294 +0.073329,294 +0.072326,294 +0.069506,294 +0.072625,294 +0.072249,294 +0.072306,294 +0.069604,294 +0.072639,294 +0.072928,294 +0.069496,294 +0.072464,294 +0.072455,294 +0.104865,294 +0.123952,294 +0.086093,294 +0.070427,294 +0.070317,294 +0.071085,294 +0.070397,294 +0.070592,294 +0.070531,294 +0.070553,294 +0.070144,294 +0.070019,294 +0.070232,294 +0.070128,294 +0.069989,294 +0.070661,294 +0.070622,294 +0.070228,294 +0.070136,294 +0.070735,294 +0.071010,294 +0.070106,294 +0.072252,294 +0.070903,294 +0.070173,294 +0.071147,294 +0.070767,294 +0.070937,294 +0.070518,294 +0.071030,294 +0.070945,294 +0.070058,294 +0.070628,294 +0.070684,294 +0.070469,294 +0.070892,294 +0.070566,294 +0.070380,294 +0.069266,294 +0.070158,294 +0.066924,296 +0.065989,296 +0.066792,296 +0.071059,296 +0.066570,296 +0.066726,296 +0.066726,296 +0.065890,296 +0.066737,296 +0.066712,296 +0.065697,296 +0.067572,296 +0.066782,296 +0.065651,296 +0.066919,296 +0.066653,296 +0.065605,296 +0.066935,296 +0.069359,296 +0.065816,296 +0.066748,296 +0.069562,296 +0.065701,296 +0.066538,296 +0.066545,296 +0.065713,296 +0.066771,296 +0.066588,296 +0.065797,296 +0.066558,296 +0.066710,296 +0.065667,296 +0.066725,296 +0.067926,296 +0.066058,296 +0.067089,296 +0.066650,296 +0.066134,296 +0.067048,296 +0.066233,296 +0.066122,296 +0.066731,296 +0.065608,296 +0.066676,296 +0.066550,296 +0.065618,296 +0.066656,296 +0.066657,296 +0.065731,296 +0.067849,296 +0.066753,296 +0.065648,296 +0.066515,296 +0.066662,296 +0.065703,296 +0.066702,296 +0.066753,296 +0.065804,296 +0.066577,296 +0.066754,296 +0.065707,296 +0.066704,296 +0.066666,296 +0.065873,296 +0.068169,296 +0.066783,296 +0.065783,296 +0.066619,296 +0.066828,296 +0.065808,296 +0.066684,296 +0.066990,296 +0.065875,296 +0.066807,296 +0.065919,296 +0.065617,296 +0.065887,296 +0.065956,296 +0.066141,296 +0.065855,296 +0.065801,296 +0.065621,296 +0.066005,296 +0.067027,296 +0.065780,296 +0.065900,296 +0.065676,296 +0.065972,296 +0.066076,296 +0.065811,296 +0.065789,296 +0.078423,296 +0.070391,296 +0.088537,296 +0.083934,296 +0.074624,296 +0.074875,296 +0.074878,296 +0.072253,296 +0.072570,296 +0.081909,298 +0.079450,298 +0.073185,298 +0.072747,298 +0.072461,298 +0.072164,298 +0.072826,298 +0.072595,298 +0.072652,298 +0.072581,298 +0.072825,298 +0.078690,298 +0.080412,298 +0.079329,298 +0.080308,298 +0.079911,298 +0.077494,298 +0.073448,298 +0.077835,298 +0.073131,298 +0.081008,298 +0.079288,298 +0.080261,298 +0.076548,298 +0.075494,298 +0.079484,298 +0.082832,298 +0.078936,298 +0.079092,298 +0.078865,298 +0.075786,298 +0.079212,298 +0.077011,298 +0.074678,298 +0.074451,298 +0.072372,298 +0.073247,298 +0.072424,298 +0.074625,298 +0.074462,298 +0.076295,298 +0.073360,298 +0.072790,298 +0.073887,298 +0.074409,298 +0.073295,298 +0.072906,298 +0.073051,298 +0.072361,298 +0.072727,298 +0.072425,298 +0.073496,298 +0.072491,298 +0.072717,298 +0.072248,298 +0.073342,298 +0.072399,298 +0.072332,298 +0.072550,298 +0.072592,298 +0.072652,298 +0.073236,298 +0.076327,298 +0.074498,298 +0.073960,298 +0.072665,298 +0.072811,298 +0.073851,298 +0.078967,298 +0.077097,298 +0.076110,298 +0.075197,298 +0.075843,298 +0.075148,298 +0.076042,298 +0.074501,298 +0.075122,298 +0.073719,298 +0.074472,298 +0.074512,298 +0.073973,298 +0.074826,298 +0.073913,298 +0.073266,298 +0.072438,298 +0.073866,298 +0.073519,298 +0.074649,298 +0.072506,298 +0.073378,298 +0.073498,298 +0.072656,298 +0.073167,298 +0.074034,298 +0.073469,298 +0.072580,298 +0.073423,298 +0.073679,298 +0.078404,298 +0.079920,298 diff --git a/buch/papers/multiplikation/code/meas/winograd.txt b/buch/papers/multiplikation/code/meas/winograd.txt new file mode 100644 index 0000000..3a4d88b --- /dev/null +++ b/buch/papers/multiplikation/code/meas/winograd.txt @@ -0,0 +1,11 @@ +0.000000,2 +0.000001,4 +0.000002,8 +0.000011,16 +0.000091,32 +0.000663,64 +0.005182,128 +0.046038,256 +0.533429,512 +4.257458,1024 +130.378038,2048 diff --git a/buch/papers/multiplikation/code/meas_1024.pdf b/buch/papers/multiplikation/code/meas_1024.pdf Binary files differnew file mode 100644 index 0000000..fd0a108 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_1024.pdf diff --git a/buch/papers/multiplikation/code/meas_1024.txt b/buch/papers/multiplikation/code/meas_1024.txt new file mode 100644 index 0000000..c5ce619 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_1024.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 6.400000000000000000e+01 1.280000000000000000e+02 2.560000000000000000e+02 5.120000000000000000e+02 1.024000000000000000e+03 +1.502037048339843750e-05 6.628036499023437500e-05 4.780292510986328125e-04 2.713203430175781250e-03 2.115225791931152344e-02 1.758832931518554688e-01 1.338865518569946289e+00 1.009106445312500000e+01 8.192077994346618652e+01 7.835870332717895508e+02 +6.675720214843750000e-06 7.200241088867187500e-05 5.540847778320312500e-04 3.144979476928710938e-03 2.545046806335449219e-02 2.083067893981933594e-01 1.659256219863891602e+00 1.319160294532775879e+01 1.046767003536224365e+02 9.679818902015686035e+02 +1.668930053710937500e-05 1.628398895263671875e-04 7.648468017578125000e-04 4.426956176757812500e-03 2.922415733337402344e-02 1.800994873046875000e-01 1.286747694015502930e+00 9.412034273147583008e+00 6.263725924491882324e+01 4.427414393424987793e+02 +2.408027648925781250e-05 8.463859558105468750e-05 4.761219024658203125e-04 2.339839935302734375e-03 1.682758331298828125e-02 1.299476623535156250e-01 1.048770904541015625e+00 8.114667415618896484e+00 6.373566389083862305e+01 6.489995403289794922e+02 +1.573562622070312500e-05 7.152557373046875000e-06 7.152557373046875000e-06 2.074241638183593750e-05 5.388259887695312500e-05 6.365776062011718750e-05 3.257751464843750000e-03 1.396179199218750000e-03 3.274917602539062500e-03 2.186250686645507812e-02 diff --git a/buch/papers/multiplikation/code/meas_128.pdf b/buch/papers/multiplikation/code/meas_128.pdf Binary files differnew file mode 100644 index 0000000..ed1ec63 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_128.pdf diff --git a/buch/papers/multiplikation/code/meas_128.txt b/buch/papers/multiplikation/code/meas_128.txt new file mode 100644 index 0000000..976bbdf --- /dev/null +++ b/buch/papers/multiplikation/code/meas_128.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 6.400000000000000000e+01 1.280000000000000000e+02 +1.978874206542968750e-05 1.134872436523437500e-04 4.298686981201171875e-04 2.815246582031250000e-03 2.616596221923828125e-02 1.767718791961669922e-01 1.293319463729858398e+00 +6.675720214843750000e-06 1.251697540283203125e-04 4.818439483642578125e-04 3.490447998046875000e-03 2.465796470642089844e-02 2.014584541320800781e-01 1.630620479583740234e+00 +2.408027648925781250e-05 2.126693725585937500e-04 1.172780990600585938e-03 4.364490509033203125e-03 3.148293495178222656e-02 2.010228633880615234e-01 1.429297924041748047e+00 +2.932548522949218750e-05 1.466274261474609375e-04 4.270076751708984375e-04 2.837419509887695312e-03 1.723575592041015625e-02 1.308519840240478516e-01 1.015527009963989258e+00 +3.337860107421875000e-05 1.096725463867187500e-05 9.536743164062500000e-06 3.600120544433593750e-05 2.837181091308593750e-05 5.912780761718750000e-05 1.981019973754882812e-03 diff --git a/buch/papers/multiplikation/code/meas_16.pdf b/buch/papers/multiplikation/code/meas_16.pdf Binary files differnew file mode 100644 index 0000000..c2c3834 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_16.pdf diff --git a/buch/papers/multiplikation/code/meas_16.txt b/buch/papers/multiplikation/code/meas_16.txt new file mode 100644 index 0000000..69f85bd --- /dev/null +++ b/buch/papers/multiplikation/code/meas_16.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 +1.549720764160156250e-05 6.914138793945312500e-05 5.259513854980468750e-04 2.841711044311523438e-03 +6.914138793945312500e-06 7.557868957519531250e-05 4.496574401855468750e-04 3.437519073486328125e-03 +1.883506774902343750e-05 1.499652862548828125e-04 8.952617645263671875e-04 4.348516464233398438e-03 +2.694129943847656250e-05 1.082420349121093750e-04 4.131793975830078125e-04 2.580165863037109375e-03 +1.621246337890625000e-05 1.120567321777343750e-05 9.298324584960937500e-06 1.239776611328125000e-05 diff --git a/buch/papers/multiplikation/code/meas_256.pdf b/buch/papers/multiplikation/code/meas_256.pdf Binary files differnew file mode 100644 index 0000000..5f049dc --- /dev/null +++ b/buch/papers/multiplikation/code/meas_256.pdf diff --git a/buch/papers/multiplikation/code/meas_256.txt b/buch/papers/multiplikation/code/meas_256.txt new file mode 100644 index 0000000..15035c6 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_256.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 6.400000000000000000e+01 1.280000000000000000e+02 2.560000000000000000e+02 +1.049041748046875000e-05 5.340576171875000000e-05 5.936622619628906250e-04 2.707719802856445312e-03 2.246093750000000000e-02 1.631326675415039062e-01 1.335460901260375977e+00 1.052024245262145996e+01 +4.768371582031250000e-06 5.531311035156250000e-05 8.208751678466796875e-04 3.099203109741210938e-03 2.490711212158203125e-02 2.070860862731933594e-01 1.739669799804687500e+00 1.384817218780517578e+01 +1.478195190429687500e-05 1.132488250732421875e-04 5.970001220703125000e-04 3.906726837158203125e-03 3.041696548461914062e-02 2.000186443328857422e-01 1.392681598663330078e+00 9.388872385025024414e+00 +1.716613769531250000e-05 6.866455078125000000e-05 5.314350128173828125e-04 2.688407897949218750e-03 1.695108413696289062e-02 1.297233104705810547e-01 1.087257385253906250e+00 8.699601650238037109e+00 +2.336502075195312500e-05 4.529953002929687500e-06 8.106231689453125000e-06 4.291534423828125000e-05 6.008148193359375000e-05 8.988380432128906250e-05 1.647472381591796875e-04 4.460811614990234375e-04 diff --git a/buch/papers/multiplikation/code/meas_32.pdf b/buch/papers/multiplikation/code/meas_32.pdf Binary files differnew file mode 100644 index 0000000..94c3731 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_32.pdf diff --git a/buch/papers/multiplikation/code/meas_32.txt b/buch/papers/multiplikation/code/meas_32.txt new file mode 100644 index 0000000..afdb6d5 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_32.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 +1.215934753417968750e-05 5.459785461425781250e-05 3.700256347656250000e-04 3.249406814575195312e-03 1.996850967407226562e-02 +4.529953002929687500e-06 5.650520324707031250e-05 4.577636718750000000e-04 4.029273986816406250e-03 2.444481849670410156e-02 +1.311302185058593750e-05 1.165866851806640625e-04 6.275177001953125000e-04 4.323244094848632812e-03 2.624726295471191406e-02 +1.835823059082031250e-05 6.890296936035156250e-05 3.914833068847656250e-04 2.423048019409179688e-03 1.761770248413085938e-02 +1.263618469238281250e-05 5.006790161132812500e-06 5.960464477539062500e-06 1.144409179687500000e-05 3.600120544433593750e-05 diff --git a/buch/papers/multiplikation/code/meas_512.pdf b/buch/papers/multiplikation/code/meas_512.pdf Binary files differnew file mode 100644 index 0000000..4d8f04b --- /dev/null +++ b/buch/papers/multiplikation/code/meas_512.pdf diff --git a/buch/papers/multiplikation/code/meas_512.txt b/buch/papers/multiplikation/code/meas_512.txt new file mode 100644 index 0000000..1b2089d --- /dev/null +++ b/buch/papers/multiplikation/code/meas_512.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 6.400000000000000000e+01 1.280000000000000000e+02 2.560000000000000000e+02 5.120000000000000000e+02 +1.358985900878906250e-05 5.817413330078125000e-05 4.582405090332031250e-04 3.082036972045898438e-03 2.020335197448730469e-02 1.636352539062500000e-01 1.280331134796142578e+00 1.093638324737548828e+01 8.666778349876403809e+01 +6.198883056640625000e-06 6.270408630371093750e-05 4.820823669433593750e-04 3.279924392700195312e-03 2.462601661682128906e-02 2.034928798675537109e-01 1.630282878875732422e+00 1.372955965995788574e+01 1.104150602817535400e+02 +1.621246337890625000e-05 1.292228698730468750e-04 6.661415100097656250e-04 4.615545272827148438e-03 2.836179733276367188e-02 1.843333244323730469e-01 1.310264825820922852e+00 9.937873125076293945e+00 6.667592120170593262e+01 +2.217292785644531250e-05 7.486343383789062500e-05 4.060268402099609375e-04 2.455949783325195312e-03 1.685857772827148438e-02 1.299629211425781250e-01 1.173750638961791992e+00 8.648802757263183594e+00 6.876212453842163086e+01 +2.431869506835937500e-05 5.006790161132812500e-06 6.914138793945312500e-06 8.106231689453125000e-06 2.717971801757812500e-05 6.461143493652343750e-05 1.480579376220703125e-04 5.280971527099609375e-04 3.390312194824218750e-03 diff --git a/buch/papers/multiplikation/code/meas_64.pdf b/buch/papers/multiplikation/code/meas_64.pdf Binary files differnew file mode 100644 index 0000000..3a90949 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_64.pdf diff --git a/buch/papers/multiplikation/code/meas_64.txt b/buch/papers/multiplikation/code/meas_64.txt new file mode 100644 index 0000000..ae6ff9b --- /dev/null +++ b/buch/papers/multiplikation/code/meas_64.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 6.400000000000000000e+01 +1.645088195800781250e-05 7.295608520507812500e-05 3.807544708251953125e-04 2.672195434570312500e-03 2.010774612426757812e-02 1.662156581878662109e-01 +7.390975952148437500e-06 7.843971252441406250e-05 4.265308380126953125e-04 3.107070922851562500e-03 2.457642555236816406e-02 2.122807502746582031e-01 +1.931190490722656250e-05 1.568794250488281250e-04 7.593631744384765625e-04 3.937005996704101562e-03 3.596329689025878906e-02 2.131938934326171875e-01 +2.622604370117187500e-05 9.226799011230468750e-05 3.504753112792968750e-04 2.469539642333984375e-03 1.652932167053222656e-02 1.281068325042724609e-01 +1.788139343261718750e-05 7.152557373046875000e-06 6.914138793945312500e-06 1.120567321777343750e-05 2.884864807128906250e-05 6.914138793945312500e-05 diff --git a/buch/papers/multiplikation/code/meas_8.pdf b/buch/papers/multiplikation/code/meas_8.pdf Binary files differnew file mode 100644 index 0000000..16d177d --- /dev/null +++ b/buch/papers/multiplikation/code/meas_8.pdf diff --git a/buch/papers/multiplikation/code/meas_8.txt b/buch/papers/multiplikation/code/meas_8.txt new file mode 100644 index 0000000..6cf6515 --- /dev/null +++ b/buch/papers/multiplikation/code/meas_8.txt @@ -0,0 +1,6 @@ +2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 +1.144409179687500000e-05 5.412101745605468750e-05 3.845691680908203125e-04 +4.768371582031250000e-06 5.698204040527343750e-05 5.209445953369140625e-04 +1.382827758789062500e-05 1.180171966552734375e-04 6.978511810302734375e-04 +1.859664916992187500e-05 7.033348083496093750e-05 3.886222839355468750e-04 +1.525878906250000000e-05 4.529953002929687500e-06 7.390975952148437500e-06 diff --git a/buch/papers/multiplikation/code/test.tex b/buch/papers/multiplikation/code/test.tex new file mode 100644 index 0000000..40ea239 --- /dev/null +++ b/buch/papers/multiplikation/code/test.tex @@ -0,0 +1,92 @@ +% This file was created by tikzplotlib v0.9.8. +\begin{tikzpicture} + +\definecolor{color0}{rgb}{0.886274509803922,0.290196078431373,0.2} +\definecolor{color1}{rgb}{0.203921568627451,0.541176470588235,0.741176470588235} +\definecolor{color2}{rgb}{0.596078431372549,0.556862745098039,0.835294117647059} +\definecolor{color3}{rgb}{0.984313725490196,0.756862745098039,0.368627450980392} + +\begin{axis}[ +axis background/.style={fill=white!89.8039215686275!black}, +axis line style={white}, +legend cell align={left}, +legend style={ + fill opacity=0.8, + draw opacity=1, + text opacity=1, + at={(0.03,0.97)}, + anchor=north west, + draw=white!80!black, + fill=white!89.8039215686275!black +}, +tick align=outside, +tick pos=left, +x grid style={white}, +xlabel={n}, +xmajorgrids, +xmin=-4.3, xmax=134.3, +xtick style={color=white!33.3333333333333!black}, +y grid style={white}, +ylabel={time (s)}, +ymajorgrids, +ymin=-0.0834965705871582, ymax=1.75356960296631, +ytick style={color=white!33.3333333333333!black} +] +\addplot [line width=2pt, color0] +table {% +2 1.57356262207031e-05 +4 5.96046447753906e-05 +8 0.000428915023803711 +16 0.00276041030883789 +32 0.0217020511627197 +64 0.160412073135376 +128 1.3419406414032 +}; +\addlegendentry{Standard MM} +\addplot [line width=2pt, color1] +table {% +2 6.43730163574219e-06 +4 6.69956207275391e-05 +8 0.00048065185546875 +16 0.00336766242980957 +32 0.0257236957550049 +64 0.231612205505371 +128 1.67006659507751 +}; +\addlegendentry{Divide and conquer MM} +\addplot [line width=2pt, color2] +table {% +2 2.90870666503906e-05 +4 0.000133275985717773 +8 0.000703096389770508 +16 0.00453472137451172 +32 0.0282893180847168 +64 0.181003332138062 +128 1.40816903114319 +}; +\addlegendentry{Strassen MM} +\addplot [line width=2pt, white!46.6666666666667!black] +table {% +2 2.19345092773438e-05 +4 9.01222229003906e-05 +8 0.000406503677368164 +16 0.00258469581604004 +32 0.0171687602996826 +64 0.126588344573975 +128 1.02698183059692 +}; +\addlegendentry{Winograd MM} +\addplot [line width=2pt, color3] +table {% +2 1.45435333251953e-05 +4 1.1444091796875e-05 +8 7.39097595214844e-06 +16 1.28746032714844e-05 +32 2.83718109130859e-05 +64 0.000111103057861328 +128 0.000159025192260742 +}; +\addlegendentry{np MM} +\end{axis} + +\end{tikzpicture} diff --git a/buch/papers/multiplikation/einlteung.tex b/buch/papers/multiplikation/einlteung.tex new file mode 100755 index 0000000..bc4bfcf --- /dev/null +++ b/buch/papers/multiplikation/einlteung.tex @@ -0,0 +1,52 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Einleitung \label{multiplikation:section:einleitung}} +\rhead{Einleitung} + +Die Multiplikation zweier Matrizen ist eine wichtige Operation die in verschiedensten Teilen der Mathematik Anwendung findet. +Die Beschreibung der Multiplikation aus der Definition 2.10 (\textcolor{blue} {Kein Hyperlink zu einer Definition?)}: + +Eine $m\times n$-Matrix $\mathbf{A}\in M_{m\times n}(\Bbbk)$ und eine +$n\times p$-Matrix $\mathbf{B}\in M_{n\times l}(\Bbbk)$ haben als Produkt +eine $n\times l$-Matrix $\mathbf{C}=\mathbf{AB}\in M_{n\times l}(\Bbbk)$ mit den +Koeffizienten +\begin{equation} +c_{ij} = \sum_{k=1}^n a_{ik} b_{kj}. +\label{multiplikation:eq:MM} +\end{equation} +Grafisch kann die Matrizenmultiplikation $AB=C$ wie in \ref{multiplikation:fig:mm_viz} visualisiert werden. +\begin{figure} + \center + \includegraphics[]{papers/multiplikation/images/mm_visualisation} + \caption{Matrizen Multiplikation} + \label{multiplikation:fig:mm_viz} +\end{figure} +Im Fall einer Matrizengr\"osse von $2\times 2$ +\begin{equation} + \begin{bmatrix} +A_{11} & A_{12}\\ +A_{21} & A_{22} +\end{bmatrix} +\begin{bmatrix} +B_{11} & B_{12}\\ +B_{21} & B_{22} +\end{bmatrix} += +\begin{bmatrix} +C_{11} & C_{12}\\ +C_{21} & C_{22} +\end{bmatrix} +\end{equation} +kann die Gleichung der einzelnen Terme +\begin{equation} \label{multiplikation:eq:MM_exp} +\begin{split} +C_{11} &= A_{11} \cdot B_{11} + A_{12} \cdot B_{21}\\ +C_{12} &= A_{11} \cdot B_{12} + A_{12} \cdot B_{22}\\ +C_{21} &= A_{21} \cdot B_{11} + A_{22} \cdot B_{21}\\ +C_{22} &= A_{21} \cdot B_{12} + A_{22} \cdot B_{22} +\end{split} +\end{equation} +explizit geschrieben werden. diff --git a/buch/papers/multiplikation/images/bigo.pdf b/buch/papers/multiplikation/images/bigo.pdf Binary files differnew file mode 100644 index 0000000..dfa2ba4 --- /dev/null +++ b/buch/papers/multiplikation/images/bigo.pdf diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex new file mode 100644 index 0000000..e3293e4 --- /dev/null +++ b/buch/papers/multiplikation/images/bigo.tex @@ -0,0 +1,107 @@ +\documentclass[border=10pt,varwidth]{standalone} +\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{times} +\usepackage{geometry} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathrsfs} +\usepackage{amsfonts} +\usepackage{amsthm} +\usepackage{lipsum} +\usepackage{amscd} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{textcomp} +\usepackage{pgfplots} +\usepackage{txfonts} +\usepackage[all]{xy} +\usepackage{paralist} +\usepackage[colorlinks=true]{hyperref} +\usepackage{array} +\usepackage{tikz} +\usepackage{slashed} +\usepackage{pdfpages} +\usepackage{cite} +\usepackage{url} +\usepackage{amsmath,amsfonts,amssymb} +\usepackage{tikz} +\usetikzlibrary{arrows,matrix,positioning} +\usetikzlibrary{overlay-beamer-styles} +\usetikzlibrary{matrix.skeleton} +\usetikzlibrary{automata,positioning} +\usetikzlibrary{decorations.text} +\usepackage{listings} +\usepackage{multirow} +\usepackage{color} + +\begin{document} + +\begin{tikzpicture} +\begin{axis}[ + axis lines = left, + xlabel = $n$ (Data Input), + ylabel = {$t$ (time)}, + legend pos=north east, + very thick, + ymax = 500, + yticklabels=\empty, + xticklabels=\empty, + scale only axis=true, + width=12cm, height=6cm, + ] +\addplot [ + domain= 1:20, + samples=100, + color=red, +] +{1}; +\addlegendentry{$\mathcal{O}(1)$} +\addplot [ + domain= 1:20, + samples=100, + color=green, +] +{x}; +\addlegendentry{$\mathcal{O}(n)$} +\addplot [ + domain= 1:20, + samples=100, + color=blue, +] +{x^2}; +\addlegendentry{$\mathcal{O}(n^2)$} +\addplot [ + domain= 1:10, + samples=100, + color=purple, +] +{x^3}; +\addlegendentry{$\mathcal{O}(n^3)$} +\addplot [ + domain= 1:10, + samples=100, + color=black, +] +{exp(x)}; +\addlegendentry{$\mathcal{O}(e^n)$} +\addplot [ + domain= 1:20, + samples=100, + color=orange, +] +{log2(x)}; +\addlegendentry{$\mathcal{O}(\log n)$} + +\addplot [ + domain= 1:20, + samples=100, + color=gray, +] +{x*log2(x)}; +\addlegendentry{$\mathcal{O}(n \log n)$} +\end{axis} +\end{tikzpicture} + +\end{document} diff --git a/buch/papers/multiplikation/images/mm_visualisation.pdf b/buch/papers/multiplikation/images/mm_visualisation.pdf Binary files differnew file mode 100644 index 0000000..9309df1 --- /dev/null +++ b/buch/papers/multiplikation/images/mm_visualisation.pdf diff --git a/buch/papers/multiplikation/images/mm_visualisation.tex b/buch/papers/multiplikation/images/mm_visualisation.tex new file mode 100644 index 0000000..6e8f789 --- /dev/null +++ b/buch/papers/multiplikation/images/mm_visualisation.tex @@ -0,0 +1,45 @@ + + \begin{tikzpicture}[ampersand replacement=\&] + + \matrix (A)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] at (0,0) + { + A_{1,1} \& \cdots \& A_{1,k} \& \cdots \& A_{1,n} \\ + \vdots \& \& \vdots \& \& \vdots \\ + A_{i,1} \& \cdots \& A_{i,k} \& \cdots \& A_{i,n} \\ + \vdots \& \& \vdots \& \& \vdots \\ + A_{m,1} \& \cdots \& A_{m,k} \& \cdots \& A_{m,n} \\ + }; + + \node [right=0.1 of A] (mul) {$\cdot$}; + + + \matrix (B)[right=0.1 of mul, matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] + { + B_{1,1} \& \cdots \& B_{1,j} \& \cdots \& B_{1,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + B_{k,1} \& \cdots \& B_{k,j} \& \cdots \& B_{k,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + B_{n,1} \& \cdots \& B_{n,j} \& \cdots \& B_{n,p} \\ + }; + + \node [right=0.1 of B] (eq) {$=$}; + + \matrix (C)[right=0.1 of eq, matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] + { + C_{1,1} \& \cdots \& C_{1,j} \& \cdots \& C_{1,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + C_{i,1} \& \cdots \& C_{i,j} \& \cdots \& C_{i,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + C_{m,1} \& \cdots \& C_{m,j} \& \cdots \& C_{m,p} \\ + }; + + + \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=green, fit=(A-3-1)(A-3-5)] {}; + \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=blue, fit=(B-1-3)(B-5-3)] {}; + \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=red, fit=(C-3-3)] {}; + + + \end{tikzpicture} + +\end{document} + diff --git a/buch/papers/multiplikation/images/strassen.pdf b/buch/papers/multiplikation/images/strassen.pdf Binary files differnew file mode 100644 index 0000000..9899dcb --- /dev/null +++ b/buch/papers/multiplikation/images/strassen.pdf diff --git a/buch/papers/multiplikation/images/strassen.tex b/buch/papers/multiplikation/images/strassen.tex new file mode 100644 index 0000000..797772b --- /dev/null +++ b/buch/papers/multiplikation/images/strassen.tex @@ -0,0 +1,140 @@ +\documentclass[border=10pt]{standalone} +\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{times} +\usepackage{geometry} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathrsfs} +\usepackage{amsfonts} +\usepackage{amsthm} +\usepackage{lipsum} +\usepackage{amscd} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{textcomp} +\usepackage{pgfplots} +\usepackage{txfonts} +\usepackage[all]{xy} +\usepackage{paralist} +\usepackage[colorlinks=true]{hyperref} +\usepackage{array} +\usepackage{tikz} +\usepackage{slashed} +\usepackage{pdfpages} +\usepackage{cite} +\usepackage{url} +\usepackage{amsmath,amsfonts,amssymb} +\usepackage{tikz} +\usetikzlibrary{arrows,matrix,positioning} +\usetikzlibrary{overlay-beamer-styles} +\usetikzlibrary{matrix.skeleton} +\usetikzlibrary{automata,positioning} +\usetikzlibrary{decorations.text} +\usepackage{listings} +\usepackage{multirow} +\usepackage{color} + +\begin{document} + +\begin{tikzpicture}[ampersand replacement=\&] + +\foreach \i in {1,...,4} +{ + \small{ + \matrix (X\i)[matrix of math nodes,nodes in empty cells, + nodes = {draw, minimum size=10mm, + anchor=center, + inner sep=0pt, outer sep=0pt}, + column sep=-\pgflinewidth, + row sep=-\pgflinewidth, + ] at (0,-\i*5) + { + A_{11}B_{11} \& A_{12}B_{11} \& A_{21}B_{11} \& A_{22}B_{11} \\ + A_{11}B_{21} \& A_{12}B_{21} \& A_{21}B_{21} \& A_{22}B_{21} \\ + A_{11}B_{11} \& A_{12}B_{12} \& A_{21}B_{12} \& A_{22}B_{12} \\ + A_{11}B_{22} \& A_{12}B_{22} \& A_{21}B_{22} \& A_{22}B_{22} \\ + };} + + \foreach \j in {1,...,7} + { + \matrix(M\i\j)[matrix of math nodes,nodes in empty cells, + nodes = {draw, minimum size=10mm, + anchor=center, + inner sep=0pt, outer sep=0pt}, + column sep=-\pgflinewidth, + row sep=-\pgflinewidth, + ] at (\j*5,-\i*5) + { + \& \& \& \\ + \& \& \& \\ + \& \& \& \\ + \& \& \& \\ + }; + } +} + +\huge{ + \node at (-3,-20) {$C_{22}=$}; + \node at (-3,-15) {$C_{21}=$} ; + \node at (-3,-10) {$C_{12}=$} ; + \node at (-3,-5) {$C_{11}=$} ; + + \node at (5,-2) {I}; + \node at (10,-2) {II}; + \node at (15,-2) {III}; + \node at (20,-2) {IV}; + \node at (25,-2) {V}; + \node at (30,-2) {VI}; + \node at (35,-2) {VII}; +} + + +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-1-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-2-2)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-3-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-4-2)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-1-3)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-2-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-3-3)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-4-4)] {}; + +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M14-1-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M14-2-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-2)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-2-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-4-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-2-2)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-4-2)] {}; + +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M23-3-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M23-4-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-2)] {}; + +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-3)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M34-1-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M34-2-4)] {}; + +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-4)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-3)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M43-3-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M43-4-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-1-3)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-1-1)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-3-3)] {}; +\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-3-1)] {}; +\end{tikzpicture} + +\end{document} diff --git a/buch/papers/multiplikation/loesungsmethoden.tex b/buch/papers/multiplikation/loesungsmethoden.tex new file mode 100755 index 0000000..83be814 --- /dev/null +++ b/buch/papers/multiplikation/loesungsmethoden.tex @@ -0,0 +1,309 @@ +% +% teil2.tex -- Beispiel-File für teil2 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% + +\section{L\"osungsmethoden} +\rhead{L\"osungsmethoden} + +In diesem Abschnitt werden mehrere Algorithmen zur Berechnung der Matrizenmultiplikation vorgestellt, auch werden Libraries zur automatisierten Verwendung von vordefinierten Algorithmen gezeigt. + +\subsection{Standard Algorithmus} + +Der Standard Methode kann im Algorithmus \ref{multiplikation:alg:smm} entnommen werden. +Hierf\"ur wurde die Gleichung \eqref{multiplikation:eq:MM} direkt implementiert. +Die \texttt{For i} Schleife iteriert \"uber alle Zeilen der $\mathbf{A}$ Matrix, die \texttt{For j} Schleife iteriert \"uber alle Spalten der $\mathbf{B}$ Matrix und die \texttt{For k} Schleife iteriert \"uber alle Eintr\"age dieser Zeilen bzw. Spalten. + +\begin{algorithm}\caption{Matrix Multiplication} + \label{multiplikation:alg:smm} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{MM}{$\textbf{A}, \textbf{B}$} + \State $sum \gets 0$ + \State $n \gets columns(\textbf{A}) == rows(\textbf{B})$ + \State $m \gets rows(\textbf{A})$ + \State $p \gets columns(\textbf{B})$ + \State $\textbf{C} \gets zeros(m,p)$ + \For{$i = 0,1,2 \dots,m-1$} + \For{$j = 0,1,2 \dots,p-1$} + \State $sum \gets 0$ + \For{$k = 0,1,2 \dots,n-1$} + \State $sum \gets sum + \textbf{A}[i][k] \cdot \textbf{B}[k][j]$ + \EndFor + \State $\textbf{C}[i][j] \gets sum $ + \EndFor + \EndFor + \State \textbf{return} $\textbf{C}$ + \EndFunction + \end{algorithmic} +\end{algorithm} + +Die Laufzeit dieser Struktur mit drei \texttt{For} Schleifen ist $\mathcal{O}(n^3)$ + +\subsubsection{Divide and Conquer Methode} + +F\"ur gewisse Algorithmen f\"uhren \textit{Divide and Conquer} Ans\"atze zu markant besseren Laufzeiten. +Das bekannteste Beispiel ist wohl die \textit{Fast Fourier Transform} wobei die Laufzeit von $\mathcal{O}(n^2)$ zu $\mathcal{O}(n \log n)$ verbessert werden kann. + +Die Matrizenmultiplikation kann ebenfalls mit solch einem Ansatz berechnet werden. +Zur vereinfachten Veranschaulichung kann die Situation, mit $\mathbf{A}$ und $\mathbf{B}$ der gr\"osse $2^n \times 2^n$ verwendet werden. +Die Matrizen $\mathbf{A}$ und $\mathbf{B}$ werden in jeweils vier Blockmatrizen der gr\"osse $2^{n-1} \times 2^{n-1}$ +\begin{equation} +\mathbf{A}\mathbf{B}= +\begin{bmatrix} +\mathbf{A}_{11} & \mathbf{A}_{12}\\ +\mathbf{A}_{21} & \mathbf{A}_{22} +\end{bmatrix} +\begin{bmatrix} +\mathbf{B}_{11} & \mathbf{B}_{12}\\ +\mathbf{B}_{21} & \mathbf{B}_{22} +\end{bmatrix} += +\begin{bmatrix} +\mathbf{C}_{11} & \mathbf{C}_{12}\\ +\mathbf{C}_{21} & \mathbf{C}_{22} +\end{bmatrix} +\end{equation} +aufgeteilt. +Die Berechnung +\begin{equation} +\mathbf{C}_{ij} = \sum_{k=1}^n \mathbf{A}_{ik} \mathbf{B}_{kj} +\label{multiplikation:eq:MM_block} +\end{equation} +ist identisch zu der Gleichung \eqref{multiplikation:eq:MM}, wobei hier f\"ur die Multiplikation die Matrizenmultiplikation verwendet wird. + +Der Algorithmus \ref{multiplikation:alg:devide_mm} zeigt den \textit{Divide and Conquer} Ansatz, +Der Grundstruktur dieser Methode besteht aus dem rekursiven Aufruf der Funktion mit den erzeugten Blockmatrizen. +Der rekursive Aufruf wird bis zu der Gr\"osse der Matrizen von $N = 2 \times 2$ durchgef\"uhrt. +\begin{algorithm}\caption{Divide and Conquer Matrix Multiplication} + \setlength{\lineskip}{7pt} + \label{multiplikation:alg:devide_mm} + \begin{algorithmic} + \Function{MM}{$\textbf{A}, \textbf{B}, n$} + \If{$n = 2$} + \State $ \mathbf{C} \gets zeros(n, n)$ + \State $C[0, 0] \gets A[0][0]\cdot B[0][0]+A[0][1]\cdot B[1][0]$ + \State $C[0, 1] \gets A[0][0]\cdot B[0][1]+A[0][1]\cdot B[1][1]$ + \State $C[1, 0] \gets A[1][0]\cdot B[0][0]+A[1][1]\cdot B[1][0]$ + \State $C[1, 1] \gets A[1][0]\cdot B[0][1]+A[1][1]\cdot B[1][1]$ + \Else + \State $ m \gets n/2$ + \State $\mathbf{A11}, \mathbf{A12}, \mathbf{A21}, \mathbf{A22} \gets \mathbf{A}[:m][:m], \mathbf{A}[:m][m:], \mathbf{A}[m:][:m], \mathbf{A}[m:][m:]$ + \State $\mathbf{B11}, \mathbf{B12}, \mathbf{B21}, \mathbf{B22} \gets \mathbf{B}[:m][:m], \mathbf{B}[:m][m:], \mathbf{B}[m:][:m], \mathbf{B}[m:][m:]$ + + \State $\mathbf{C11} \gets \text{MM}(\mathbf{A11}, \mathbf{B11},n) + \text{MM}(\mathbf{A12}, \mathbf{B21},n)$ + \State $\mathbf{C12} \gets \text{MM}(\mathbf{A11},\mathbf{B12},n) + \text{MM}(\mathbf{A12}, \mathbf{B22},n)$ + \State $\mathbf{C21} \gets \text{MM}(\mathbf{A21}, \mathbf{B11},n) + \text{MM}(\mathbf{A22}, \mathbf{B21},n)$ + \State $\mathbf{C22} \gets \text{MM}(\mathbf{A21}, \mathbf{B12},n) + \text{MM}(\mathbf{A22}, \mathbf{B22},n)$ + \State $ C \gets vstack(hstack(C11, C12), hstack(C21, C22))$ + + \EndIf + \State \textbf{return} $\textbf{C}$ + + \EndFunction + \end{algorithmic} +\end{algorithm} + +Die Laufzeit dieser rekursiven Funktion kann mit dem \textit{Master Theorem} berechnet werden. +Ohne auf diesen vertieft einzugehen, bestimmt die Anzahl rekursiver Aufrufe der Funktion die Laufzeit. +In diesem Fall wird die Funktion pro Durchlauf acht mal rekursiv aufgerufen, dies f\"uhrt +\begin{equation} \label{multiplikation:eq:laufzeitdac} + \mathcal{T}(n) = + \begin{cases} + 1 & \text{if } n \leq 2\\ + 8 \cdot \mathcal{T}(\frac{n}{2}) + n^2 & \text{if } n > 2 + \end{cases} = \mathcal{O}(n^{\log_2 8}) = \mathcal{O}(n^{3}) +\end{equation} +zu einer kubischen Laufzeit. +Die Addition zweier Matrizen $\mathbf{A} + \mathbf{B} = \mathbf{C}$ hat eine Laufzeit von $\mathcal{O}(n^{2})$ und kann neben dem dominierendem Anteil von $\mathcal{O}(n^{3})$ ignoriert werden. +In diesem Fall hat der \textit{Divide and Conquer} Ansatz zu keiner Verbesserung gef\"uhrt. + + +\subsection{Strassen's Algorithmus} + +Strassen's Algorithmus \cite{multiplikation:strassen_1969} beschreibt die Matrizenmultiplikation mit einer Vielzahl von Additionen, Subtraktionen und Multiplikationen. +Die Grundlegenden Terme +\begin{equation} \label{multiplikation:eq:strassen} +\begin{split} +\text{\textbf{P}} &= (\mathbf{A}_{11} + \mathbf{A}_{22}) \cdot (\mathbf{B}_{11} + \mathbf{B}_{22}) \\ +\text{\textbf{Q}} &= (\mathbf{A}_{21} + \mathbf{A}_{22}) \cdot \mathbf{B}_{11} \\ +\text{\textbf{R}} &= \mathbf{A}_{11} \cdot (\mathbf{B}_{12}-\mathbf{B}_{22}) \\ +\text{\textbf{S}} &= \mathbf{A}_{22} \cdot (-\mathbf{B}_{11}+\mathbf{B}_{21}) \\ +\text{\textbf{T}} &= (\mathbf{A}_{11} + \mathbf{A}_{12}) \cdot \mathbf{B}_{22} \\ +\text{\textbf{U}} &= (-\mathbf{A}_{11} + \mathbf{A}_{21}) \cdot (\mathbf{B}_{11} + \mathbf{B}_{12}) \\ +\text{\textbf{V}} &= (\mathbf{A}_{12} - \mathbf{A}_{22}) \cdot (\mathbf{B}_{21} + \mathbf{B}_{22}) +\end{split} +\end{equation} +aus $\mathbf{A}$ und $\mathbf{B}$, werden f\"ur die Berechnung der Matrix $\mathbf{C}$ +\begin{equation} \label{multiplikation:eq:strassen2} +\begin{split} +\mathbf{C}_{11} &= \text{\textbf{P}} + \text{\textbf{S}} - \text{\textbf{T}} + \text{\textbf{V}} \\ +\mathbf{C}_{21} &= \text{\textbf{R}} + \text{\textbf{T}} \\ +\mathbf{C}_{12} &= \text{\textbf{Q}} + \text{\textbf{S}}\\ +\mathbf{C}_{22} &= \text{\textbf{P}} + \text{\textbf{R}} - \text{\textbf{Q}} + \text{\textbf{U}} +\end{split} +\end{equation} +gebraucht. +\begin{algorithm}\caption{Strassen Matrix Multiplication} + \label{multiplikation:alg:strassen} + \setlength{\lineskip}{7pt} + \begin{algorithmic} + \Function{strassen}{$\textbf{A}, \textbf{B}, n$} + \If{$n = 2$} + \State $ \mathbf{C} \gets zeros((n, n))$ + \State $P \gets (A[0][0]+A[1][1])\cdot( B[0][0]+B[1][1])$ + \State $Q \gets (A[1][0]+A[1][1])\cdot B[0][0]$ + \State $R \gets A[0][0]\cdot (B[0][1]-B[1][1])$ + \State $S \gets A[1][1]\cdot (B[1][0]-B[0][0])$ + \State $T \gets (A[0][0]+A[0][1])\cdot B[1][1]$ + \State $U \gets (A[1][0]-A[0][0])\cdot (B[0][0]+B[0][1])$ + \State $V \gets (A[0][1]-A[1][1])\cdot (B[1][0]+B[1][1])$ + \State $C[0][0] \gets P+S-T+V$ + \State $C[0][1] \gets R+T$ + \State $C[1][0] \gets Q+S$ + \State $C[1][1] \gets P+R-Q+U$ + \Else + \State $ m \gets n/2$ + \State $\mathbf{A11}, \mathbf{A12}, \mathbf{A21}, \mathbf{A22} \gets \mathbf{A}[:m][:m], \mathbf{A}[:m][m:], \mathbf{A}[m:][:m], \mathbf{A}[m:][m:]$ + \State $\mathbf{B11}, \mathbf{B12}, \mathbf{B21}, \mathbf{B22} \gets \mathbf{B}[:m][:m], \mathbf{B}[:m][m:], \mathbf{B}[m:][:m], \mathbf{B}[m:][m:]$ + + \State $ \mathbf{P} \gets \text{strassen}((\mathbf{A11}+ \mathbf{A22}),(\mathbf{B11}+\mathbf{B22}), m)$ + \State $ \mathbf{Q} \gets \text{strassen}((\mathbf{A21}+ \mathbf{A22}), \mathbf{B11},m)$ + \State $ \mathbf{R} \gets \text{strassen}( \mathbf{A11},(\mathbf{B12}- \mathbf{B22}),m)$ + \State $ \mathbf{S} \gets \text{strassen}( \mathbf{A22},(\mathbf{B21}- \mathbf{B11}),m)$ + \State $ \mathbf{T} \gets \text{strassen}((\mathbf{A11}+ \mathbf{A12}), \mathbf{B22},m)$ + \State $ \mathbf{U} \gets \text{strassen}((\mathbf{A21}- \mathbf{A11}),(\mathbf{B11}+\mathbf{B12}),m)$ + \State $ \mathbf{V} \gets \text{strassen}((\mathbf{A12}- \mathbf{A22}),(\mathbf{B21}+\mathbf{B22}),m)$ + + + + \State $\mathbf{C11} \gets \mathbf{P+S-T+V}$ + \State $\mathbf{C12} \gets \mathbf{R+T}$ + \State $\mathbf{C21} \gets \mathbf{Q+S}$ + \State $\mathbf{C22} \gets \mathbf{P+R-Q+U}$ + \State $ C \gets vstack(hstack(C11, C12), hstack(C21, C22))$ + + \EndIf + \State \textbf{return} $\textbf{C}$ + + \EndFunction + \end{algorithmic} +\end{algorithm} +Strassens's Methode wird in der Abbildung \ref{multiplikation:fig:strassen} grafisch dargestellt. +\begin{figure} + \center + \includegraphics[width=\linewidth]{papers/multiplikation/images/strassen.pdf} + \caption{Strassen's Algorithmus} + \label{multiplikation:fig:strassen} +\end{figure} + +Die Funktion wird sieben mal rekursiv aufgerufen. +Dies f\"uhrt zu einer Laufzeit von +\begin{equation} \label{multiplikation:eq:laufzeitstrassen} +\mathcal{T}(n) = +\begin{cases} +1 & \text{if } n \leq 2\\ +7 \cdot \mathcal{T}(\frac{n}{2}) + n^2 & \text{if } n > 2 +\end{cases} = \mathcal{O}(n^{\log_2 7}) = \mathcal{O}(n^{2.8074}) +\end{equation} +und ist somit schneller als die Standard Methode. + +\subsection{Winograd's Algorithmus} + +Ein weiterer Ansatz lieferte Shmuel Winograd im Jahre 1968 \cite{multiplikation:winograd_1968}. +Er zeigte einen neuen Algorithmus f\"ur das +\begin{equation} + \langle x,y \rangle = \sum_{i=1}^{n}x_i y_i +\end{equation} +Skalarprodukt. +F\"ur jeden Vektor berechne +\begin{equation} + \xi = \sum_{j=1}^{ \lfloor n/2 \rfloor} x_{2j-1} \cdot x_{2j} +\end{equation} +und +\begin{equation} + \eta = \sum_{j=1}^{ \lfloor n/2 \rfloor} y_{2j-1} \cdot y_{2j}. +\end{equation} +Das Skalarprodukt ist nun geben mit +\begin{equation} + \langle x,y \rangle = + \begin{cases} + \displaystyle \quad \sum_{j=1}^{ \lfloor n/2 \rfloor} (x_{2j-1} + y_{2j})(x_{2j}+y_{2j-1})-\xi - \eta & \text{if $n$ is even}\\ + \displaystyle \quad \sum_{j=1}^{ \lfloor n/2 \rfloor} (x_{2j-1} + y_{2j})(x_{2j}+y_{2j-1})-\xi - \eta + x_n y_n & \text{if $n$ is odd}. + \end{cases} +\end{equation} + +Angenommen man hat $N$ Vektoren mit welchen man $T$ Skalarprodukte berechnen m\"ochte. +Daf\"ur werden $N\lfloor n/2 \rfloor + T\lfloor (n+1)/2 \rfloor $ Multiplikationen ben\"otigt. +Eine Matrizenmultiplikation mit $\mathbf{A}$ einer $m \times n$ und $\mathbf{B}$ einer $n \times p$ Matrix, entspricht $N=m+p$ Vektoren mit welchen man $T=mp$ Skalarprodukte berechnet. +Dies f\"uhrt zu +\begin{equation} + (m+p) \left \lfloor \frac{n}{2} \right \rfloor + mp \left \lfloor \frac{n+1}{2} \right \rfloor = \frac{mn}{2} + \frac{pn}{2} + \frac{mpn}{2} + \frac{mp}{2} +\end{equation} +Multiplikationen. +Wenn $m,p,n$ gross werden, dominiert der Term $\frac{mpn}{2}$ und es werden $\frac{mpn}{2}$ Multiplikationen ben\"otigt. +Was im Vergleich zu den $mpn$ Multiplikation der Standard Methode nur die H\"alfte ist. +Die Implementation kann im Algorithmus \ref{multiplikation:alg:winograd} entnommen werden. + +\begin{algorithm}\caption{Winograd Matrix Multiplication} + \setlength{\lineskip}{7pt} + \label{multiplikation:alg:winograd} + \begin{algorithmic} + \Function{Winograd}{$\textbf{A}, \textbf{B}, n$} + \State $ m \gets rows(\mathbf{A})$ + \State $ n \gets columns(\mathbf{A}) == rows(\mathbf{B})$ + \State $ p \gets columns(\mathbf{B})$ + \State $ \mathbf{\xi} \gets zeros(m)$ + \State $ \mathbf{\eta} \gets zeros(p)$ + + + \For{$i = 0,1,2 \dots,m-1$} + \For{$j = 0,1,2 \dots,\lfloor n/2 \rfloor-1$} + \State $\xi[i] \gets \xi[i]+A[i,2 j]A[i,2 j+1]$ + \EndFor + \EndFor + + \For{$i = 0,1,2 \dots,p-1$} + \For{$j = 0,1,2 \dots,\lfloor n/2 \rfloor-1$} + \State $\eta[i] \gets \eta[i]+B[2 j,i]B[2 j+1,i]$ + \EndFor + \EndFor + + \If{$n \% 2 == 0$} + \For{$i = 0,1,2 \dots,m-1$} + \For{$j = 0,1,2 \dots,p-1$} + \State $ab \gets 0$ + \For{$k = 0,1,2 \dots,\lfloor n/2 \rfloor-1$} + \State $ab \gets ab + (A[i,2k]+B[2k+1,j])(A[i,2k+1]+B[2k,j])$ + \EndFor + \State $C[i,j] \gets ab-\eta[j]-\xi[i]$ + \EndFor + \EndFor + \Else + \For{$i = 0,1,2 \dots,n-1$} + \For{$j = 0,1,2 \dots,n-1$} + \State $ab \gets 0$ + \For{$k = 0,1,2 \dots,\lfloor n/2 \rfloor-1$} + \State $ab \gets ab + (A[i,2k]+B[2k+1,j])(A[i,2k+1]+B[2k,j])$ + \EndFor + \State $C[i,j] \gets ab-\eta[j]-\xi[i]+A[i,-1]B[-1,j]$ + \EndFor + \EndFor + \EndIf + \State \textbf{return} $\textbf{C}$ + + \EndFunction + \end{algorithmic} +\end{algorithm} + +\subsection{Weitere Algorithmen} + +\textcolor{red}{TODO: BLAS} + +\section{Implementation} +\rhead{Implementation} +\textcolor{red}{TODO: messresultate} + +\section{Fazit} +\rhead{Fazit} diff --git a/buch/papers/multiplikation/main.tex b/buch/papers/multiplikation/main.tex index 42f2768..8d0a8df 100644..100755 --- a/buch/papers/multiplikation/main.tex +++ b/buch/papers/multiplikation/main.tex @@ -1,36 +1,18 @@ +% !TEX root = ../../buch.tex % % main.tex -- Paper zum Thema <multiplikation> % -% (c) 2020 Hochschule Rapperswil +% (c) 2021 Hochschule Rapperswil % -\chapter{Thema\label{chapter:multiplikation}} -\lhead{Thema} +\chapter{Schnelle Matrizen Multiplikation\label{chapter:multiplikation}} +\lhead{FMM} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{Michael Schmid} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} -\input{papers/multiplikation/teil0.tex} -\input{papers/multiplikation/teil1.tex} -\input{papers/multiplikation/teil2.tex} -\input{papers/multiplikation/teil3.tex} +\input{papers/multiplikation/einlteung.tex} +\input{papers/multiplikation/problemstellung.tex} +\input{papers/multiplikation/loesungsmethoden.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/multiplikation/packages.tex b/buch/papers/multiplikation/packages.tex index e4173c0..e4173c0 100644..100755 --- a/buch/papers/multiplikation/packages.tex +++ b/buch/papers/multiplikation/packages.tex diff --git a/buch/papers/multiplikation/papers/Strassen_GPU.pdf b/buch/papers/multiplikation/papers/Strassen_GPU.pdf Binary files differnew file mode 100755 index 0000000..4ce7625 --- /dev/null +++ b/buch/papers/multiplikation/papers/Strassen_GPU.pdf diff --git a/buch/papers/multiplikation/papers/Strassen_original_1969.pdf b/buch/papers/multiplikation/papers/Strassen_original_1969.pdf Binary files differnew file mode 100755 index 0000000..b647fc0 --- /dev/null +++ b/buch/papers/multiplikation/papers/Strassen_original_1969.pdf diff --git a/buch/papers/multiplikation/papers/assay_fast_MM.pdf b/buch/papers/multiplikation/papers/assay_fast_MM.pdf Binary files differnew file mode 100755 index 0000000..3cd6b63 --- /dev/null +++ b/buch/papers/multiplikation/papers/assay_fast_MM.pdf diff --git a/buch/papers/multiplikation/papers/strassen_video.txt b/buch/papers/multiplikation/papers/strassen_video.txt new file mode 100755 index 0000000..f84122c --- /dev/null +++ b/buch/papers/multiplikation/papers/strassen_video.txt @@ -0,0 +1 @@ +https://www.youtube.com/watch?v=0oJyNmEbS4w diff --git a/buch/papers/multiplikation/papers/winograd_original.pdf b/buch/papers/multiplikation/papers/winograd_original.pdf Binary files differnew file mode 100755 index 0000000..a7aba36 --- /dev/null +++ b/buch/papers/multiplikation/papers/winograd_original.pdf diff --git a/buch/papers/multiplikation/presentation/common.tex b/buch/papers/multiplikation/presentation/common.tex new file mode 100644 index 0000000..200d244 --- /dev/null +++ b/buch/papers/multiplikation/presentation/common.tex @@ -0,0 +1,79 @@ +% +% common.tex -- gemeinsame Definitionen +% +% (c) 2021 Michael Schmid, OST Campus Rapperswil +% +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{epic} +\usepackage{color} +\usepackage{array} +\usepackage{algorithm} +\usepackage{ifthen} +\usepackage{adjustbox} +\usepackage[noend]{algpseudocode} +\usepackage{neuralnetwork} +\usepackage{amsmath} +\usepackage{lmodern} +\usepackage{tikz} +\usetikzlibrary{decorations.text} +\usetikzlibrary{arrows,matrix,positioning} +\usetikzlibrary{overlay-beamer-styles} +\usetikzlibrary{matrix.skeleton} +\usepackage{pgfplots} +\usepackage{listings} +\usepackage{svg} + +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codegray}{rgb}{0.5,0.5,0.5} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{backcolour}{rgb}{0.95,0.95,0.92} +\definecolor{ost}{rgb}{164,0,136} + +\lstdefinestyle{mystyle}{ + backgroundcolor=\color{backcolour}, + commentstyle=\color{codegreen}, + keywordstyle=\color{magenta}, + numberstyle=\tiny\color{codegray}, + stringstyle=\color{codepurple}, + basicstyle=\footnotesize, + breakatwhitespace=false, + breaklines=true, + captionpos=b, + keepspaces=true, + numbers=left, + numbersep=2pt, + showspaces=false, + showstringspaces=false, + showtabs=false, + tabsize=2 +} + +\usetikzlibrary{fit} +\tikzset{% + highlight/.style={rectangle,rounded corners,fill=red!15,draw,fill opacity=0.5,inner sep=0pt} +} +\newcommand{\tikzmark}[2]{\tikz[overlay,remember picture,baseline=(#1.base)] \node (#1) {#2};} +% +\newcommand{\Highlight}[1][submatrix]{% + \tikz[overlay,remember picture]{ + \node[highlight,fit=(left.north west) (right.south east)] (#1) {};} +} + + +\lstset{style=mystyle} +\lstdefinestyle{mystyle}{ + morekeywords={cwt,contourf,datetick} +} + + +\usetikzlibrary{shapes.geometric} +\mode<beamer>{% +\usetheme[]{Frankfurt}} +\beamertemplatenavigationsymbolsempty +\title[]{Fast Matrix Multiplication} +\author[]{Michael Schmid} +\usecolortheme[named=ost]{structure} + +\date[]{31.05.2021} +\newboolean{presentation} diff --git a/buch/papers/multiplikation/presentation/presentation.nav b/buch/papers/multiplikation/presentation/presentation.nav new file mode 100644 index 0000000..2a01568 --- /dev/null +++ b/buch/papers/multiplikation/presentation/presentation.nav @@ -0,0 +1,59 @@ +\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}} +\headcommand {\beamer@framepages {1}{1}} +\headcommand {\beamer@sectionpages {1}{1}} +\headcommand {\beamer@subsectionpages {1}{1}} +\headcommand {\sectionentry {1}{Big $\mathcal {O}$}{2}{Big $\mathcal {O}$}{0}} +\headcommand {\slideentry {1}{0}{1}{2/4}{}{0}} +\headcommand {\beamer@framepages {2}{4}} +\headcommand {\slideentry {1}{0}{2}{5/6}{}{0}} +\headcommand {\beamer@framepages {5}{6}} +\headcommand {\slideentry {1}{0}{3}{7/8}{}{0}} +\headcommand {\beamer@framepages {7}{8}} +\headcommand {\slideentry {1}{0}{4}{9/10}{}{0}} +\headcommand {\beamer@framepages {9}{10}} +\headcommand {\slideentry {1}{0}{5}{11/12}{}{0}} +\headcommand {\beamer@framepages {11}{12}} +\headcommand {\slideentry {1}{0}{6}{13/13}{}{0}} +\headcommand {\beamer@framepages {13}{13}} +\headcommand {\slideentry {1}{0}{7}{14/14}{}{0}} +\headcommand {\beamer@framepages {14}{14}} +\headcommand {\beamer@sectionpages {2}{14}} +\headcommand {\beamer@subsectionpages {2}{14}} +\headcommand {\sectionentry {2}{Strassen's Algorithm}{15}{Strassen's Algorithm}{0}} +\headcommand {\slideentry {2}{0}{1}{15/15}{}{0}} +\headcommand {\beamer@framepages {15}{15}} +\headcommand {\slideentry {2}{0}{2}{16/18}{}{0}} +\headcommand {\beamer@framepages {16}{18}} +\headcommand {\slideentry {2}{0}{3}{19/19}{}{0}} +\headcommand {\beamer@framepages {19}{19}} +\headcommand {\slideentry {2}{0}{4}{20/20}{}{0}} +\headcommand {\beamer@framepages {20}{20}} +\headcommand {\slideentry {2}{0}{5}{21/23}{}{0}} +\headcommand {\beamer@framepages {21}{23}} +\headcommand {\slideentry {2}{0}{6}{24/24}{}{0}} +\headcommand {\beamer@framepages {24}{24}} +\headcommand {\slideentry {2}{0}{7}{25/25}{}{0}} +\headcommand {\beamer@framepages {25}{25}} +\headcommand {\slideentry {2}{0}{8}{26/26}{}{0}} +\headcommand {\beamer@framepages {26}{26}} +\headcommand {\slideentry {2}{0}{9}{27/29}{}{0}} +\headcommand {\beamer@framepages {27}{29}} +\headcommand {\slideentry {2}{0}{10}{30/32}{}{0}} +\headcommand {\beamer@framepages {30}{32}} +\headcommand {\beamer@sectionpages {15}{32}} +\headcommand {\beamer@subsectionpages {15}{32}} +\headcommand {\sectionentry {3}{Measurements}{33}{Measurements}{0}} +\headcommand {\slideentry {3}{0}{1}{33/40}{}{0}} +\headcommand {\beamer@framepages {33}{40}} +\headcommand {\slideentry {3}{0}{2}{41/49}{}{0}} +\headcommand {\beamer@framepages {41}{49}} +\headcommand {\beamer@sectionpages {33}{49}} +\headcommand {\beamer@subsectionpages {33}{49}} +\headcommand {\sectionentry {4}{How To Matrix Multiply}{50}{How To Matrix Multiply}{0}} +\headcommand {\slideentry {4}{0}{1}{50/50}{}{0}} +\headcommand {\beamer@framepages {50}{50}} +\headcommand {\beamer@partpages {1}{50}} +\headcommand {\beamer@subsectionpages {50}{50}} +\headcommand {\beamer@sectionpages {50}{50}} +\headcommand {\beamer@documentpages {50}} +\headcommand {\gdef \inserttotalframenumber {21}} diff --git a/buch/papers/multiplikation/presentation/presentation.pdf b/buch/papers/multiplikation/presentation/presentation.pdf Binary files differnew file mode 100644 index 0000000..842e68c --- /dev/null +++ b/buch/papers/multiplikation/presentation/presentation.pdf diff --git a/buch/papers/multiplikation/presentation/presentation.snm b/buch/papers/multiplikation/presentation/presentation.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/buch/papers/multiplikation/presentation/presentation.snm diff --git a/buch/papers/multiplikation/presentation/presentation.tex b/buch/papers/multiplikation/presentation/presentation.tex new file mode 100644 index 0000000..2a4af45 --- /dev/null +++ b/buch/papers/multiplikation/presentation/presentation.tex @@ -0,0 +1,12 @@ +% +% MathSem-yyy-xxx.tex -- Präsentation +% +% (c) 2021 Michael Schmid, OST campus Rapperswil +% + +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +%\setboolean{presentation}{true} +\begin{document} +\input{slides/slides.tex} +\end{document} diff --git a/buch/papers/multiplikation/presentation/slides/algo.tex b/buch/papers/multiplikation/presentation/slides/algo.tex new file mode 100644 index 0000000..0c3d130 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/algo.tex @@ -0,0 +1,111 @@ +\begin{frame} + \frametitle{Algorithm} + \begin{columns} + \begin{column}{0.6\textwidth} + \begin{algorithm}[H]\caption{Square Matrix Multiplication} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{MM}{$\textbf{A}, \textbf{B}, \textbf{C}$} + \State $sum \gets 0$ + \State $n \gets columns(\textbf{A}) == rows(\textbf{B})$ + \State $m \gets rows(\textbf{A})$ + \State $p \gets columns(\textbf{B})$ + + \For{$i = 0,1,2 \dots,m-1$} + \For{$j = 0,1,2 \dots,p-1$} + \State $sum \gets 0$ + \For{$k = 0,1,2 \dots,n-1$} + \State $sum \gets sum + \textbf{A}[i][k] \cdot \textbf{B}[k][j]$ + \EndFor + \State $\textbf{C}[i][j] \gets sum $ + \EndFor + \EndFor + \State \textbf{return} $\textbf{C}$ + \EndFunction + \end{algorithmic} + \end{algorithm} +\end{column} +\begin{column}{0.4\textwidth} + \scalebox{0.6}{\parbox{\linewidth}{ + + \begin{tikzpicture}[ampersand replacement=\&,remember picture,overlay] + + \matrix (A)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] at (2,-2.8) + { + A_{1,1} \& \cdots \& A_{1,k} \& \cdots \& A_{1,n} \\ + \vdots \& \& \vdots \& \& \vdots \\ + A_{i,1} \& \cdots \& A_{i,k} \& \cdots \& A_{i,n} \\ + \vdots \& \& \vdots \& \& \vdots \\ + A_{m,1} \& \cdots \& A_{m,k} \& \cdots \& A_{m,n} \\ + }; + + \matrix (B)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] at (7.5,1.2) + { + B_{1,1} \& \cdots \& B_{1,j} \& \cdots \& B_{1,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + B_{k,1} \& \cdots \& B_{k,j} \& \cdots \& B_{k,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + B_{n,1} \& \cdots \& B_{n,j} \& \cdots \& B_{n,p} \\ + }; + + \matrix (C)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] at (7.5,-2.8) + { + C_{1,1} \& \cdots \& C_{1,j} \& \cdots \& C_{1,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + C_{i,1} \& \cdots \& C_{i,j} \& \cdots \& C_{i,p} \\ + \vdots \& \& \vdots \& \& \vdots \\ + C_{m,1} \& \cdots \& C_{m,j} \& \cdots \& C_{m,p} \\ + }; + + + \begin{scope}[on background layer] + \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=green, fit=(A-3-1)(A-3-5)] {}; + \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=blue, fit=(B-1-3)(B-5-3)] {}; + \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=red, fit=(C-3-3)] {}; + + \end{scope} + + + + + \end{tikzpicture} + }} + \end{column} +\end{columns} +\end{frame} + + +\begin{frame} + \frametitle{Algorithm} + +\begin{columns} + \begin{column}{0.6\textwidth} +\begin{algorithm}[H]\caption{Square Matrix Multiplication} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{MM}{$\textbf{A}, \textbf{B}, \textbf{C}$} + \State $sum \gets 0$ + \State $n \gets columns(\textbf{A}) == rows(\textbf{B})$ + \State $m \gets rows(\textbf{A})$ + \State $p \gets columns(\textbf{B})$ + + \For{$i = 0,1,2 \dots,m-1$} + \For{$j = 0,1,2 \dots,p-1$} + \State $sum \gets 0$ + \For{$k = 0,1,2 \dots,n-1$} + \State $sum \gets sum + \textbf{A}[i][k] \cdot \textbf{B}[k][j]$ + \EndFor + \State $\textbf{C}[i][j] \gets sum $ + \EndFor + \EndFor + \State \textbf{return} $\textbf{C}$ + \EndFunction + \end{algorithmic} +\end{algorithm} +\end{column} +\begin{column}{0.4\textwidth} +\Huge$\mathcal{O}(n^3)$ +\end{column} +\end{columns} + +\end{frame} diff --git a/buch/papers/multiplikation/presentation/slides/bigO.tex b/buch/papers/multiplikation/presentation/slides/bigO.tex new file mode 100644 index 0000000..d425da8 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/bigO.tex @@ -0,0 +1,251 @@ + +\begin{frame} + \frametitle{Big $\mathcal{O}$ notation} +\begin{itemize} + \item <1-> Time complexity of an algorithm + \item <2-> How many multiplications in a function + \item <3-> Drop Constants +\end{itemize} +\end{frame} + + +\begin{frame} + \frametitle{Big $\mathcal{O}$ notation} + \onslide<1->{ + + \begin{algorithm}[H]\caption{Foo 1} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{foo}{$a, b$} + \State \textbf{return} $a+b$ + \EndFunction + \end{algorithmic} + \end{algorithm} +} +\onslide<2->{ +$\mathcal{O}(1)$ + } +\end{frame} + +\begin{frame} + \frametitle{Big $\mathcal{O}$ notation} + \onslide<1->{ + + \begin{algorithm}[H]\caption{Foo 2} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{foo}{$a, b$} + \State $ x \gets a+b $ + \State $ y \gets a \cdot b $ + \State \textbf{return} $x+y$ + \EndFunction + \end{algorithmic} + \end{algorithm} +} +\onslide<2->{ +$\mathcal{O}(1) + \mathcal{O}(1) = 2\mathcal{O}(1) = \mathcal{O}(1) $ + } +\end{frame} + +\begin{frame} + \frametitle{Big $\mathcal{O}$ notation} + \onslide<1->{ + + \begin{algorithm}[H]\caption{Foo 3} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{foo}{$\mathbf{A}, \mathbf{B}$,n} + \State $ sum \gets 0$ + \For{$i = 0,1,2 \dots,n$} + \State $ sum \gets sum + A[i] \cdot B[i] $ + \EndFor + + \State \textbf{return} $sum$ + + \EndFunction + \end{algorithmic} + \end{algorithm} +} +\onslide<2->{ +$\mathcal{O}(n)$ + } +\end{frame} + +\begin{frame} + \frametitle{Big $\mathcal{O}$ notation} + \onslide<1->{ + + \begin{algorithm}[H]\caption{Foo 4} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{foo}{$\mathbf{A}, \mathbf{B}$,n} + \State $ sum \gets 0$ + \For{$i = 0,1,2 \dots,n$} + \For{$j = 0,1,2 \dots,n$} + \State $ sum \gets sum + A[i] \cdot B[j] $ + \EndFor + \EndFor + \State \textbf{return} $sum$ + \EndFunction + \end{algorithmic} + \end{algorithm} +} +\onslide<2->{ +$\mathcal{O}(n^2)$ + } +\end{frame} + +% \begin{frame} +% \frametitle{Big $\mathcal{O}$ notation} +% \onslide<1->{ +% +% \begin{algorithm}[H]\caption{Fibonacci} +% \setlength{\lineskip}{7pt} +% \begin{algorithmic}[1] +% \Function{fib}{$n$} +% \If{$n <= 1$} +% \State \textbf{return} $1$ +% \Else +% \State \textbf{return} fib($n-1$) + fib($n-2$) +% \EndIf +% +% \EndFunction +% \end{algorithmic} +% \end{algorithm} +% } +% \onslide<2->{ +% \[ +% \langle x,y \rangle = +% \begin{cases} +% \displaystyle $\mathcal{O}(1)$ & \text{if $n \leq 2$}\\ +% \displaystyle $ 2 \mathcal{T}(\frac{n}{2})$ & \text{if $n > 2$} +% \end{cases} +% \] } +% \end{frame} + + +\begin{frame} + \frametitle{Big $\mathcal{O}$ notation} +\begin{tikzpicture} +\begin{axis}[ + axis lines = left, + xlabel = $n$ (Data Input), + ylabel = {$t$ (time)}, + legend pos=north east, + very thick, + ymax = 20, + yticklabels=\empty, + xticklabels=\empty, + scale only axis=true, + width=12cm, height=6cm, + ] +%Below the red parabola is defined +\addplot [ + domain= 1:6, + samples=100, + color=red, +] +{1}; +\addlegendentry{$\mathcal{O}(1)$} +%Here the blue parabloa is defined +\addplot [ + domain= 1:6, + samples=100, + color=green, +] +{x}; +\addlegendentry{$\mathcal{O}(n)$} +\addplot [ + domain= 1:6, + samples=100, + color=blue, +] +{x^2}; +\addlegendentry{$\mathcal{O}(n^2)$} +\addplot [ + domain= 1:6, + samples=100, + color=purple, +] +{x^3}; +\addlegendentry{$\mathcal{O}(n^3)$} +\addplot [ + domain= 1:3, + samples=100, + color=black, +] +{exp(x)}; +\addlegendentry{$\mathcal{O}(e^n)$} +\addplot [ + domain= 1:6, + samples=100, + color=orange, +] +{log2(x)}; +\addlegendentry{$\mathcal{O}(\log n)$} +\end{axis} +\end{tikzpicture} + +\end{frame} + +\begin{frame} + \frametitle{Big $\mathcal{O}$ notation} +\begin{tikzpicture} +\begin{axis}[ + axis lines = left, + xlabel = $n$ (Data Input), + ylabel = {$t$ (time)}, + legend pos=north east, + very thick, + ymax = 500, + yticklabels=\empty, + xticklabels=\empty, + scale only axis=true, + width=12cm, height=6cm, + ] +\addplot [ + domain= 1:20, + samples=100, + color=red, +] +{1}; +\addlegendentry{$\mathcal{O}(1)$} +\addplot [ + domain= 1:20, + samples=100, + color=green, +] +{x}; +\addlegendentry{$\mathcal{O}(n)$} +\addplot [ + domain= 1:20, + samples=100, + color=blue, +] +{x^2}; +\addlegendentry{$\mathcal{O}(n^2)$} +\addplot [ + domain= 1:10, + samples=100, + color=purple, +] +{x^3}; +\addlegendentry{$\mathcal{O}(n^3)$} +\addplot [ + domain= 1:10, + samples=100, + color=black, +] +{exp(x)}; +\addlegendentry{$\mathcal{O}(e^n)$} +\addplot [ + domain= 1:20, + samples=100, + color=orange, +] +{log2(x)}; +\addlegendentry{$\mathcal{O}(\log n)$} +\end{axis} +\end{tikzpicture} + +\end{frame} diff --git a/buch/papers/multiplikation/presentation/slides/blas.tex b/buch/papers/multiplikation/presentation/slides/blas.tex new file mode 100644 index 0000000..ed498a3 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/blas.tex @@ -0,0 +1,18 @@ +\begin{frame} +\frametitle{BLAS, LAPACK} +\begin{itemize} + \item Basic Linear Algebra Subprograms + \begin{itemize} + \item $\mathbf{y} = \alpha \mathbf{x}+\mathbf{y}$ + \item $\mathbf{y} = \alpha \mathbf{A}\mathbf{x}+ \beta \mathbf{y}$ + \item $\mathbf{C} = \alpha \mathbf{A}\mathbf{B}+ \beta \mathbf{C}$ + + \end{itemize} + \item Linear Algebra Package + \begin{itemize} + \item QR decomposition + \item Singular value decomposition + \item Eigenvalues + \end{itemize} +\end{itemize} +\end{frame} diff --git a/buch/papers/multiplikation/presentation/slides/conclusuion.tex b/buch/papers/multiplikation/presentation/slides/conclusuion.tex new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/conclusuion.tex diff --git a/buch/papers/multiplikation/presentation/slides/logo.pdf b/buch/papers/multiplikation/presentation/slides/logo.pdf Binary files differnew file mode 100644 index 0000000..d78ca88 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/logo.pdf diff --git a/buch/papers/multiplikation/presentation/slides/meas.tex b/buch/papers/multiplikation/presentation/slides/meas.tex new file mode 100644 index 0000000..489c010 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/meas.tex @@ -0,0 +1,42 @@ +\begin{frame} + \frametitle{Measurements Python} + \only<1>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_8.pdf}} + \only<2>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_16.pdf}} + \only<3>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_32.pdf}} + \only<4>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_64.pdf}} + \only<5>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_128.pdf}} + \only<6>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_256.pdf}} + \only<7>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_512.pdf}} + \only<8>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/meas_1024.pdf}} +\end{frame} + + +\begin{frame} + \frametitle{Measurements C} + \only<1>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_8.pdf}} + \only<2>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_16.pdf}} + \only<3>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_32.pdf}} + \only<4>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_64.pdf}} + \only<5>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_128.pdf}} + \only<6>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_256.pdf}} + \only<7>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_512.pdf}} + \only<8>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_1024.pdf}} + \only<9>{ + \includegraphics[width=\textwidth,height=0.9\textheight,keepaspectratio]{../code/c_meas_2048.pdf}} +\end{frame} diff --git a/buch/papers/multiplikation/presentation/slides/nn.tex b/buch/papers/multiplikation/presentation/slides/nn.tex new file mode 100644 index 0000000..e74e970 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/nn.tex @@ -0,0 +1,97 @@ + +\begin{frame} + \frametitle{Neural Network} + \centering +\newcommand{\inputnum}{4} + +% Hidden layer neurons'number +\newcommand{\hiddennumA}{5} +\newcommand{\hiddennumB}{6} + +% Output layer neurons'number +\newcommand{\outputnum}{4} + +\begin{tikzpicture} + + +% Input Layer +\foreach \i in {1,...,\inputnum} +{ + \node[circle, + minimum size = 6mm, + fill=blue!30] (Input-\i) at (0,-\i) {}; +} + +% Hidden Layer1 +\foreach \i in {1,...,\hiddennumA} +{ + \node[circle, + minimum size = 6mm, + fill=red!50, + yshift=(\hiddennumA-\inputnum)*5 mm + ] (Hidden1-\i) at (2.5,-\i) {}; +} + +% Hidden Layer2 +\foreach \i in {1,...,\hiddennumB} +{ + \node[circle, + minimum size = 6mm, + fill=red!50, + yshift=(\hiddennumB-\inputnum)*5 mm + ] (Hidden2-\i) at (5,-\i) {}; +} + +% Output Layer +\foreach \i in {1,...,\outputnum} +{ + \node[circle, + minimum size = 6mm, + fill=green!50, + yshift=(\outputnum-\inputnum)*5 mm + ] (Output-\i) at (7.5,-\i) {}; +} + +% Connect neurons In-Hidden +\foreach \i in {1,...,\inputnum} +{ + \foreach \j in {1,...,\hiddennumA} + { + \draw[->, shorten >=1pt] (Input-\i) -- (Hidden1-\j); + } +} + +% Connect neurons In-Hidden +\foreach \i in {1,...,\hiddennumA} +{ + \foreach \j in {1,...,\hiddennumB} + { + \draw[->, shorten >=1pt] (Hidden1-\i) -- (Hidden2-\j); + } +} + +% Connect neurons Hidden-Out +\foreach \i in {1,...,\hiddennumB} +{ + \foreach \j in {1,...,\outputnum} + { + \draw[->, shorten >=1pt] (Hidden2-\i) -- (Output-\j); + } +} + +% Inputs +\foreach \i in {1,...,\inputnum} +{ + \draw[<-, shorten <=1pt] (Input-\i) -- ++(-1,0) + node[left]{\LARGE{$x_{\i}$}}; +} + +% Outputs +\foreach \i in {1,...,\outputnum} +{ + \draw[->, shorten <=1pt] (Output-\i) -- ++(1,0) + node[right]{\LARGE{$y_{\i}$}}; +} + +\end{tikzpicture} +\end{frame} diff --git a/buch/papers/multiplikation/presentation/slides/parcomp.tex b/buch/papers/multiplikation/presentation/slides/parcomp.tex new file mode 100644 index 0000000..1ba39ee --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/parcomp.tex @@ -0,0 +1,66 @@ +% !TEX root = presentation.tex + +\begin{frame} + \frametitle{Vector-Matrix Multiplication} +\center{ + \begin{tikzpicture}[ampersand replacement=\&] + + \matrix (A)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] + { + A_{1,1} \& A_{1,2} \& A_{1,3} \& A_{1,4} \\ + }; + + \matrix (B)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] at (5,-0.95) + { + B_{1,1} \& B_{1,2} \& B_{1,3} \& B_{1,4} \& B_{1,5} \\ + B_{2,1} \& B_{2,2} \& B_{2,3} \& B_{2,4} \& B_{2,5} \\ + B_{3,1} \& B_{3,2} \& B_{3,3} \& B_{3,4} \& B_{3,5} \\ + B_{4,1} \& B_{4,2} \& B_{4,3} \& B_{4,4} \& B_{4,5} \\ + }; + + \matrix (C)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] at (5,-3) + { + C_{1,1} \& C_{1,2} \& C_{1,3} \& C_{1,4} \& C_{1,5}\\ + }; + + \foreach \i in {1,...,4} + { + \pgfmathtruncatemacro{\ii}{\i+1} + \onslide<\ii>{ + + \foreach \j in {1,...,5} + { + \draw[thick] (A-1-\i.south) to [out=-90,in=135]node[visible on=<\i->, anchor=north]{} (B-\i-\j.center); + + } + } + } + + + \end{tikzpicture} +} +\end{frame} + + +\begin{frame} + \frametitle{DSP Architecture} +\scalebox{2}{ + \begin{tikzpicture} + \node (mul) at (0,0) [circle,draw=black,inner sep=0pt,minimum size=0.5cm] {X}; + \node (mac) at (2,0) [circle,draw=black,inner sep=0pt,minimum size=0.5cm] {\textbf{+}}; + + \node at (-2,0.3) {$A[n]$}; + \node at (0.4,2) {$B[n]$}; + \node at (4,0.3) {$C[n]$}; + + \draw[thick, ->] (-2,0) --++ (mul); + \draw[thick, ->] (0,2) --++ (mul); + \draw[thick, ->] (mul) -- (mac); + \draw[thick] (mac) --++ (1,0) node (i) {}; + \draw[thick, ->] (i.center) --++ (0,1) --++ (-1,0) -- (mac); + \draw[thick, ->] (i.center) --++ (1,0); + + + \end{tikzpicture} + } +\end{frame} diff --git a/buch/papers/multiplikation/presentation/slides/slides.tex b/buch/papers/multiplikation/presentation/slides/slides.tex new file mode 100644 index 0000000..64edb86 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/slides.tex @@ -0,0 +1,15 @@ +% !TEX root = presentation.tex +\begin{frame} +\titlepage +\end{frame} +% +\section{Big $\mathcal{O}$} +\input{slides/BigO.tex} +\section{Strassen's Algorithm} +\input{slides/strassen.tex} +% \input{slides/nn.tex} +\section{Measurements} +\input{slides/meas.tex} +% \input{slides/parcomp.tex} +\section{How To Matrix Multiply} +\input{slides/blas.tex} diff --git a/buch/papers/multiplikation/presentation/slides/strassen.tex b/buch/papers/multiplikation/presentation/slides/strassen.tex new file mode 100644 index 0000000..c3398d5 --- /dev/null +++ b/buch/papers/multiplikation/presentation/slides/strassen.tex @@ -0,0 +1,429 @@ +\begin{frame} + \frametitle{Strassen's Algorithm} + \includegraphics[page=1,width=\textwidth,height=0.8\textheight,keepaspectratio]{../papers/Strassen_original_1969.pdf} + \includegraphics[page=2,width=\textwidth,height=0.8\textheight,keepaspectratio]{../papers/Strassen_original_1969.pdf} \includegraphics[page=3,width=\textwidth,height=0.8\textheight,keepaspectratio]{../papers/Strassen_original_1969.pdf} + \end{frame} + +\begin{frame} + \frametitle{Strassen's Algorithm} + \centering + \large +\onslide<1->{ + $ + \mathbf{A B = C} + $ +} + +\onslide<2->{ + + +\medskip + $ + \begin{bmatrix} + A_{11} & A_{12}\\ + A_{21} & A_{22} + \end{bmatrix} + \begin{bmatrix} + B_{11} & B_{12}\\ + B_{21} & B_{22} + \end{bmatrix} + = + \begin{bmatrix} + C_{11} & C_{12}\\ + C_{21} & C_{22} + \end{bmatrix} + $ + } + + + \onslide<3->{ + +\medskip +$ +C_{11} = A_{11} \cdot B_{11} + A_{12} \cdot B_{21} +$ + +$ +C_{12} = A_{11} \cdot B_{12} + A_{12} \cdot B_{22} +$ + +$ +C_{21} = A_{21} \cdot B_{11} + A_{22} \cdot B_{21} +$ + +$ +C_{22} = A_{21} \cdot B_{12} + A_{22} \cdot B_{22} +$ +} +\end{frame} + +\input{slides/algo.tex} + + + +\begin{frame} + \frametitle{Strassen's Algorithm} + \begin{columns} + \begin{column}{0.5\textwidth} + \onslide<1->{ + \large + \begin{math} + \begin{aligned} + \text{I} &= (A_{11} + A_{22}) \cdot (B_{11} + B_{22}) \\ + \text{II} &= (A_{21} + A_{22}) \cdot B_{11} \\ + \text{III} &= A_{11} \cdot (B_{12}-B_{22}) \\ + \text{IV} &= A_{22} \cdot (-B_{11}+B_{21}) \\ + \text{V} &= (A_{11} + A_{12}) \cdot B_{22} \\ + \text{VI} &= (-A_{11} + A_{21}) \cdot (B_{11} + B_{12}) \\ + \text{VII} &= (A_{12} - A_{22}) \cdot (B_{21} + B_{22}) \\ + \end{aligned} + \end{math} + } + \end{column} + + \begin{column}{0.5\textwidth} + \onslide<2->{ + \large + \begin{math} + \begin{aligned} + C_{11} &= \text{I} + \text{IV} - \text{V} + \text{VII} \\ + C_{21} &= \text{II} + \text{IV} \\ + C_{12} &= \text{III} + \text{V}\\ + C_{22} &= \text{I} + \text{III} - \text{II} + \text{VI} \\ + \end{aligned} + \end{math} + } + \end{column} +\end{columns} + +\onslide<3->{ + +\bigskip +\centering +\tiny +\begin{math} +\begin{aligned} + C_{11} &= (A_{11} + A_{22}) \cdot (B_{11} + B_{22}) + A_{22} \cdot (-B_{11}+B_{21}) - (A_{11} + A_{12}) \cdot B_{22} + (A_{12} - A_{22}) \cdot (B_{21} + B_{22}) \\ + C_{11} &= A_{11}B_{11} + A_{11}B_{22} + A_{22}B_{11} + A_{22}B_{22} -A_{22}B_{11}+A_{22}B_{21} - A_{11}B_{22} - A_{12}B_{22}+ A_{12}B_{21} + A_{12}B_{22} - A_{22}B_{21} - A_{22}B_{22} \\ + C_{11} &= A_{11}B_{11} + A_{12}B_{21} +\end{aligned} +\end{math} +} + +\end{frame} + + +\begin{frame} +\begin{adjustbox}{width=\textwidth} +\begin{tikzpicture}[ampersand replacement=\&] + + \foreach \i in {1,...,4} + { + \small{ + \matrix (X\i)[matrix of math nodes,nodes in empty cells, + nodes = {draw, minimum size=10mm, + anchor=center, + inner sep=0pt, outer sep=0pt}, + column sep=-\pgflinewidth, + row sep=-\pgflinewidth, + ] at (0,-\i*5) + { + A_{11}B_{11} \& A_{12}B_{11} \& A_{21}B_{11} \& A_{22}B_{11} \\ + A_{11}B_{21} \& A_{12}B_{21} \& A_{21}B_{21} \& A_{22}B_{21} \\ + A_{11}B_{11} \& A_{12}B_{12} \& A_{21}B_{12} \& A_{22}B_{12} \\ + A_{11}B_{22} \& A_{12}B_{22} \& A_{21}B_{22} \& A_{22}B_{22} \\ + };} + + \foreach \j in {1,...,7} + { + \matrix(M\i\j)[matrix of math nodes,nodes in empty cells, + nodes = {draw, minimum size=10mm, + anchor=center, + inner sep=0pt, outer sep=0pt}, + column sep=-\pgflinewidth, + row sep=-\pgflinewidth, + ] at (\j*5,-\i*5) + { + \& \& \& \\ + \& \& \& \\ + \& \& \& \\ + \& \& \& \\ + }; + } + } + +\huge{ + \node at (-3,-20) {$C_{22}=$}; + \node at (-3,-15) {$C_{21}=$} ; + \node at (-3,-10) {$C_{12}=$} ; + \node at (-3,-5) {$C_{11}=$} ; + + \node at (5,-2) {I}; + \node at (10,-2) {II}; + \node at (15,-2) {III}; + \node at (20,-2) {IV}; + \node at (25,-2) {V}; + \node at (30,-2) {VI}; + \node at (35,-2) {VII}; + } + + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-2-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-3-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-4-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-2-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-3-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-4-4)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M14-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M14-2-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-2-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-4-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-2-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-4-2)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M23-3-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M23-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-2)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M34-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M34-2-4)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M43-3-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M43-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-3-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-3-1)] {}; +\end{tikzpicture} +\end{adjustbox} +\end{frame} + + +\begin{frame} + \frametitle{Strassen's Algorithm} + \begin{columns} + \begin{column}{0.5\textwidth} + \large + \begin{math} + \begin{aligned} + \text{I} &= (A_{11} + A_{22}) \cdot (B_{11} + B_{22}) \\ + \text{II} &= (A_{21} + A_{22}) \cdot B_{11} \\ + \text{III} &= A_{11} \cdot (B_{12}-B_{22}) \\ + \text{IV} &= A_{22} \cdot (-B_{11}+B_{21}) \\ + \text{V} &= (A_{11} + A_{12}) \cdot B_{22} \\ + \text{VI} &= (-A_{11} + A_{21}) \cdot (B_{11} + B_{12}) \\ + \text{VII} &= (A_{12} - A_{22}) \cdot (B_{21} + B_{22}) \\ + \end{aligned} + \end{math} + + \end{column} + + \begin{column}{0.5\textwidth} + \large + \begin{math} + \begin{aligned} + C_{11} &= \text{I} + \text{IV} - \text{V} + \text{VII} \\ + C_{21} &= \text{II} + \text{IV} \\ + C_{12} &= \text{III} + \text{V}\\ + C_{22} &= \text{I} + \text{III} - \text{II} + \text{VI} \\ + \end{aligned} + \end{math} + + \end{column} +\end{columns} +\end{frame} + + + +\begin{frame} + \frametitle{Strassen's Algorithm} + +\begin{columns} + \begin{column}{0.5\textwidth} +\large +\begin{math} +\begin{aligned} +\text{\textbf{I}} &= (\mathbf{A_{11}} + \mathbf{A_{22}}) \cdot (\mathbf{B_{11}} + \mathbf{B_{22}}) \\ +\text{\textbf{II}} &= (\mathbf{A_{21}} + \mathbf{A_{22}}) \cdot \mathbf{B_{11}} \\ +\text{\textbf{III}} &= \mathbf{A_{11}} \cdot (\mathbf{B_{12}}-\mathbf{B_{22}}) \\ +\text{\textbf{IV}} &= \mathbf{A_{22}} \cdot (-\mathbf{B_{11}}+\mathbf{B_{21}}) \\ +\text{\textbf{V}} &= (\mathbf{A_{11}} + \mathbf{A_{12}}) \cdot \mathbf{B_{22}} \\ +\text{\textbf{VI}} &= (-\mathbf{A_{11}} + \mathbf{A_{21}}) \cdot (\mathbf{B_{11}} + \mathbf{B_{12}}) \\ +\text{\textbf{VII}} &= (\mathbf{A_{12}} - \mathbf{A_{22}}) \cdot (\mathbf{B_{21}} + \mathbf{B_{22}}) \\ +\end{aligned} +\end{math} + +\end{column} + +\begin{column}{0.5\textwidth} + \large + \begin{math} + \begin{aligned} + \mathbf{C_{11}} &= \text{\textbf{I}} + \text{\textbf{IV}} - \text{\textbf{V}} + \text{\textbf{VII}} \\ + \mathbf{C_{21}} &= \text{\textbf{II}} + \text{\textbf{IV}} \\ + \mathbf{C_{12}} &= \text{\textbf{III}} + \text{\textbf{V}}\\ + \mathbf{C_{22}} &= \text{\textbf{I}} + \text{\textbf{III}} - \text{\textbf{II}} + \text{\textbf{VI}} \\ + \end{aligned} + \end{math} + +\end{column} +\end{columns} + +\end{frame} + +\begin{frame} + \frametitle{Algorithm} + \onslide<1->{ + + \scalebox{0.45}{\parbox{\linewidth}{ + \begin{algorithm}[H]\caption{Strassen Matrix Multiplication} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{strassen}{$\textbf{A}, \textbf{B}, n$} + \If{$n = 2$} + \State $ \mathbf{C} \gets zeros((n, n))$ + \State $P \gets (A[0][0]+A[1][1])\cdot( B[0][0]+B[1][1])$ + \State $Q \gets (A[1][0]+A[1][1])\cdot B[0][0]$ + \State $R \gets A[0][0]\cdot (B[0][1]-B[1][1])$ + \State $S \gets A[1][1]\cdot (B[1][0]-B[0][0])$ + \State $T \gets (A[0][0]+A[0][1])\cdot B[1][1]$ + \State $U \gets (A[1][0]-A[0][0])\cdot (B[0][0]+B[0][1])$ + \State $V \gets (A[0][1]-A[1][1])\cdot (B[1][0]+B[1][1])$ + \State $C[0][0] \gets P+S-T+V$ + \State $C[0][1] \gets R+T$ + \State $C[1][0] \gets Q+S$ + \State $C[1][1] \gets P+R-Q+U$ + \Else + \State $ m \gets n/2$ + \State $\mathbf{A11}, \mathbf{A12}, \mathbf{A21}, \mathbf{A22} \gets \mathbf{A}[:m][:m], \mathbf{A}[:m][m:], \mathbf{A}[m:][:m], \mathbf{A}[m:][m:]$ + \State $\mathbf{B11}, \mathbf{B12}, \mathbf{B21}, \mathbf{B22} \gets \mathbf{B}[:m][:m], \mathbf{B}[:m][m:], \mathbf{B}[m:][:m], \mathbf{B}[m:][m:]$ + + \State $ \mathbf{P} \gets \text{strassen}((\mathbf{A11}+ \mathbf{A22}),(\mathbf{B11}+\mathbf{B22}), m)$ + \State $ \mathbf{Q} \gets \text{strassen}((\mathbf{A21}+ \mathbf{A22}), \mathbf{B11},m)$ + \State $ \mathbf{R} \gets \text{strassen}( \mathbf{A11},(\mathbf{B12}- \mathbf{B22}),m)$ + \State $ \mathbf{S} \gets \text{strassen}( \mathbf{A22},(\mathbf{B21}- \mathbf{B11}),m)$ + \State $ \mathbf{T} \gets \text{strassen}((\mathbf{A11}+ \mathbf{A12}), \mathbf{B22},m)$ + \State $ \mathbf{U} \gets \text{strassen}((\mathbf{A21}- \mathbf{A11}),(\mathbf{B11}+\mathbf{B12}),m)$ + \State $ \mathbf{V} \gets \text{strassen}((\mathbf{A12}- \mathbf{A22}),(\mathbf{B21}+\mathbf{B22}),m)$ + + + + \State $\mathbf{C11} \gets \mathbf{P+S-T+V}$ + \State $\mathbf{C12} \gets \mathbf{R+T}$ + \State $\mathbf{C21} \gets \mathbf{Q+S}$ + \State $\mathbf{C22} \gets \mathbf{P+R-Q+U}$ + \State $ C \gets vstack((hstack((C11, C12)), hstack((C21, C22))))$ + + \EndIf + \State \textbf{return} $\textbf{C}$ + + \EndFunction + \end{algorithmic} + \end{algorithm} + }}} +% \[ +% \mathcal{T}(n) = \left\{\begin{array}{lr} +% 1, & \text{if} n \leq 2\\ +% 7 \mathcal{T}(\frac{n}{2}) + n^2, & \text{if} n > 2\\ +% \end{array}\right\} +% \] +\only<2>{ + $ + \mathcal{T}(n) = + \begin{cases} + 1 & \text{if } n \leq 2\\ + 7 \cdot \mathcal{T}(\frac{n}{2}) + n^2 & \text{if } n > 2 + \end{cases} = \mathcal{O}(n^{\log_2 7})$ + +} +\only<3>{ + $ + \mathcal{T}(n) = + \begin{cases} + 1 & \text{if } n \leq 2\\ + 7 \cdot \mathcal{T}(\frac{n}{2}) + n^2 & \text{if } n > 2 + \end{cases} = \mathcal{O}(n^{2.81})$ + +} + +\end{frame} + +\begin{frame} + \frametitle{Algorithm} + \onslide<1->{ + + \scalebox{0.45}{\parbox{\linewidth}{ + \begin{algorithm}[H]\caption{Strassen Matrix Multiplication} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{MM}{$\textbf{A}, \textbf{B}, n$} + \If{$n = 2$} + \State $ \mathbf{C} \gets zeros((n, n))$ + \State $C[0, 0] \gets A[0][0]*B[0][0]+A[0][1]*B[1][0]$ + \State $C[0, 1] \gets A[0][0]*B[0][1]+A[0][1]*B[1][1]$ + \State $C[1, 0] \gets A[1][0]*B[0][0]+A[1][1]*B[1][0]$ + \State $C[1, 1] \gets A[1][0]*B[0][1]+A[1][1]*B[1][1]$ + \Else + \State $ m \gets n/2$ + \State $\mathbf{A11}, \mathbf{A12}, \mathbf{A21}, \mathbf{A22} \gets \mathbf{A}[:m][:m], \mathbf{A}[:m][m:], \mathbf{A}[m:][:m], \mathbf{A}[m:][m:]$ + \State $\mathbf{B11}, \mathbf{B12}, \mathbf{B21}, \mathbf{B22} \gets \mathbf{B}[:m][:m], \mathbf{B}[:m][m:], \mathbf{B}[m:][:m], \mathbf{B}[m:][m:]$ + + \State $\mathbf{C11} \gets \text{MM}(\mathbf{A11}, \mathbf{B11}) + \text{MM}(\mathbf{A12}, \mathbf{B21})$ + \State $\mathbf{C12} \gets \text{MM}(\mathbf{A11},\mathbf{B12}) + \text{MM}(\mathbf{A12},\mathbf{B22})$ + \State $\mathbf{C21} \gets \text{MM}(\mathbf{A21}, \mathbf{B11}) + \text{MM}(\mathbf{A22}, \mathbf{B21})$ + \State $\mathbf{C22} \gets \text{MM}(\mathbf{A21}, \mathbf{B12}) + \text{MM}(\mathbf{A22}, \mathbf{B22})$ + \State $ C \gets vstack((hstack((C11, C12)), hstack((C21, C22))))$ + + \EndIf + \State \textbf{return} $\textbf{C}$ + + \EndFunction + \end{algorithmic} + \end{algorithm} + \bigskip + \bigskip + \bigskip + \bigskip + \bigskip + }}} + +\only<2>{ + + + $ + \mathcal{T}(n) = + \begin{cases} + 1 & \text{if } n \leq 2\\ + 8 \cdot \mathcal{T}(\frac{n}{2}) + n^2 & \text{if } n > 2 + \end{cases} = \mathcal{O}(n^{\log_2 8})$ + +} +\only<3>{ + $ + \mathcal{T}(n) = + \begin{cases} + 1 & \text{if } n \leq 2\\ + 8 \cdot \mathcal{T}(\frac{n}{2}) + n^2 & \text{if } n > 2 + \end{cases} = \mathcal{O}(n^{3})$ + +} + +\end{frame} diff --git a/buch/papers/multiplikation/presentation/tikz/algo.pdf b/buch/papers/multiplikation/presentation/tikz/algo.pdf Binary files differnew file mode 100644 index 0000000..752f42e --- /dev/null +++ b/buch/papers/multiplikation/presentation/tikz/algo.pdf diff --git a/buch/papers/multiplikation/presentation/tikz/algo.tex b/buch/papers/multiplikation/presentation/tikz/algo.tex new file mode 100644 index 0000000..0b2c567 --- /dev/null +++ b/buch/papers/multiplikation/presentation/tikz/algo.tex @@ -0,0 +1,52 @@ +\documentclass[border=10pt]{article} +\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{times} +\usepackage{geometry} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathrsfs} +\usepackage{amsfonts} +\usepackage{amsthm} +\usepackage{lipsum} +\usepackage{amscd} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{textcomp} +\usepackage{txfonts} +\usepackage[all]{xy} +\usepackage{paralist} +\usepackage[colorlinks=true]{hyperref} +\usepackage{array} +\usepackage{tikz} +\usepackage{slashed} +\usepackage{pdfpages} +\usepackage{cite} +\usepackage{url} +\usepackage{algorithm} +\usepackage[noend]{algpseudocode} +\usepackage{listings} +\usepackage{multirow} +\usepackage{color} + +\begin{document} + +\begin{algorithm}[H]\caption{Square Matrix Multiplication} + \setlength{\lineskip}{7pt} + \begin{algorithmic}[1] + \Function{MM}{$\textbf{A}, \textbf{B}, \textbf{C}, n$} + \State $sum \gets 0$ + \For{$i = 0,1,2 \dots,n-1$} + \For{$j = 0,1,2 \dots,n-1$} + \State $sum \gets 0$ + \For{$k = 0,1,2 \dots,n-1$} + \State $sum \gets sum + \textbf{A}[i][k] \cdot \textbf{B}[k][j]$ + \EndFor + \State $\textbf{C}[i][j] \gets sum $ + \EndFor + \EndFor + \EndFunction + \end{algorithmic} +\end{algorithm} +\end{document} diff --git a/buch/papers/multiplikation/problemstellung.tex b/buch/papers/multiplikation/problemstellung.tex new file mode 100755 index 0000000..b20a791 --- /dev/null +++ b/buch/papers/multiplikation/problemstellung.tex @@ -0,0 +1,104 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Problemstellung} +\rhead{Problemstellung} +Dank der breiten Anwendung der Matrizenmultiplikation ist eine effiziente L\"osung dieser Operation von grosser Bedeutung. +Das Ziel dieses Papers ist verschiedenen Algorithmen der Matrizenmultiplikation vorzustellen. +Wobei gezielt auf Algorithmen, welche das Problem schneller als der Standard Algorithmus L\"osen eingegangen wird. + +\subsection{Big $\mathcal{O}$ Notation} +Die Big $\mathcal{O}$ Notation beschreibt die Laufzeitkomplexit\"at eines Algorithmus \cite{multiplikation:bigo}. +$f(x) \in \mathcal{O}(g(x))$ besagt das die Funktion $f$ nicht wesentlich schneller w\"achst als $g$ wenn $x \rightarrow \infty$. +Vereinfacht werden f\"ur Algorithmen die folgende Notation verwendet: +\begin{itemize} + \item $f \in \mathcal{O}(1) \rightarrow f$ ist beschr\"ankt + \item $f \in \mathcal{O}(n) \rightarrow f$ w\"achst linear + \item $f \in \mathcal{O}(n^2) \rightarrow f$ w\"achst quadratisch + \item $f \in \mathcal{O}(\log n) \rightarrow f$ w\"achst logarithmisch + \item $f \in \mathcal{O}(n \log n) \rightarrow f$ hat super-lineares Wachstum + \item $f \in \mathcal{O}(e^n) \rightarrow f$ w\"achst exponentiell + \item usw. +\end{itemize} + +In der Abbildung \ref{multiplikation:fig:bigo} k\"onnen die Verschiedenen Laufzeiten miteinander verglichen werden. + +\begin{figure} + \center + \includegraphics[]{papers/multiplikation/images/bigo} + \caption{Verschiedene Laufzeiten} + \label{multiplikation:fig:bigo} +\end{figure} + +\subsubsection{Beispiel Algorithmen} +\paragraph{Beschr\"ankter Algorithmus} + +Ein Beispiel eines Beschr\"ankter Verhalten $\mathcal{O}(1)$, kann im Algorithmus \ref{multiplikation:alg:b1} entnommen werden. + +\begin{algorithm}\caption{} + \label{multiplikation:alg:b1} + \setlength{\lineskip}{7pt} + \begin{algorithmic} + \Function{B1}{$a, b$} + \State \textbf{return} $a+b$ + \EndFunction + \end{algorithmic} +\end{algorithm} + +Wobei Konstanten nicht beachtet werden, der Algorithmus \ref{multiplikation:alg:b2} f\"uhrt ebenso zu $\mathcal{O}(1)$ und nicht zu $\mathcal{O}(2)$. + +\begin{algorithm}\caption{} + \label{multiplikation:alg:b2} + \setlength{\lineskip}{7pt} + \begin{algorithmic} + \Function{B2}{$a, b$} + \State $ x \gets a+b $ + \State $ y \gets a \cdot b $ + \State \textbf{return} $x+y$ + \EndFunction + \end{algorithmic} +\end{algorithm} + +\paragraph{Linearer Algorithmus} + +Folgender Algorithmus \ref{multiplikation:alg:l1} hat ein lineares $\mathcal{O}(n)$ Verhalten. + +\begin{algorithm}\caption{} + \setlength{\lineskip}{7pt} + \begin{algorithmic} + \label{multiplikation:alg:l1} + \Function{L}{$\mathbf{A}, \mathbf{B}$,n} + \State $ sum \gets 0$ + \For{$i = 0,1,2 \dots,n$} + \State $ sum \gets sum + A[i] \cdot B[i] $ + \EndFor + + \State \textbf{return} $sum$ + + \EndFunction + \end{algorithmic} +\end{algorithm} + +\paragraph{Quadratischer Algorithmus} + +Folgender Algorithmus \ref{multiplikation:alg:q1} hat ein quadratisches $\mathcal{O}(n^2)$ Verhalten. + +\begin{algorithm}[H]\caption{} + \label{multiplikation:alg:q1} + \setlength{\lineskip}{7pt} + \begin{algorithmic} + \Function{Q}{$\mathbf{A}, \mathbf{B}$,n} + \State $ sum \gets 0$ + \For{$i = 0,1,2 \dots,n$} + \For{$j = 0,1,2 \dots,n$} + \State $ sum \gets sum + A[i] \cdot B[j] $ + \EndFor + \EndFor + \State \textbf{return} $sum$ + \EndFunction + \end{algorithmic} +\end{algorithm} + + diff --git a/buch/papers/multiplikation/references.bib b/buch/papers/multiplikation/references.bib index 7149fb1..9d76e8e 100644..100755 --- a/buch/papers/multiplikation/references.bib +++ b/buch/papers/multiplikation/references.bib @@ -33,3 +33,33 @@ url = {https://doi.org/10.1016/j.acha.2017.11.004} } +@article{multiplikation:winograd_1968, + title={A New Algorithm for Inner Product}, + volume={C-17}, + DOI={10.1109/tc.1968.227420}, + number={7}, + journal={IEEE Transactions on Computers}, + author={Winograd, S.}, + year={1968}, + pages={693–694} +} + +@article{multiplikation:strassen_1969, + title={Gaussian elimination is not optimal}, + volume={13}, + DOI={10.1007/bf02165411}, + number={4}, + journal={Numerische Mathematik}, + author={Strassen, Volker}, + year={1969}, + pages={354–356} +} + +@online{multiplikation:bigo, + title = {Big O notation}, + url = {https://en.wikipedia.org/wiki/Big_O_notation}, + date = {2021-07-27}, + year = {2021}, + month = {7}, + day = {27} +} diff --git a/buch/papers/multiplikation/teil0.tex b/buch/papers/multiplikation/teil0.tex deleted file mode 100644 index 082b7f5..0000000 --- a/buch/papers/multiplikation/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{multiplikation:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{multiplikation:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/multiplikation/teil1.tex b/buch/papers/multiplikation/teil1.tex deleted file mode 100644 index 0a6903a..0000000 --- a/buch/papers/multiplikation/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{multiplikation:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{multiplikation:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{multiplikation:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{multiplikation:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{multiplikation:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/multiplikation/teil2.tex b/buch/papers/multiplikation/teil2.tex deleted file mode 100644 index efbf31a..0000000 --- a/buch/papers/multiplikation/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{multiplikation:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{multiplikation:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/multiplikation/teil3.tex b/buch/papers/multiplikation/teil3.tex deleted file mode 100644 index f58508b..0000000 --- a/buch/papers/multiplikation/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{multiplikation:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{multiplikation:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/multiplikation/tikz_formulas/algo.fdb_latexmk b/buch/papers/multiplikation/tikz_formulas/algo.fdb_latexmk new file mode 100644 index 0000000..5f14129 --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo.fdb_latexmk @@ -0,0 +1,254 @@ +# Fdb version 3 +["pdflatex"] 1620305767 "algo.tex" "algo.pdf" "algo" 1621586452 + "/dev/null" 1621583990 0 d41d8cd98f00b204e9800998ecf8427e "" + "/etc/texmf/web2c/texmf.cnf" 1619433543 475 c0e671620eb5563b2130f56340a5fde8 "" + "/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc" 1165713224 4850 80dc9bab7f31fb78a000ccfed0e27cab "" + "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm1000.tfm" 1136768653 3584 adb004a0c8e7c46ee66cad73671f37b4 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm" 1229303445 688 37338d6ab346c2f1466b29e195316aa4 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs5.tfm" 1229303445 684 3a51bd4fd9600428d5264cf25f04bb9a "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs7.tfm" 1229303445 692 1b6510779f0f05e9cbf03e0f6c8361e6 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm" 1136768653 1020 c53143d3e3747b5c1149bd9a5ecd7b55 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm" 1136768653 1056 e2202af076e43d03fc17f87e104021b0 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm" 1136768653 4572 2c370d27bbb031f7592de9d41dc8cfca "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm" 1136768653 4452 0fd0a792eaab7113e4d4f1b941ff0367 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm" 1136768653 4640 ce59980bcbe9e6236fab46d0b5212c7e "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm" 1136768653 1004 c0e991f864f31f017ea4ff9e451b76d4 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm" 1136768653 6892 772bf8e6c154137db8568fa8a47a6ceb "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm" 1136768653 6716 6d25a377562601272906e3bfe6b2817a "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm" 1136768653 1080 b674b4ba143004461509a754a0984b67 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm" 1136768653 688 f56006d6e56f46e63d9f63252958b828 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm" 1136768653 2584 cf4a6a7c2a518d47468fe29ef0913ba0 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm" 1232065820 1944 f854e259cb2839e49d4aa2949544a6e1 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm" 1136768653 1180 72784d0ee5a983fba99a0986b31b0493 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm" 1136768653 2408 aec793a3c45e495f7ad15b227c91f508 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm" 1136768653 1268 1d124f224979493f8fd017a7597ea1cd "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm" 1136768653 972 2c9ffac4bbd20f91c01aaef9bf3f8710 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm" 1136768653 988 098ca7e8cc5647b9ac21b82dbdce1f01 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm" 1136768653 1084 75e807e9e71f7a312e4e1187dce5e93b "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyatip10.tfm" 1381187214 608 50246cc71b0635b0ba0a5c10a0bf4257 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybsql10.tfm" 1381187214 608 4db60f15ea23b4ec2d796c6d568a63fa "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybtip10.tfm" 1381187214 608 50246cc71b0635b0ba0a5c10a0bf4257 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycirc10.tfm" 1381187214 844 3393210079fb4ed9347e214b3bfd7c1a "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmat10.tfm" 1381187214 608 f124f78ed50a1817738d2adb190cf2bd "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmbt10.tfm" 1381187214 608 f124f78ed50a1817738d2adb190cf2bd "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xydash10.tfm" 1381187214 984 5c01c46b93e3ba8369f3f8edc6e62aef "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyluat10.tfm" 1381187214 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xylubt10.tfm" 1381187214 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxmi.pfb" 1232065820 13806 49b888f4605a088e66b9eb4fee320a6e "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxr.pfb" 1136849748 6339 e2b78706efdc360ee6aec9b6e20211a7 "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/txex.pfb" 1136849748 17531 c91f2d6943f51d7c46d6b7b9cedd50ba "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/txsy.pfb" 1136849748 20336 69267d8a81bca8b24c9b42694a4a28f9 "" + "/usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmb8a.pfb" 1136849748 44729 811d6c62865936705a31c797a1d5dada "" + "/usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmr8a.pfb" 1136849748 46026 6dab18b61c907687b520c72847215a68 "" + "/usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmri8a.pfb" 1136849748 45458 a3faba884469519614ca56ba5f6b1de1 "" + "/usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/t1xb.vf" 1136768653 2144 bab2875eda5b2344ea7b1db74ccc03a4 "" + "/usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/t1xr.vf" 1136768653 2140 99e5b3a34695df6221a167ffa8b498d6 "" + "/usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txmi.vf" 1232065820 960 cfcc9d587b40b769f64408b3ca115941 "" + "/usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txr.vf" 1136768653 904 e582cae2d8ae3f48a0a520440ebcdb51 "" + "/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1461363279 71627 94eb9990bed73c364d7f53f960cc8c5b "" + "/usr/share/texlive/texmf-dist/tex/generic/atbegshi/atbegshi.sty" 1575674566 24708 5584a51a7101caf7e6bbf1fc27d8f7b1 "" + "/usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty" 1576625341 40635 c40361e206be584d448876bba8a64a3b "" + "/usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty" 1576016050 33961 6b5c75130e435b2bfdb9f480a09a39f9 "" + "/usr/share/texlive/texmf-dist/tex/generic/etexcmds/etexcmds.sty" 1576625273 7734 b98cbb34c81f667027c1e3ebdbfce34b "" + "/usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty" 1576625223 8371 9d55b8bd010bc717624922fb3477d92e "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty" 1572645307 492 1994775aa15b0d1289725a0b1bbc2d4c "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/ifpdf.sty" 1572645307 480 5778104efadad304ced77548ca2184b1 "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty" 1573336935 6902 30fdaf7dc5636b8e3afa306210c45cae "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty" 1572645307 1057 525c2192b5febbd8c1f662c9468335bb "" + "/usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty" 1575499628 8356 7bbb2c2373aa810be568c29e333da8ed "" + "/usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty" 1576625065 31769 002a487f55041f8e805cfbf6385ffd97 "" + "/usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty" 1576878844 5412 d5a2436094cd7be85769db90f29250a6 "" + "/usr/share/texlive/texmf-dist/tex/generic/kvsetkeys/kvsetkeys.sty" 1576624944 13807 952b0226d4efca026f0e19dd266dcc22 "" + "/usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty" 1576624883 18552 1e1cc7b75da0dfaacce7cdcb27d306bf "" + "/usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty" 1576015897 19007 15924f7228aca6c6d184b115f4baa231 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex" 1557692582 992 fb3cda354707a54fda62787a411c7c22 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex" 1546728038 43820 bc6cf5aa959817914ace33f5c6232161 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex" 1557692582 19324 c9a64402f22bd8d81821141a357af653 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex" 1546728038 6038 d639d02574be9a72f3c602c2a3510e02 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex" 1546728038 6948 284bbe3c9a7ca0a826c1c03895e69b9f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex" 1546728038 4883 a6f3eb1f71d8c4affaf43a169828b043 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex" 1546728038 2544 3b1b198fd49f01e328adc9162a07b213 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex" 1576793519 44189 1fd6229dad4c898883516c032f2ca5d2 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex" 1546728038 17311 3092579be20ef0f229c42ad3f09da85c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex" 1546728038 21302 d6c4b340248adbe650ebf6ca76bdccca "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex" 1562964315 9690 7585efa5a591822837f837bc5bc35621 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex" 1576793519 33335 942ccafe284041918d36e54696b98aa7 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex" 1546728038 2965 502761b60f43ab2de5ecb2f4625163ae "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex" 1546728038 5196 f8c5c775d4d6e2cb050392127cabda72 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex" 1576793519 20726 ed6ec1d6f0f35e7a93de4e79af83dbce "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex" 1557692582 35249 144a6b9c4df4644618bb3a0a40472608 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex" 1546728038 21989 266e83c51fe41eb8b8d5e6896dc71cc1 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex" 1546728038 8842 5cc856e132fac404805c6da091779283 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex" 1546728038 319 8fc6edce901e074ba09de320a8fc686b "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex" 1546728038 3986 c962be8d57437fcaf853d2babd8ed403 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex" 1546728038 4572 980c82f01c0e3983edadbbc373d304cb "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex" 1546728038 3643 4a4bd51bd85886cc39d4073af8cf77a9 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex" 1546728038 4202 e655aa2657da1088ec7745ece2876c4c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex" 1546728038 3937 20cd45386ca23052ce976464f0ada984 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex" 1546728038 919 da625675781832f2b61a7048a51ef656 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex" 1576793519 11544 2a5d66a3270abf4ef673e8a0b7734a90 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex" 1576967981 187592 7922ceab1864698dec4c84978d5b182f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex" 1546728038 31874 d843d507175f2bdfa3abf01f0349dac8 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex" 1546728038 32995 a4d54c043ae5274ceaaddeb36ad43a6f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex" 1546728038 62281 fd68e6d2c2dc178611c8f4d2d86e79ae "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfint.code.tex" 1557692582 3063 8c415c68a0f3394e45cfeca0b65f6ee6 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex" 1557692582 521 c70cf6ad609de83a27ee7929eb356332 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex" 1557692582 13391 933cab19c6d27039dbfc487330d1005a "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex" 1557692582 104938 15f2d8bdabd6bf9ca70f62cd8e3d4940 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex" 1557692582 10157 218d58ab074e5bd0d027de45ec64cc00 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex" 1576793519 28176 568b081ec39645f2db1a29fbd0c635e2 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex" 1562964315 9054 388d21239a1b6df2cc8beaae31c976b0 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex" 1557692582 3865 cddf7ddc80f018587c55afdcc79fc333 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex" 1557692582 3177 27d85c44fbfe09ff3b2cf2879e3ea434 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex" 1557692582 10925 df50b8a6e5660a585e3a2bf55726dcc8 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex" 1562964315 7787 1750fc3f164703caf31fc8ea9218c67e "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex" 1557692582 3379 cbd0948a550bd7a495a160ca6beee9ed "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex" 1557692582 92405 bba89470858d7b0788a9c09331c39653 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex" 1576793519 36526 453db1f8626a56b5ebb0fad496d6a39f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex" 1576793519 8471 b18959397c76e1e582402ab9f592ed9f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex" 1576793519 21201 46a4dded6619f990ac7347f99fbaac9f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex" 1557692582 16121 9e240115374a8d489f2f786115df83a9 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex" 1576793519 43259 3e05ba63539916af2eaca603c2eda780 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/pgf.revision.tex" 1578520427 465 1f401ab1e7fc6cb7ede39e96c66531fd "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg" 1557692582 926 70ff613fabeb70f5d1673dc0c93987bd "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def" 1557692582 5546 3586827e6032c95512b2a6682d2979a3 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def" 1562964315 12603 c02869ea216d842c29d52fae8738264e "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex" 1557692582 60269 e86bc0081af83a4ad47e4500ee09a2e4 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex" 1557692582 1896 82c274ff520f9e450ccea4e3ef4edc12 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex" 1557692582 7778 a25a32a10ca820357491d4c7b3ac02ea "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex" 1562964315 23777 cb6c8f02f87d86d621f5cb92c44f4998 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex" 1576793519 36815 f7f1772c398f07af2cb741992963045c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex" 1562964315 37439 bd44d50aef702b03193f731207931834 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex" 1557692582 4494 7e5ace0ccf59408f2cf63219a5d36927 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex" 1557692582 7250 03b2b9fb5fa38e7ca5cc3c45860fb210 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex" 1576793519 28309 488ccc6c701bbdd1bf671f708757aa5c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def" 1562964315 6286 1bd76fc45da9929ab2a64f51cba3ab6f "" + "/usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty" 1576624663 7008 f92eaa0a3872ed622bbf538217cd2ab7 "" + "/usr/share/texlive/texmf-dist/tex/generic/xkeyval/keyval.tex" 1403829539 2725 fc34ef3ccb37ba15a640e8fca6190bca "" + "/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex" 1417732693 19231 26434a5656c684f5ffb1f26f98006baa "" + "/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex" 1403829539 7677 6f5ce7c1124cad7ec57d05b2562bd8fe "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xy.sty" 1312310545 4692 1e1bcf75c622af1eefd9169948208302 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xy.tex" 1381187214 115380 413d5f789929a45aab7d12ce0d0aee7d "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyall.tex" 1312310545 1449 24340b6befc66d28ee1ebb657efb5892 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyarrow.tex" 1312310545 22657 990ce136a3cc15728ba417a2e78b25c8 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycmtip.tex" 1312310545 1374 43fb8dc80dd748631d78096701166d76 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycolor.tex" 1312310545 4586 edd672434f45626662368282c0322160 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycurve.tex" 1312310545 109670 d412ee1ff259daefee5e927172e2f9a8 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyframe.tex" 1337903317 24249 186931a828664624939ab0b347e3952c "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xygraph.tex" 1312310545 9619 b7e4d9a6936ba2ad6119a280abde9641 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyidioms.tex" 1312310545 2907 1ee562fde0b53c9cd16f7a604f33fdf0 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyline.tex" 1312310545 10928 c3a572983ccc9fc596b4e9ce454d5652 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xymatrix.tex" 1312310545 22583 25b1e7edeee41f181ee9733429da4a9c "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-co.tex" 1312310545 8442 90cb8a3b00c2081384c1ce988d2ba0a3 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-cu.tex" 1312310545 39762 25a964ebb390bcfcd35c040f477eef1d "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-fr.tex" 1312310545 16485 5686b19cc46d046c885428794ed9c114 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-li.tex" 1312310545 2619 1a12b316e2132654e44ba2cd21def637 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-ro.tex" 1312310545 5290 e16fc85c85f64d0a5c04708bf3312d00 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf.tex" 1312310545 18763 e61049d36bdfccb226f22e582d70d368 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyrecat.tex" 1312310545 1391 c8763fc8e281cb6ecf697988b6608e4a "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyrotate.tex" 1312310545 7008 cb768d8d63a12d35607cbb3c4e7ba163 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xytips.tex" 1381187214 3689 0d51788a4141bc66ab896f7ac63495fd "" + "/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty" 1513722769 12604 3dec726c041422879dc3268237f09026 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1359763108 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" + "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1359763108 13829 94730e64147574077f8ecfea9bb69af4 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1523134290 2211 ca7ce284ab93c8eecdc6029dc5ccbd73 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amscd.sty" 1523134290 5309 0c9ef5db85b924cdbb316f080dfd826e "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty" 1523134290 4161 7f6eb9092061a11f87d08ed13515b48d "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty" 1580683321 85660 baee036978c7a91f4e2bba43f05e5945 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty" 1523134290 4116 32e6abd27229755a83a8b7f18e583890 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty" 1523134290 2432 8ff93b1137020e8f21930562a874ae66 "" + "/usr/share/texlive/texmf-dist/tex/latex/aobs-tikz/tikzlibraryoverlay-beamer-styles.code.tex" 1389658833 4047 82a015585c1ef210fb6750d6322afa7f "" + "/usr/share/texlive/texmf-dist/tex/latex/atveryend/atveryend.sty" 1576191570 19336 ce7ae9438967282886b3b036cfad1e4d "" + "/usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty" 1576625391 3935 57aa3c3e203a5c2effb4d2bd2efbc323 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/article.cls" 1580683321 20023 e427dd9e17e239bf926ef3aab67fe35e "" + "/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty" 1581632200 4947 0c2888dd88121ae675fc6e82213623ba "" + "/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty" 1580683321 5159 892429808d9e0e2b3548aaefd9a06ed0 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty" 1580683321 5050 8933a39ad74377accd18991c5eb90c58 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo" 1580683321 8446 9874cccac5fee462272c582807dbbf56 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty" 1581112666 2821 2c0928feafd5527387e29a1af774d030 "" + "/usr/share/texlive/texmf-dist/tex/latex/carlisle/slashed.sty" 1137109962 5327 8b3c95b5f71136add36a4a0bb1507594 "" + "/usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty" 1425427964 26218 19edeff8cdc2bcb704e8051dc55eb5a7 "" + "/usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1579991033 13886 d1306dcf79a944f6988e688c1785f9ce "" + "/usr/share/texlive/texmf-dist/tex/latex/eso-pic/eso-pic.sty" 1526160256 11991 c1669f88e13f8bb6243df144e456b477 "" + "/usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty" 1548974385 11128 a53805799bebfed6358fc1658a18e41f "" + "/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty" 1578002852 41601 9cf6c5257b1bc7af01a58859749dd37a "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg" 1459978653 1213 620bba36b25224fa9b7e1ccb4ecb76fd "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1465944070 1224 978390e9c2234eab29404bc21b268d1e "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def" 1515537368 17334 520b9b85ad8a2a48eda3f643e27a5179 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty" 1580683321 16932 04729abe63b66ec59ea56edcd722b058 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty" 1580683321 9067 1b996612394a52e1efe89c8bfe8a5892 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/lscape.sty" 1580683321 1753 f80abc75c0e3a4915097779c2649cc98 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty" 1580683321 3976 d7fa7d81d2870d509d25b17d0245e735 "" + "/usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty" 1580250785 17914 4c28a13fc3d975e6e81c9bea1d697276 "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def" 1579642962 50630 3d9728faf8630190cf601ce2cbe470d9 "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty" 1579642962 238752 60dd338d71b6a4ab2192131f73dc908b "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty" 1579642962 13244 0070bcab7b5a88187847128d22faf4d8 "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def" 1579642962 14134 32b36577d311ddb6522413c7581ee968 "" + "/usr/share/texlive/texmf-dist/tex/latex/jknapltx/mathrsfs.sty" 1137110241 300 12fa6f636b617656f2810ee82cb05015 "" + "/usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd" 1137110241 548 cc4e3557704bfed27c7002773fad6c90 "" + "/usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty" 1575152344 22520 c4c2dab203104295e1e618be7e5c0f5b "" + "/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def" 1580854751 25404 9d60f463a00d154207ec0048dee27cf0 "" + "/usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty" 1581719662 4381 04628f3002bdd1d9c43ef984fd60ae18 "" + "/usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty" 1581719662 81717 e93576ac4b24ce6e121ebd6ec6cf2893 "" + "/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1279039959 678 4792914a8f45be57bb98413425e4c7af "" + "/usr/share/texlive/texmf-dist/tex/latex/letltxmacro/letltxmacro.sty" 1575499565 5766 13a9e8766c47f30327caf893ece86ac8 "" + "/usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.ltd.tex" 1546728170 98047 c6fa29828cc60471827afe275c8bd77f "" + "/usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.sty" 1546638616 18060 8cf65af2c4529eed91b5d364b50d3ada "" + "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg" 1568236792 1830 bbaba8afaf42cc048ec4d4ff73467521 "" + "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty" 1568236792 80511 830f3f1d3ab7448dd84233e9c2f6462c "" + "/usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty" 1568236792 77022 32914f01b528131c47be2a1040d3856d "" + "/usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/pgflibrarymatrix.skeleton.code.tex" 1565039202 19612 007f8469df07e9ef0f680e346cc01945 "" + "/usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/tikzlibrarymatrix.skeleton.code.tex" 1565039202 7267 4d597b08b2429acaa1e526052d9509ed "" + "/usr/share/texlive/texmf-dist/tex/latex/ms/everyshi.sty" 1177890616 3878 6aa7c08ff2621006e0603349e40a30a8 "" + "/usr/share/texlive/texmf-dist/tex/latex/multirow/multirow.sty" 1559339157 5486 a1d954b09782ba0acd8a8abfd98e1028 "" + "/usr/share/texlive/texmf-dist/tex/latex/paralist/paralist.sty" 1485124581 14857 82c76ebe8f06becf69ab309565b2a0cb "" + "/usr/share/texlive/texmf-dist/tex/latex/pdflscape/pdflscape.sty" 1575674318 6575 25396d208d8f2b9395d06ef315d5886c "" + "/usr/share/texlive/texmf-dist/tex/latex/pdfpages/pdfpages.sty" 1580249532 54071 88f1e37dc9e1f95352061a066ed07263 "" + "/usr/share/texlive/texmf-dist/tex/latex/pdfpages/pppdftex.def" 1580249532 6418 197ed301e61ce5b7f446e70345a43a62 "" + "/usr/share/texlive/texmf-dist/tex/latex/pdftexcmds/pdftexcmds.sty" 1574631863 19963 36fd8e818f9f0f32e2db8413d4970122 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty" 1546728038 1090 d20f587ea9464d1841bd0d13d3ff9856 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty" 1288312291 410 5bf12ea7330e5f12c445332a4fe9a263 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty" 1546728038 21013 e98e1aaaf40d31632787c2bd25d24b57 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty" 1546728038 989 2cf3da8e8ec55131c49389428d565e37 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty" 1203877327 339 592cf35cba3d400082b8a9a5d0199d70 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty" 1393459310 306 0796eafca5e159e6ec2167a6d22d81b1 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty" 1393459310 443 0b2e781830192df35c0fd357cf13e26e "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty" 1393459310 348 8927fde343487e003b01a4c2ca34073b "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty" 1203727794 274 4cad6e665cc93ac2ac979039a94fa1e1 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty" 1203877327 325 2bcd023400636339210573e2b3ee298b "" + "/usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty" 1156702453 857 6c716f26c5eadfb81029fcd6ce2d45e6 "" + "/usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty" 1576624809 9878 9e94e8fa600d95f9c7731bb21dfb67a4 "" + "/usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty" 1575674187 9715 b051d5b493d9fe5f4bc251462d039e5f "" + "/usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cfg" 1522098998 1015 662b4d7ad816b857a598284525f5c75e "" + "/usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cls" 1522098998 28890 df75e6d37f47b7e27bff3f37375336b3 "" + "/usr/share/texlive/texmf-dist/tex/latex/tools/array.sty" 1580683321 12560 ce3f59ceae9d9a27bfe037d6bf1d903c "" + "/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty" 1580683321 10216 5efd55f2010055e7b7875afd6a75be82 "" + "/usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty" 1580683321 4120 d1680a5ff60d0aea9c327e07c030f4e9 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/omltxmi.fd" 1137111002 492 e7f8afe4428797548d4301de03a1b15f "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/omstxsy.fd" 1137111002 329 6ac7e19535b9f1d64e4d8e3f77dc30a3 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/omxtxex.fd" 1137111002 312 11fe1916b0a13a81a05234a6fc7f8738 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/ot1txr.fd" 1137111002 1271 4e3afbd8e832f2f9c7f064894e6e68e4 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/t1txr.fd" 1137111002 1242 cbf8a0d4f750f9833a0bfb05fb39f1cb "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/txfonts.sty" 1206746551 50381 d367461010070c7a491b1f6979ab2062 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxexa.fd" 1137111002 310 1b00b0b05685b816e4c6caccce437e0d "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxmia.fd" 1137111002 334 87436a82076ca2e35cd305f852507afc "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsya.fd" 1137111002 310 cee07e4964749ccbc77d84fc49726a79 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyb.fd" 1137111002 310 8c5467c8932c259af51b0f116c9734bd "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyc.fd" 1137111002 310 4b5d6fe830337242ef847b3bff48ba21 "" + "/usr/share/texlive/texmf-dist/tex/latex/url/url.sty" 1388531844 12796 8edb7d69a20b857904dd0ea757c14ec9 "" + "/usr/share/texlive/texmf-dist/tex/latex/varwidth/varwidth.sty" 1238697683 10894 d359a13923460b2a73d4312d613554c8 "" + "/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty" 1463002160 55589 34128738f682d033422ca125f82e5d62 "" + "/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty" 1417732693 4962 9c1069474ff71dbc47d5006555e352d3 "" + "/usr/share/texlive/texmf-dist/web2c/texmf.cnf" 1581979058 38841 ce3692aa899bb693b90b87eaa5d4d84e "" + "/usr/share/texmf/web2c/texmf.cnf" 1581979058 38841 ce3692aa899bb693b90b87eaa5d4d84e "" + "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1619433582 4770781 1ed1abab22da9c3e2cc82e4db562318b "" + "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1619433611 8255863 afe1ed795207f6401d11bafd6327aa55 "" + "algo.aux" 1620305767 767 9191aef204e325cc808d7c85cedac35f "pdflatex" + "algo.out" 1620305767 43 8eacde2f35419fc00651f55d16e47ae8 "pdflatex" + "algo.tex" 1621585209 3156 4070ef1cd3442b3ab588aedcc8a306bd "" + (generated) + "algo.aux" + "algo.log" + "algo.pdf" + "algo.out" diff --git a/buch/papers/multiplikation/tikz_formulas/algo.fls b/buch/papers/multiplikation/tikz_formulas/algo.fls new file mode 100644 index 0000000..16d387b --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo.fls @@ -0,0 +1,438 @@ +PWD /home/nunigan/Documents/MSE/FS21/SeminarMatrizen/buch/papers/multiplikation/tikz_formulas +INPUT /etc/texmf/web2c/texmf.cnf +INPUT /usr/share/texmf/web2c/texmf.cnf +INPUT /usr/share/texlive/texmf-dist/web2c/texmf.cnf +INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt +INPUT algo.tex +OUTPUT algo.log +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xkeyval/keyval.tex +INPUT /dev/null +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/article.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/article.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/size10.clo +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/size10.clo +INPUT /usr/share/texlive/texmf-dist/tex/latex/varwidth/varwidth.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/varwidth/varwidth.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +INPUT /usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm1000.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/mathrsfs.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/mathrsfs.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.ltd.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.ltd.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amscd.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amscd.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/txfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/txfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xy.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xy.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xy.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyrecat.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyidioms.tex +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xydash10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyatip10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybtip10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybsql10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycirc10.tfm +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifpdf.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifpdf.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyall.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyall.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycurve.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycurve.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyframe.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyframe.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycmtip.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycmtip.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xytips.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xytips.tex +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmat10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmbt10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyluat10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xylubt10.tfm +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyline.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyline.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyrotate.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyrotate.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycolor.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycolor.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xymatrix.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xymatrix.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyarrow.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyarrow.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xygraph.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xygraph.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-co.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-cu.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-fr.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-li.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-ro.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/paralist/paralist.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/paralist/paralist.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdftexcmds/pdftexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdftexcmds/pdftexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvsetkeys/kvsetkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvsetkeys/kvsetkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/letltxmacro/letltxmacro.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/letltxmacro/letltxmacro.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/etexcmds/etexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/etexcmds/etexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/url/url.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/url/url.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/atbegshi/atbegshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/atbegshi/atbegshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/atveryend/atveryend.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/atveryend/atveryend.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/array.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/array.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/ms/everyshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/ms/everyshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/pgf.revision.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/pgf.revision.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfint.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/carlisle/slashed.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/carlisle/slashed.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pdfpages.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pdfpages.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/eso-pic/eso-pic.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/eso-pic/eso-pic.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pppdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pppdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/aobs-tikz/tikzlibraryoverlay-beamer-styles.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/aobs-tikz/tikzlibraryoverlay-beamer-styles.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/tikzlibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/tikzlibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/pgflibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/pgflibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/multirow/multirow.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/multirow/multirow.sty +INPUT algo.aux +INPUT algo.aux +OUTPUT algo.aux +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omltxmi.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omltxmi.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omstxsy.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omstxsy.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omxtxex.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omxtxex.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxexa.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxexa.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/t1txr.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/t1txr.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT /usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii +INPUT /usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii +INPUT /usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/ot1txr.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/ot1txr.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsya.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsya.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyb.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyb.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs7.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs5.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxmia.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxmia.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyc.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyc.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty +INPUT algo.out +INPUT algo.out +INPUT algo.out +INPUT algo.out +OUTPUT algo.pdf +INPUT ./algo.out +INPUT ./algo.out +OUTPUT algo.out +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdflscape/pdflscape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdflscape/pdflscape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/lscape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/lscape.sty +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT /var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/t1xb.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT algo.aux +INPUT ./algo.out +INPUT ./algo.out +INPUT /usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxmi.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxr.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/txex.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/txsy.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmb8a.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmr8a.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmri8a.pfb diff --git a/buch/papers/multiplikation/tikz_formulas/algo.pdf b/buch/papers/multiplikation/tikz_formulas/algo.pdf Binary files differnew file mode 100644 index 0000000..f711224 --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo.pdf diff --git a/buch/papers/multiplikation/tikz_formulas/algo.tex b/buch/papers/multiplikation/tikz_formulas/algo.tex new file mode 100755 index 0000000..1e437c2 --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo.tex @@ -0,0 +1,131 @@ +\documentclass[border=10pt,varwidth]{standalone} +\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{times} +\usepackage{geometry} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathrsfs} +\usepackage{amsfonts} +\usepackage{amsthm} +\usepackage{lipsum} +\usepackage{amscd} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{textcomp} +\usepackage{txfonts} +\usepackage[all]{xy} +\usepackage{paralist} +\usepackage[colorlinks=true]{hyperref} +\usepackage{array} +\usepackage{tikz} +\usepackage{slashed} +\usepackage{pdfpages} +\usepackage{cite} +\usepackage{url} +\usepackage{amsmath,amsfonts,amssymb} +\usepackage{tikz} +\usetikzlibrary{arrows,matrix,positioning} +\usetikzlibrary{overlay-beamer-styles} +\usetikzlibrary{matrix.skeleton} +\usetikzlibrary{automata,positioning} +\usepackage{listings} +\usepackage{multirow} +\usepackage{color} + +\begin{document} + +$ +A= +\begin{bmatrix} +A_{11} & A_{12}\\ +A_{21} & A_{22} +\end{bmatrix}, +B= +\begin{bmatrix} +B_{11} & B_{12}\\ +B_{21} & B_{22} +\end{bmatrix}, +C= +\begin{bmatrix} +C_{11} & C_{12}\\ +C_{21} & C_{22} +\end{bmatrix} +$ + +\medskip +$ +A \cdot B = C +$ + +\medskip +$ +C_{11} = A_{11} \cdot B_{11} + A_{12} \cdot B_{21}\\ +C_{12} = A_{11} \cdot B_{12} + A_{12} \cdot B_{22}\\ +C_{21} = A_{21} \cdot B_{11} + A_{22} \cdot B_{21}\\ +C_{22} = A_{21} \cdot B_{12} + A_{22} \cdot B_{22} +$ + +\medskip +\begin{math} +\begin{aligned} +\text{I} &= (A_{11} + A_{22}) \cdot (B_{11} + B_{22}) \\ +\text{II} &= (A_{21} + A_{22}) \cdot B_{11} \\ +\text{III} &= A_{11} \cdot (B_{12}-B_{22}) \\ +\text{IV} &= A_{22} \cdot (-B_{11}+B_{21}) \\ +\text{V} &= (A_{11} + A_{12}) \cdot B_{22} \\ +\text{VI} &= (-A_{11} + A_{21}) \cdot (B_{11} + B_{12})) \\ +\text{VII} &= (A_{12} - A_{22}) \cdot (B_{21} + B_{22}) \\ +\end{aligned} +\end{math} + + +\medskip +\begin{math} +\begin{aligned} +C_{11} &= \text{I} + \text{IV} - \text{V} + \text{VII} \\ +C_{21} &= \text{II} + \text{IV} \\ +C_{12} &= \text{III} + \text{V}\\ +C_{22} &= \text{I} + \text{III} - \text{II} + \text{VI} \\ +\end{aligned} +\end{math} + + +\medskip +\begin{math} +\begin{aligned} +C_{11} &= \text{II} + \text{IV} \\ +C_{11} &= (A_{11} + A_{22}) \cdot (B_{11} + B_{22}) + A_{22} \cdot (-B_{11}+B_{21}) - (A_{11} + A_{12}) \cdot B_{22} + (A_{12} - A_{22}) \cdot (B_{21} + B_{22})C_{21} \\ +C_{11} &= A_{11}B_{11} + A_{11}B_{22} + A_{22}B_{11} + A_{22}B_{22} -A_{22}B_{11}+A_{22}B_{21} - A_{11}B_{22} - A_{12}B_{22}+ A_{12}B_{21} + A_{12}B_{22} - A_{22}B_{21} - A_{22}B_{22} \\ +C_{11} &= A_{11}B_{11} + A_{12}B_{21} +\end{aligned} +\end{math} + +\section{Winograd} + +$ +x_1 y_1 + x_2 y_2 = (x_1 +y_2)(y_1 + x_2)-x_1 x_2 - y_1 y_2 +$ + +$ +x = (x_1, \cdots, x_n), y=(y_1, \cdots, y_n) +$ + +\[ +\xi = \sum_{j=1}^{ \lfloor n/2 \rfloor} x_{2j-1} \cdot x_{2j} +\] + +\[ +\eta = \sum_{j=1}^{ \lfloor n/2 \rfloor} y_{2j-1} \cdot y_{2j} +\] + +\[ +\langle x,y \rangle = +\begin{cases} + \displaystyle \sum_{j=1}^{ \lfloor n/2 \rfloor} (x_{2j-1} + y_{2j})(x_{2j}+y_{2j-1})-\xi - \eta & \text{if $n$ is even}\\ +\displaystyle \sum_{j=1}^{ \lfloor n/2 \rfloor} (x_{2j-1} + y_{2j})(x_{2j}+y_{2j-1})-\xi - \eta + x_n y_n & \text{if $n$ is odd} +\end{cases} +\] + +\end{document} diff --git a/buch/papers/multiplikation/tikz_formulas/algo_graph.fdb_latexmk b/buch/papers/multiplikation/tikz_formulas/algo_graph.fdb_latexmk new file mode 100644 index 0000000..ddfa880 --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo_graph.fdb_latexmk @@ -0,0 +1,245 @@ +# Fdb version 3 +["pdflatex"] 1621585121 "algo_graph.tex" "algo_graph.pdf" "algo_graph" 1621585184 + "/dev/null" 1621583990 0 d41d8cd98f00b204e9800998ecf8427e "" + "/etc/texmf/web2c/texmf.cnf" 1619433543 475 c0e671620eb5563b2130f56340a5fde8 "" + "/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc" 1165713224 4850 80dc9bab7f31fb78a000ccfed0e27cab "" + "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm1000.tfm" 1136768653 3584 adb004a0c8e7c46ee66cad73671f37b4 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm" 1229303445 688 37338d6ab346c2f1466b29e195316aa4 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs5.tfm" 1229303445 684 3a51bd4fd9600428d5264cf25f04bb9a "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs7.tfm" 1229303445 692 1b6510779f0f05e9cbf03e0f6c8361e6 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm" 1136768653 1056 e2202af076e43d03fc17f87e104021b0 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm" 1136768653 4452 0fd0a792eaab7113e4d4f1b941ff0367 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm" 1136768653 4640 ce59980bcbe9e6236fab46d0b5212c7e "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm" 1136768653 1004 c0e991f864f31f017ea4ff9e451b76d4 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm" 1136768653 6716 6d25a377562601272906e3bfe6b2817a "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm" 1136768653 1080 b674b4ba143004461509a754a0984b67 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm" 1136768653 688 f56006d6e56f46e63d9f63252958b828 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm" 1136768653 2584 cf4a6a7c2a518d47468fe29ef0913ba0 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm" 1232065820 1944 f854e259cb2839e49d4aa2949544a6e1 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm" 1136768653 1180 72784d0ee5a983fba99a0986b31b0493 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm" 1136768653 2408 aec793a3c45e495f7ad15b227c91f508 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm" 1136768653 1268 1d124f224979493f8fd017a7597ea1cd "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm" 1136768653 972 2c9ffac4bbd20f91c01aaef9bf3f8710 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm" 1136768653 988 098ca7e8cc5647b9ac21b82dbdce1f01 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm" 1136768653 1084 75e807e9e71f7a312e4e1187dce5e93b "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyatip10.tfm" 1381187214 608 50246cc71b0635b0ba0a5c10a0bf4257 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybsql10.tfm" 1381187214 608 4db60f15ea23b4ec2d796c6d568a63fa "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybtip10.tfm" 1381187214 608 50246cc71b0635b0ba0a5c10a0bf4257 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycirc10.tfm" 1381187214 844 3393210079fb4ed9347e214b3bfd7c1a "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmat10.tfm" 1381187214 608 f124f78ed50a1817738d2adb190cf2bd "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmbt10.tfm" 1381187214 608 f124f78ed50a1817738d2adb190cf2bd "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xydash10.tfm" 1381187214 984 5c01c46b93e3ba8369f3f8edc6e62aef "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyluat10.tfm" 1381187214 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xylubt10.tfm" 1381187214 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxr.pfb" 1136849748 6339 e2b78706efdc360ee6aec9b6e20211a7 "" + "/usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmr8a.pfb" 1136849748 46026 6dab18b61c907687b520c72847215a68 "" + "/usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmri8a.pfb" 1136849748 45458 a3faba884469519614ca56ba5f6b1de1 "" + "/usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/t1xr.vf" 1136768653 2140 99e5b3a34695df6221a167ffa8b498d6 "" + "/usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txmi.vf" 1232065820 960 cfcc9d587b40b769f64408b3ca115941 "" + "/usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txr.vf" 1136768653 904 e582cae2d8ae3f48a0a520440ebcdb51 "" + "/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1461363279 71627 94eb9990bed73c364d7f53f960cc8c5b "" + "/usr/share/texlive/texmf-dist/tex/generic/atbegshi/atbegshi.sty" 1575674566 24708 5584a51a7101caf7e6bbf1fc27d8f7b1 "" + "/usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty" 1576625341 40635 c40361e206be584d448876bba8a64a3b "" + "/usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty" 1576016050 33961 6b5c75130e435b2bfdb9f480a09a39f9 "" + "/usr/share/texlive/texmf-dist/tex/generic/etexcmds/etexcmds.sty" 1576625273 7734 b98cbb34c81f667027c1e3ebdbfce34b "" + "/usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty" 1576625223 8371 9d55b8bd010bc717624922fb3477d92e "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty" 1572645307 492 1994775aa15b0d1289725a0b1bbc2d4c "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/ifpdf.sty" 1572645307 480 5778104efadad304ced77548ca2184b1 "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty" 1573336935 6902 30fdaf7dc5636b8e3afa306210c45cae "" + "/usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty" 1572645307 1057 525c2192b5febbd8c1f662c9468335bb "" + "/usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty" 1575499628 8356 7bbb2c2373aa810be568c29e333da8ed "" + "/usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty" 1576625065 31769 002a487f55041f8e805cfbf6385ffd97 "" + "/usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty" 1576878844 5412 d5a2436094cd7be85769db90f29250a6 "" + "/usr/share/texlive/texmf-dist/tex/generic/kvsetkeys/kvsetkeys.sty" 1576624944 13807 952b0226d4efca026f0e19dd266dcc22 "" + "/usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty" 1576624883 18552 1e1cc7b75da0dfaacce7cdcb27d306bf "" + "/usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty" 1576015897 19007 15924f7228aca6c6d184b115f4baa231 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex" 1557692582 992 fb3cda354707a54fda62787a411c7c22 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex" 1546728038 43820 bc6cf5aa959817914ace33f5c6232161 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex" 1557692582 19324 c9a64402f22bd8d81821141a357af653 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex" 1546728038 6038 d639d02574be9a72f3c602c2a3510e02 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex" 1546728038 6948 284bbe3c9a7ca0a826c1c03895e69b9f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex" 1546728038 4883 a6f3eb1f71d8c4affaf43a169828b043 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex" 1546728038 2544 3b1b198fd49f01e328adc9162a07b213 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex" 1576793519 44189 1fd6229dad4c898883516c032f2ca5d2 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex" 1546728038 17311 3092579be20ef0f229c42ad3f09da85c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex" 1546728038 21302 d6c4b340248adbe650ebf6ca76bdccca "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex" 1562964315 9690 7585efa5a591822837f837bc5bc35621 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex" 1576793519 33335 942ccafe284041918d36e54696b98aa7 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex" 1546728038 2965 502761b60f43ab2de5ecb2f4625163ae "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex" 1546728038 5196 f8c5c775d4d6e2cb050392127cabda72 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex" 1576793519 20726 ed6ec1d6f0f35e7a93de4e79af83dbce "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex" 1557692582 35249 144a6b9c4df4644618bb3a0a40472608 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex" 1546728038 21989 266e83c51fe41eb8b8d5e6896dc71cc1 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex" 1546728038 8842 5cc856e132fac404805c6da091779283 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex" 1546728038 319 8fc6edce901e074ba09de320a8fc686b "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex" 1546728038 3986 c962be8d57437fcaf853d2babd8ed403 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex" 1546728038 4572 980c82f01c0e3983edadbbc373d304cb "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex" 1546728038 3643 4a4bd51bd85886cc39d4073af8cf77a9 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex" 1546728038 4202 e655aa2657da1088ec7745ece2876c4c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex" 1546728038 3937 20cd45386ca23052ce976464f0ada984 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex" 1546728038 919 da625675781832f2b61a7048a51ef656 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex" 1576793519 11544 2a5d66a3270abf4ef673e8a0b7734a90 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex" 1576967981 187592 7922ceab1864698dec4c84978d5b182f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex" 1546728038 31874 d843d507175f2bdfa3abf01f0349dac8 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex" 1546728038 32995 a4d54c043ae5274ceaaddeb36ad43a6f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex" 1546728038 62281 fd68e6d2c2dc178611c8f4d2d86e79ae "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfint.code.tex" 1557692582 3063 8c415c68a0f3394e45cfeca0b65f6ee6 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex" 1557692582 521 c70cf6ad609de83a27ee7929eb356332 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex" 1557692582 13391 933cab19c6d27039dbfc487330d1005a "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex" 1557692582 104938 15f2d8bdabd6bf9ca70f62cd8e3d4940 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex" 1557692582 10157 218d58ab074e5bd0d027de45ec64cc00 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex" 1576793519 28176 568b081ec39645f2db1a29fbd0c635e2 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex" 1562964315 9054 388d21239a1b6df2cc8beaae31c976b0 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex" 1557692582 3865 cddf7ddc80f018587c55afdcc79fc333 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex" 1557692582 3177 27d85c44fbfe09ff3b2cf2879e3ea434 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex" 1557692582 10925 df50b8a6e5660a585e3a2bf55726dcc8 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex" 1562964315 7787 1750fc3f164703caf31fc8ea9218c67e "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex" 1557692582 3379 cbd0948a550bd7a495a160ca6beee9ed "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex" 1557692582 92405 bba89470858d7b0788a9c09331c39653 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex" 1576793519 36526 453db1f8626a56b5ebb0fad496d6a39f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex" 1576793519 8471 b18959397c76e1e582402ab9f592ed9f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex" 1576793519 21201 46a4dded6619f990ac7347f99fbaac9f "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex" 1557692582 16121 9e240115374a8d489f2f786115df83a9 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex" 1576793519 43259 3e05ba63539916af2eaca603c2eda780 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/pgf.revision.tex" 1578520427 465 1f401ab1e7fc6cb7ede39e96c66531fd "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg" 1557692582 926 70ff613fabeb70f5d1673dc0c93987bd "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def" 1557692582 5546 3586827e6032c95512b2a6682d2979a3 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def" 1562964315 12603 c02869ea216d842c29d52fae8738264e "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex" 1557692582 60269 e86bc0081af83a4ad47e4500ee09a2e4 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex" 1557692582 1896 82c274ff520f9e450ccea4e3ef4edc12 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex" 1557692582 7778 a25a32a10ca820357491d4c7b3ac02ea "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex" 1562964315 23777 cb6c8f02f87d86d621f5cb92c44f4998 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex" 1576793519 36815 f7f1772c398f07af2cb741992963045c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex" 1562964315 37439 bd44d50aef702b03193f731207931834 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex" 1557692582 4494 7e5ace0ccf59408f2cf63219a5d36927 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex" 1557692582 7250 03b2b9fb5fa38e7ca5cc3c45860fb210 "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex" 1576793519 28309 488ccc6c701bbdd1bf671f708757aa5c "" + "/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def" 1562964315 6286 1bd76fc45da9929ab2a64f51cba3ab6f "" + "/usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty" 1576624663 7008 f92eaa0a3872ed622bbf538217cd2ab7 "" + "/usr/share/texlive/texmf-dist/tex/generic/xkeyval/keyval.tex" 1403829539 2725 fc34ef3ccb37ba15a640e8fca6190bca "" + "/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex" 1417732693 19231 26434a5656c684f5ffb1f26f98006baa "" + "/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex" 1403829539 7677 6f5ce7c1124cad7ec57d05b2562bd8fe "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xy.sty" 1312310545 4692 1e1bcf75c622af1eefd9169948208302 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xy.tex" 1381187214 115380 413d5f789929a45aab7d12ce0d0aee7d "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyall.tex" 1312310545 1449 24340b6befc66d28ee1ebb657efb5892 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyarrow.tex" 1312310545 22657 990ce136a3cc15728ba417a2e78b25c8 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycmtip.tex" 1312310545 1374 43fb8dc80dd748631d78096701166d76 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycolor.tex" 1312310545 4586 edd672434f45626662368282c0322160 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycurve.tex" 1312310545 109670 d412ee1ff259daefee5e927172e2f9a8 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyframe.tex" 1337903317 24249 186931a828664624939ab0b347e3952c "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xygraph.tex" 1312310545 9619 b7e4d9a6936ba2ad6119a280abde9641 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyidioms.tex" 1312310545 2907 1ee562fde0b53c9cd16f7a604f33fdf0 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyline.tex" 1312310545 10928 c3a572983ccc9fc596b4e9ce454d5652 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xymatrix.tex" 1312310545 22583 25b1e7edeee41f181ee9733429da4a9c "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-co.tex" 1312310545 8442 90cb8a3b00c2081384c1ce988d2ba0a3 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-cu.tex" 1312310545 39762 25a964ebb390bcfcd35c040f477eef1d "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-fr.tex" 1312310545 16485 5686b19cc46d046c885428794ed9c114 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-li.tex" 1312310545 2619 1a12b316e2132654e44ba2cd21def637 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-ro.tex" 1312310545 5290 e16fc85c85f64d0a5c04708bf3312d00 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf.tex" 1312310545 18763 e61049d36bdfccb226f22e582d70d368 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyrecat.tex" 1312310545 1391 c8763fc8e281cb6ecf697988b6608e4a "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyrotate.tex" 1312310545 7008 cb768d8d63a12d35607cbb3c4e7ba163 "" + "/usr/share/texlive/texmf-dist/tex/generic/xypic/xytips.tex" 1381187214 3689 0d51788a4141bc66ab896f7ac63495fd "" + "/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty" 1513722769 12604 3dec726c041422879dc3268237f09026 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1359763108 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" + "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1359763108 13829 94730e64147574077f8ecfea9bb69af4 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1523134290 2211 ca7ce284ab93c8eecdc6029dc5ccbd73 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amscd.sty" 1523134290 5309 0c9ef5db85b924cdbb316f080dfd826e "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty" 1523134290 4161 7f6eb9092061a11f87d08ed13515b48d "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty" 1580683321 85660 baee036978c7a91f4e2bba43f05e5945 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty" 1523134290 4116 32e6abd27229755a83a8b7f18e583890 "" + "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty" 1523134290 2432 8ff93b1137020e8f21930562a874ae66 "" + "/usr/share/texlive/texmf-dist/tex/latex/aobs-tikz/tikzlibraryoverlay-beamer-styles.code.tex" 1389658833 4047 82a015585c1ef210fb6750d6322afa7f "" + "/usr/share/texlive/texmf-dist/tex/latex/atveryend/atveryend.sty" 1576191570 19336 ce7ae9438967282886b3b036cfad1e4d "" + "/usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty" 1576625391 3935 57aa3c3e203a5c2effb4d2bd2efbc323 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/article.cls" 1580683321 20023 e427dd9e17e239bf926ef3aab67fe35e "" + "/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty" 1581632200 4947 0c2888dd88121ae675fc6e82213623ba "" + "/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty" 1580683321 5159 892429808d9e0e2b3548aaefd9a06ed0 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty" 1580683321 5050 8933a39ad74377accd18991c5eb90c58 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo" 1580683321 8446 9874cccac5fee462272c582807dbbf56 "" + "/usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty" 1581112666 2821 2c0928feafd5527387e29a1af774d030 "" + "/usr/share/texlive/texmf-dist/tex/latex/carlisle/slashed.sty" 1137109962 5327 8b3c95b5f71136add36a4a0bb1507594 "" + "/usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty" 1425427964 26218 19edeff8cdc2bcb704e8051dc55eb5a7 "" + "/usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1579991033 13886 d1306dcf79a944f6988e688c1785f9ce "" + "/usr/share/texlive/texmf-dist/tex/latex/eso-pic/eso-pic.sty" 1526160256 11991 c1669f88e13f8bb6243df144e456b477 "" + "/usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty" 1548974385 11128 a53805799bebfed6358fc1658a18e41f "" + "/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty" 1578002852 41601 9cf6c5257b1bc7af01a58859749dd37a "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg" 1459978653 1213 620bba36b25224fa9b7e1ccb4ecb76fd "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1465944070 1224 978390e9c2234eab29404bc21b268d1e "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def" 1515537368 17334 520b9b85ad8a2a48eda3f643e27a5179 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty" 1580683321 16932 04729abe63b66ec59ea56edcd722b058 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty" 1580683321 9067 1b996612394a52e1efe89c8bfe8a5892 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/lscape.sty" 1580683321 1753 f80abc75c0e3a4915097779c2649cc98 "" + "/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty" 1580683321 3976 d7fa7d81d2870d509d25b17d0245e735 "" + "/usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty" 1580250785 17914 4c28a13fc3d975e6e81c9bea1d697276 "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def" 1579642962 50630 3d9728faf8630190cf601ce2cbe470d9 "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty" 1579642962 238752 60dd338d71b6a4ab2192131f73dc908b "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty" 1579642962 13244 0070bcab7b5a88187847128d22faf4d8 "" + "/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def" 1579642962 14134 32b36577d311ddb6522413c7581ee968 "" + "/usr/share/texlive/texmf-dist/tex/latex/jknapltx/mathrsfs.sty" 1137110241 300 12fa6f636b617656f2810ee82cb05015 "" + "/usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd" 1137110241 548 cc4e3557704bfed27c7002773fad6c90 "" + "/usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty" 1575152344 22520 c4c2dab203104295e1e618be7e5c0f5b "" + "/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def" 1580854751 25404 9d60f463a00d154207ec0048dee27cf0 "" + "/usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty" 1581719662 4381 04628f3002bdd1d9c43ef984fd60ae18 "" + "/usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty" 1581719662 81717 e93576ac4b24ce6e121ebd6ec6cf2893 "" + "/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1279039959 678 4792914a8f45be57bb98413425e4c7af "" + "/usr/share/texlive/texmf-dist/tex/latex/letltxmacro/letltxmacro.sty" 1575499565 5766 13a9e8766c47f30327caf893ece86ac8 "" + "/usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.ltd.tex" 1546728170 98047 c6fa29828cc60471827afe275c8bd77f "" + "/usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.sty" 1546638616 18060 8cf65af2c4529eed91b5d364b50d3ada "" + "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg" 1568236792 1830 bbaba8afaf42cc048ec4d4ff73467521 "" + "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty" 1568236792 80511 830f3f1d3ab7448dd84233e9c2f6462c "" + "/usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty" 1568236792 77022 32914f01b528131c47be2a1040d3856d "" + "/usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/pgflibrarymatrix.skeleton.code.tex" 1565039202 19612 007f8469df07e9ef0f680e346cc01945 "" + "/usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/tikzlibrarymatrix.skeleton.code.tex" 1565039202 7267 4d597b08b2429acaa1e526052d9509ed "" + "/usr/share/texlive/texmf-dist/tex/latex/ms/everyshi.sty" 1177890616 3878 6aa7c08ff2621006e0603349e40a30a8 "" + "/usr/share/texlive/texmf-dist/tex/latex/multirow/multirow.sty" 1559339157 5486 a1d954b09782ba0acd8a8abfd98e1028 "" + "/usr/share/texlive/texmf-dist/tex/latex/paralist/paralist.sty" 1485124581 14857 82c76ebe8f06becf69ab309565b2a0cb "" + "/usr/share/texlive/texmf-dist/tex/latex/pdflscape/pdflscape.sty" 1575674318 6575 25396d208d8f2b9395d06ef315d5886c "" + "/usr/share/texlive/texmf-dist/tex/latex/pdfpages/pdfpages.sty" 1580249532 54071 88f1e37dc9e1f95352061a066ed07263 "" + "/usr/share/texlive/texmf-dist/tex/latex/pdfpages/pppdftex.def" 1580249532 6418 197ed301e61ce5b7f446e70345a43a62 "" + "/usr/share/texlive/texmf-dist/tex/latex/pdftexcmds/pdftexcmds.sty" 1574631863 19963 36fd8e818f9f0f32e2db8413d4970122 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty" 1546728038 1090 d20f587ea9464d1841bd0d13d3ff9856 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty" 1288312291 410 5bf12ea7330e5f12c445332a4fe9a263 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty" 1546728038 21013 e98e1aaaf40d31632787c2bd25d24b57 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty" 1546728038 989 2cf3da8e8ec55131c49389428d565e37 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty" 1203877327 339 592cf35cba3d400082b8a9a5d0199d70 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty" 1393459310 306 0796eafca5e159e6ec2167a6d22d81b1 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty" 1393459310 443 0b2e781830192df35c0fd357cf13e26e "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty" 1393459310 348 8927fde343487e003b01a4c2ca34073b "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty" 1203727794 274 4cad6e665cc93ac2ac979039a94fa1e1 "" + "/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty" 1203877327 325 2bcd023400636339210573e2b3ee298b "" + "/usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty" 1156702453 857 6c716f26c5eadfb81029fcd6ce2d45e6 "" + "/usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty" 1576624809 9878 9e94e8fa600d95f9c7731bb21dfb67a4 "" + "/usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty" 1575674187 9715 b051d5b493d9fe5f4bc251462d039e5f "" + "/usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cfg" 1522098998 1015 662b4d7ad816b857a598284525f5c75e "" + "/usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cls" 1522098998 28890 df75e6d37f47b7e27bff3f37375336b3 "" + "/usr/share/texlive/texmf-dist/tex/latex/tools/array.sty" 1580683321 12560 ce3f59ceae9d9a27bfe037d6bf1d903c "" + "/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty" 1580683321 10216 5efd55f2010055e7b7875afd6a75be82 "" + "/usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty" 1580683321 4120 d1680a5ff60d0aea9c327e07c030f4e9 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/omltxmi.fd" 1137111002 492 e7f8afe4428797548d4301de03a1b15f "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/omstxsy.fd" 1137111002 329 6ac7e19535b9f1d64e4d8e3f77dc30a3 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/omxtxex.fd" 1137111002 312 11fe1916b0a13a81a05234a6fc7f8738 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/ot1txr.fd" 1137111002 1271 4e3afbd8e832f2f9c7f064894e6e68e4 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/t1txr.fd" 1137111002 1242 cbf8a0d4f750f9833a0bfb05fb39f1cb "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/txfonts.sty" 1206746551 50381 d367461010070c7a491b1f6979ab2062 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxexa.fd" 1137111002 310 1b00b0b05685b816e4c6caccce437e0d "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxmia.fd" 1137111002 334 87436a82076ca2e35cd305f852507afc "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsya.fd" 1137111002 310 cee07e4964749ccbc77d84fc49726a79 "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyb.fd" 1137111002 310 8c5467c8932c259af51b0f116c9734bd "" + "/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyc.fd" 1137111002 310 4b5d6fe830337242ef847b3bff48ba21 "" + "/usr/share/texlive/texmf-dist/tex/latex/url/url.sty" 1388531844 12796 8edb7d69a20b857904dd0ea757c14ec9 "" + "/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty" 1463002160 55589 34128738f682d033422ca125f82e5d62 "" + "/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty" 1417732693 4962 9c1069474ff71dbc47d5006555e352d3 "" + "/usr/share/texlive/texmf-dist/web2c/texmf.cnf" 1581979058 38841 ce3692aa899bb693b90b87eaa5d4d84e "" + "/usr/share/texmf/web2c/texmf.cnf" 1581979058 38841 ce3692aa899bb693b90b87eaa5d4d84e "" + "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1619433582 4770781 1ed1abab22da9c3e2cc82e4db562318b "" + "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1619433611 8255863 afe1ed795207f6401d11bafd6327aa55 "" + "algo_graph.aux" 1621585123 662 b2b94621371df8d9296b8bf5bec1b851 "pdflatex" + "algo_graph.out" 1621585122 0 d41d8cd98f00b204e9800998ecf8427e "pdflatex" + "algo_graph.tex" 1621585144 5895 0e03594e6e25b7f3671b72694de0d3f4 "" + (generated) + "algo_graph.out" + "algo_graph.pdf" + "algo_graph.aux" + "algo_graph.log" diff --git a/buch/papers/multiplikation/tikz_formulas/algo_graph.fls b/buch/papers/multiplikation/tikz_formulas/algo_graph.fls new file mode 100644 index 0000000..bd1c14e --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo_graph.fls @@ -0,0 +1,485 @@ +PWD /home/nunigan/Documents/MSE/FS21/SeminarMatrizen/buch/papers/multiplikation/tikz_formulas +INPUT /etc/texmf/web2c/texmf.cnf +INPUT /usr/share/texmf/web2c/texmf.cnf +INPUT /usr/share/texlive/texmf-dist/web2c/texmf.cnf +INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt +INPUT algo_graph.tex +OUTPUT algo_graph.log +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/shellesc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifluatex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xkeyval/keyval.tex +INPUT /dev/null +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/standalone/standalone.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/article.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/article.cls +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/size10.clo +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/size10.clo +INPUT /usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +INPUT /usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm1000.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/mathrsfs.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/mathrsfs.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.ltd.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/lipsum/lipsum.ltd.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amscd.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amscd.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/txfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/txfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xy.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xy.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xy.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyrecat.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyidioms.tex +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xydash10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyatip10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybtip10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybsql10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycirc10.tfm +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifpdf.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/iftex/ifpdf.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyall.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyall.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycurve.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycurve.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyframe.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyframe.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycmtip.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycmtip.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xytips.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xytips.tex +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmat10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmbt10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyluat10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xylubt10.tfm +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyline.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyline.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyrotate.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyrotate.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycolor.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xycolor.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xymatrix.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xymatrix.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyarrow.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xyarrow.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xygraph.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xygraph.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-co.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-cu.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-fr.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-li.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-ro.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/paralist/paralist.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/paralist/paralist.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdftexcmds/pdftexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdftexcmds/pdftexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvsetkeys/kvsetkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvsetkeys/kvsetkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/letltxmacro/letltxmacro.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/letltxmacro/letltxmacro.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/etexcmds/etexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/etexcmds/etexcmds.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/url/url.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/url/url.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/atbegshi/atbegshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/atbegshi/atbegshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/atveryend/atveryend.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/atveryend/atveryend.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/array.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/array.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/ms/everyshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/ms/everyshi.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/pgf.revision.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/pgf.revision.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfint.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/carlisle/slashed.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/carlisle/slashed.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pdfpages.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pdfpages.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/eso-pic/eso-pic.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/eso-pic/eso-pic.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pppdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdfpages/pppdftex.def +INPUT /usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/aobs-tikz/tikzlibraryoverlay-beamer-styles.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/aobs-tikz/tikzlibraryoverlay-beamer-styles.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/tikzlibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/tikzlibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/pgflibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/matrix-skeleton/pgflibrarymatrix.skeleton.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/multirow/multirow.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/multirow/multirow.sty +INPUT algo_graph.aux +INPUT algo_graph.aux +OUTPUT algo_graph.aux +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omltxmi.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omltxmi.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omstxsy.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omstxsy.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omxtxex.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/omxtxex.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxexa.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxexa.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/t1txr.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/t1txr.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT /usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii +INPUT /usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii +INPUT /usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/ot1txr.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/ot1txr.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsya.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsya.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyb.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyb.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs7.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs5.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxmia.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxmia.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyc.fd +INPUT /usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyc.fd +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty +INPUT /usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty +INPUT algo_graph.out +INPUT algo_graph.out +INPUT algo_graph.out +INPUT algo_graph.out +INPUT ./algo_graph.out +INPUT ./algo_graph.out +OUTPUT algo_graph.out +OUTPUT algo_graph.pdf +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdflscape/pdflscape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/pdflscape/pdflscape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/lscape.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/lscape.sty +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs5.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/t1xr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsy.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txex.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsya.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyb.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txmia.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txsyc.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/txexa.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT /var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txmi.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxmi.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmri.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/txr.vf +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxptmr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/txfonts/rtxr.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/txfonts/t1xr.vf +INPUT algo_graph.aux +INPUT ./algo_graph.out +INPUT ./algo_graph.out +INPUT /usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxr.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmr8a.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmri8a.pfb diff --git a/buch/papers/multiplikation/tikz_formulas/algo_graph.pdf b/buch/papers/multiplikation/tikz_formulas/algo_graph.pdf Binary files differnew file mode 100755 index 0000000..7f5a984 --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo_graph.pdf diff --git a/buch/papers/multiplikation/tikz_formulas/algo_graph.tex b/buch/papers/multiplikation/tikz_formulas/algo_graph.tex new file mode 100755 index 0000000..ad4228b --- /dev/null +++ b/buch/papers/multiplikation/tikz_formulas/algo_graph.tex @@ -0,0 +1,140 @@ +\documentclass[border=10pt]{standalone} +\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{times} +\usepackage{geometry} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathrsfs} +\usepackage{amsfonts} +\usepackage{amsthm} +\usepackage{lipsum} +\usepackage{amscd} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{textcomp} +\usepackage{txfonts} +\usepackage[all]{xy} +\usepackage{paralist} +\usepackage[colorlinks=true]{hyperref} +\usepackage{array} +\usepackage{tikz} +\usepackage{slashed} +\usepackage{pdfpages} +\usepackage{cite} +\usepackage{url} +\usepackage{amsmath,amsfonts,amssymb} +\usepackage{tikz} +\usetikzlibrary{arrows,matrix,positioning} +\usetikzlibrary{overlay-beamer-styles} +\usetikzlibrary{matrix.skeleton} +\usetikzlibrary{automata,positioning} +\usepackage{listings} +\usepackage{multirow} +\usepackage{color} + +\begin{document} + +\begin{tikzpicture}[ampersand replacement=\&] + + \foreach \i in {1,...,4} + { + \small{ + \matrix (X\i)[matrix of math nodes,nodes in empty cells, + nodes = {draw, minimum size=10mm, + anchor=center, + inner sep=0pt, outer sep=0pt}, + column sep=-\pgflinewidth, + row sep=-\pgflinewidth, + ] at (0,-\i*5) + { + A_{11}B_{11} \& A_{12}B_{11} \& A_{21}B_{11} \& A_{22}B_{11} \\ + A_{11}B_{21} \& A_{12}B_{21} \& A_{21}B_{21} \& A_{22}B_{21} \\ + A_{11}B_{11} \& A_{12}B_{12} \& A_{21}B_{12} \& A_{22}B_{12} \\ + A_{11}B_{22} \& A_{12}B_{22} \& A_{21}B_{22} \& A_{22}B_{22} \\ + };} + + \foreach \j in {1,...,7} + { + \matrix(M\i\j)[matrix of math nodes,nodes in empty cells, + nodes = {draw, minimum size=10mm, + anchor=center, + inner sep=0pt, outer sep=0pt}, + column sep=-\pgflinewidth, + row sep=-\pgflinewidth, + ] at (\j*5,-\i*5) + { + \& \& \& \\ + \& \& \& \\ + \& \& \& \\ + \& \& \& \\ + }; + } + } + +\huge{ + \node at (-3,-20) {$C_{22}=$}; + \node at (-3,-15) {$C_{21}=$} ; + \node at (-3,-10) {$C_{12}=$} ; + \node at (-3,-5) {$C_{11}=$} ; + + \node at (5,-2) {I}; + \node at (10,-2) {II}; + \node at (15,-2) {III}; + \node at (20,-2) {IV}; + \node at (25,-2) {V}; + \node at (30,-2) {VI}; + \node at (35,-2) {VII}; + } + + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-2-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-3-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-4-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-2-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-3-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-4-4)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M14-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M14-2-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-2-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-4-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-2-2)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-4-2)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M23-3-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M23-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-2)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M34-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M34-2-4)] {}; + + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-4)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M43-3-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M43-4-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-1-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-1-1)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-3-3)] {}; + \node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-3-1)] {}; +\end{tikzpicture} + + + +\end{document} diff --git a/buch/papers/munkres/figures/Matrixdarstellung.png b/buch/papers/munkres/figures/Matrixdarstellung.png Binary files differnew file mode 100644 index 0000000..91a376d --- /dev/null +++ b/buch/papers/munkres/figures/Matrixdarstellung.png diff --git a/buch/papers/munkres/main.tex b/buch/papers/munkres/main.tex index 8915a3d..e5282dc 100644 --- a/buch/papers/munkres/main.tex +++ b/buch/papers/munkres/main.tex @@ -3,8 +3,8 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Munkres-Algorithmus\label{chapter:munkres}} -\lhead{Munkres-Algorithmus} +\chapter{Das Zuordnungsproblem und der Munkres-Algorithmus\label{chapter:munkres}} +\lhead{Das Zuordnungsproblem und der Munkres-Algorithmus} \begin{refsection} \chapterauthor{Marc Kühne} diff --git a/buch/papers/munkres/teil0.tex b/buch/papers/munkres/teil0.tex index 1ef0538..0578429 100644 --- a/buch/papers/munkres/teil0.tex +++ b/buch/papers/munkres/teil0.tex @@ -3,19 +3,8 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Geschichte\label{munkres:section:teil0}} -\rhead{Geschichte} -Die Ungarische Methode wurde 1955 von Harold Kuhn entwickelt und veröffentlicht. -Der Name ``Ungarische Methode'' ergab sich, weil der Algorithmus -weitestgehend auf den früheren Arbeiten zweier ungarischer Mathematiker -basierte: Dénes Kőnig und Jenő Egerváry. -James Munkres überprüfte den Algorithmus im Jahr 1957 und stellte fest, -dass der Algorithmus (stark) polynomiell ist. -Seitdem ist der Algorithmus auch als Kuhn-Munkres oder -Munkres-Zuordnungsalgorithmus bekannt. -Die Zeitkomplexität des ursprünglichen Algorithmus war $O(n^4)$, -später wurde zudem festgestellt, dass er modifiziert werden kann, -um eine $O(n^3)$-Laufzeit zu erreichen. - - +\section{Einleitung\label{munkres:section:teil0}} +\rhead{Einleitung} +Im Bereich der Unternehmensplanung (Operations Research) gibt es verschiedene Fragestellungen. Eine davon ist das sogenannte Transportproblem. Zum Transport einheitlicher Objekte von mehreren Angebots- zu mehreren Nachfrageorten ist ein optimaler, d. h. kostenminimaler Plan zu finden, wobei die vorhandenen und zu liefernden Mengen an den einzelnen Standorten gegeben sowie die jeweiligen Transportkosten pro Einheit zwischen allen Standorten bekannt sind. +Nun gibt es im Bereich des klassischen Transportproblems Sonderfälle. Ein Sonderfall ist z.B. das Zuordnungsproblem. diff --git a/buch/papers/munkres/teil1.tex b/buch/papers/munkres/teil1.tex index 7cbbbfd..c13732c 100644 --- a/buch/papers/munkres/teil1.tex +++ b/buch/papers/munkres/teil1.tex @@ -3,19 +3,56 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Was ist die ungarische Methode? +\section{Beschrieb des Zuordnungsproblems \label{munkres:section:teil1}} \rhead{Problemstellung} -Es ist ein kombinatorischer Optimierungsalgorithmus, der das Zuordnungsproblem -in polynomieller Zeit löst. -\begin{itemize} -\item -Polynom = vielgliedrig -\end{itemize} -Der Begriff polynomielle Laufzeit bedeutet, dass die Laufzeit des Programms -wie $n^2$, $n^3$, $n^4$, etc.~wächst und vernünftig skaliert. -Mit der ungarischen Methode können also lineare Optimierungsprobleme gelöst -werden, die bei gewichteten Zuordnungen in bipartiten Graphen entstehen. -Mit ihr kann die eindeutige Zuordnung von Objekten aus zwei Gruppen so -optimiert werden, dass die Gesamtkosten minimiert werden bzw.~der -Gesamtgewinn maximiert werden kann. + +Das spezielle an einem Zuordnungsproblem ist, dass es an jedem Ort nur eine Einheit angeboten bzw. nachgefragt wird. Es werden hier nicht Mengen möglichst kostenminimal von einem zum anderen +Ort transportiert, sondern es geht um die kostenminimale Zuordnung von z.B. Personen, oder Bau-Materialien auf bestimmte Orte, Stellen oder Aufgaben. +Um dieses Problem in einer einfachen, händischen Art und Weise zu lösen wurde der Munkres-Algorithmus, auch die Ungarische Methode genannt, entwickelt. Diese Methode ist ein weiteres Hauptthema dieses Kapitels. + +\subsection{Zuordnungsproblem an einem konkreten Beispiel +\label{munkres:subsection:bonorum}} + +\subsection{Zuordnungsproblem abstrakt +\label{munkres:subsection:bonorum}} + +Es sind alle Angebots- und Bedarfsmengen gleich 1 +\begin{equation} +a_{i}=b_{j}=1 +\end{equation} + +\subsection{alternative Darstellungen des Zuordnungsproblems +\label{munkres:subsection:bonorum}} +\begin{equation} +Netzwerk +\end{equation} +\begin{equation} +Matrix +\end{equation} +\begin{equation} +Bitpartiter Graph +\end{equation} +Ein bipartiter Graph ist ein mathematisches Modell für Beziehungen +zwischen den Elementen zweier Mengen. +Es eignet sich sehr gut zur Untersuchung von Zuordnungsproblemen» +\begin{figure} +\centering +\includegraphics[width=5cm]{papers/munkres/figures/Netzwerkdarstellung} +\caption{Typische Netzwerkdarstellung eines Zuordnungsproblems.} +\label{munkres:Vr2} +\end{figure} + +\begin{figure} +\centering +\includegraphics[width=5cm]{papers/munkres/figures/Matrixdarstellung} +\caption{Typische 4x4 Matrixdarstellung eines Zuordnungsproblems.} +\label{munkres:Vr2} +\end{figure} + +\begin{figure} +\centering +\includegraphics[width=5cm]{papers/munkres/figures/bipartiter_graph} +\caption{$K_{3,3}$ vollständig bipartiter Graph mit 3 Knoten pro Teilmenge.} +\label{munkres:Vr2} +\end{figure} diff --git a/buch/papers/munkres/teil2.tex b/buch/papers/munkres/teil2.tex index 29db8d7..9a44cd4 100644 --- a/buch/papers/munkres/teil2.tex +++ b/buch/papers/munkres/teil2.tex @@ -3,86 +3,11 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Das Zuordnungsproblem +\section{Schwierigkeit der Lösung (Permutationen) \label{munkres:section:teil2}} -\rhead{Das Zuordnungsproblem} -Das (lineare) Zuordnungsproblem ist ein diskretes Optimierungsproblem aus -der Graphentheorie. -Es handelt sich um einen Spezialfall eines maximalen Matchings -minimalen Gewichtes in einem bipartiten, gewichteten Graphen +\rhead{Schwierigkeit der Lösung (Permutationen)} -Vereinfacht gesagt sind Zuordnungsprobleme spezielle Transportprobleme. -Der Unterschied zu klassischen Transportproblemen liegen darin, -dass hier nicht Mengen möglichst kostenminimal von einem zum anderen -Ort transportiert werden sollen, sondern es geht um die kostenminimale -Zuordnung von z.~B.~Personen, oder Bau-Materialien auf bestimmte -Orte, Stellen oder Aufgaben. -Dabei sind alle Angebots- und Bedarfsmenge gleich 1 -\begin{equation} -a_{i}=b_{j}=1 -\end{equation} +Eine Permutation ist eine Anordnung von Objekten in einer bestimmten Reihenfolge oder eine Umordnung von Objekten aus einer vorgegebenen Reihung. Ist eine maximale Zuordnung (maximales Matching) gefunden, so steht in jeder Zeile und jeder Spalte der Matrix genau ein Element, das zur optimalen Lösung gehört, eine solche Gruppe von Positionen wird auch als Transversale der Matrix bezeichnet. -\subsection{Zuordnungsproblem in Netzwerkdarstellung -\label{munkres:subsection:bonorum}} - -\begin{figure} -\centering -\includegraphics[width=5cm]{papers/munkres/figures/Netzwerkdarstellung} -\caption{Typische Netzwerkdarstellung eines Zuordnungsproblems.} -\label{munkres:Vr2} -\end{figure} - -\subsection{Matrix Formulierung -\label{munkres:subsection:bonorum}} -In der Matrixformulierung ist eine nicht-negative $n\times n$-Matrix -gegeben, wobei das Element in der $i$-ten Zeile und $j$-ten Spalte -die Kosten für die Zuweisung des $j$-ten Jobs an den $i$-ten Arbeiter -darstellt. -Wir müssen eine Zuordnung der Jobs zu den Arbeitern finden, so dass -jeder Job einem Arbeiter zugewiesen wird und jeder Arbeiter einen -Job zugewiesen bekommt, so dass die Gesamtkosten der Zuordnung -minimal sind. -Dies kann als Permutation der Zeilen und Spalten einer Kostenmatrix -$C$ ausgedrückt werden, um die Spur einer Matrix zu minimieren: -\begin{equation} -\min(L,R)Tr (LCR) -\end{equation} -wobei $L$ und $R$ Permutationsmatrizen sind. -Wenn das Ziel ist, die Zuordnung zu finden, die die maximalen Kosten -ergibt, kann das Problem durch Negieren der Kostenmatrix $C$ gelöst -werden. - -\subsection{Suche der optimalen Lösung -\label{munkres:subsection:bonorum}} -Ist eine maximale Zuordnung (maximales Matching) gefunden, so steht -in jeder Zeile und jeder Spalte der Matrix genau ein Element, das -zur optimalen Lösung gehört, eine solche Gruppe von Positionen wird -auch als Transversale der Matrix bezeichnet. -Deshalb kann die Problemstellung auch anders formuliert werden: Man -ordne die Zeilen- oder die Spaltenvektoren so um, dass die Summe -der Elemente in der Hauptdiagonale maximal wird. -Hieraus wird sofort ersichtlich, dass es in einer -$n\times n$-Matrix genau so viele Möglichkeiten gibt, die Zeilen- -bzw.~Spaltenvektoren zu ordnen, wie es Permutationen von $n$ Elementen -gibt, also $n!$. -Außer bei kleinen Matrizen ist es nahezu aussichtslos, die optimale -Lösung durch Berechnung aller Möglichkeiten zu finden. -Schon bei einer $10\times 10$-Matrix gibt es nahezu 3,63 Millionen (3.628.800) -zu berücksichtigender Permutationen. - -\subsection{Formulierung Bipartiter Graph -\label{munkres:subsection:bonorum}} -Der Algorithmus ist einfacher zu beschreiben, wenn wir das Problem -anhand eines bipartiten Graphen formulieren. -Wir haben einen vollständigen zweistufigen Graphen $G=(S,T;E)$ mit -$n$ Arbeiter-Eckpunkten ($S$) und $n$ Job-Scheitelpunkte ($T$), und -jede Kante hat einen nichtnegativen Preis $c(i,j)$. -Wir wollen ein perfektes Matching mit minimalen Gesamtkosten finden. - -\begin{figure} -\centering -\includegraphics[width=5cm]{papers/munkres/figures/bipartiter_graph} -\caption{$K_{3,3}$ vollständig bipartiter Graph mit 3 Knoten pro Teilmenge.} -\label{munkres:Vr2} -\end{figure} +Die Problemstellung kann auch so formuliert werden, dass man die Zeilen- oder die Spaltenvektoren so umordnet soll, dass die Summe der Elemente in der Hauptdiagonale maximal wird. Hieraus wird sofort ersichtlich, dass es in einer n×n-Matrix genau so viele Möglichkeiten gibt, die Zeilen- bzw. Spaltenvektoren zu ordnen, wie es Permutationen von n Elementen gibt, also n!. Außer bei kleinen Matrizen ist es nahezu aussichtslos, die optimale Lösung durch Berechnung aller Möglichkeiten zu finden. Schon bei einer 10×10-Matrix gibt es nahezu 3,63 Millionen (3.628.800) zu berücksichtigender Permutationen. diff --git a/buch/papers/munkres/teil3.tex b/buch/papers/munkres/teil3.tex index 806cd83..cd47c92 100644 --- a/buch/papers/munkres/teil3.tex +++ b/buch/papers/munkres/teil3.tex @@ -3,102 +3,44 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Der Algorithmus in Form von bipartiten Graphen +\section{Der Munkres-Algorithmus (Ungarische Methode) \label{munkres:section:teil3}} -\rhead{Der Algorithmus in Form von bipartiten Graphen} -Mit der ungarischen Methode können also lineare Optimierungsprobleme -gelöst werden, die bei gewichteten Zuordnungen in bipartiten Graphen -entstehen. +\rhead{Der Munkres-Algorithmus (Ungarische Methode)} -Mit ihr kann die eindeutige Zuordnung von Objekten aus zwei Gruppen -so optimiert werden, dass die Gesamtkosten minimiert werden bzw.~der -Gesamtgewinn maximiert werden kann. +Mit der ungarischen Methode können also lineare Optimierungsprobleme gelöst +werden, die bei gewichteten Zuordnungen in bipartiten Graphen entstehen. +Mit ihr kann die eindeutige Zuordnung von Objekten aus zwei Gruppen so +optimiert werden, dass die Gesamtkosten minimiert werden bzw.~der +Gesamtgewinn maximiert werden kann. -Ein bipartiter Graph ist ein mathematisches Modell für Beziehungen -zwischen den Elementen zweier Mengen. -Es eignet sich sehr gut zur Untersuchung von Zuordnungsproblemen» - -\subsection{Beweis, dass der Algorithmus Fortschritte macht +\subsection{Geschichte \label{munkres:subsection:malorum}} -Wir müssen zeigen, dass der Algorithmus, solange das Matching nicht -die maximal mögliche Größe hat, immer in der Lage ist, Fortschritte -zu machen --- das heißt, entweder die Anzahl der übereinstimmenden -Kanten zu erhöhen oder mindestens eine Kante zu straffen. -Es genügt zu zeigen, dass bei jedem Schritt mindestens eine der -folgenden Bedingungen erfüllt ist: - -\begin{itemize} -\item -$M$ die maximal mögliche Größe. -\item -$Gy$ enthält einen Erweiterungspfad. -\item -$G$ enthält einen losen Pfad: einen Pfad von einem Knoten in $Rs$ -zu einem Knoten in $T$ / $Z$ die aus einer beliebigen Anzahl von -festen Kanten, gefolgt von einer einzelnen losen Kante, besteht. -Die freie Kante einer freien Bahn ist also $Z$ (beinhaltet $T$), -so garantiert es, dass Delta gut definiert ist. -\end{itemize} -Wenn $M$ die maximal mögliche Größe hat, sind wir natürlich fertig. -Andernfalls muss es nach Berges Lemma im zugrundeliegenden Graphen -$G$ einen Augmentierungspfad $P$ in Bezug auf $M$ geben. -Dieser Pfad darf jedoch nicht in $G_y$ existieren: Obwohl jede -geradzahlige Kante in $P$ durch die Definition von $M$ fest ist, -können ungeradzahlige Kanten lose sein und in $G_y$ fehlen. -Ein Endpunkt von $P$ liegt in $R_{S}$, der andere in $R_T$; w.l.o.g., -nehmen Sie an, es beginnt in $R_{S}$. -Wenn jede Kante von $P$ dicht ist, dann bleibt sie ein augmentierender -Pfad in $G_y$ und wir sind fertig. -Andernfalls sei $uv$ die erste lose Kante auf $P$. -Wenn $v$ kein Element von $Z$ ist, dann haben wir einen losen Pfad -gefunden und sind fertig. -Andernfalls ist $v$ von irgendeinem anderen Pfad $Q$ aus festen -Kanten von einem Knoten in $R_{S}$ erreichbar. -Sei $P_{v}$ der Teilpfad von $P$, der bei $v$ beginnt und bis zum -Ende reicht, und sei $P'$ der Pfad, der gebildet wird, indem man -entlang $Q$ gebildet wird, bis ein Scheitelpunkt auf $P_{v}$ erreicht -wird, und dann weiter bis zum Ende von $P_{v}$. -Beachten Sie, dass $P'$ ein erweiternder Pfad in $G$ mit mindestens -einer losen Kante weniger als $P$ ist. -$P$ kann durch $P'$ ersetzt und dieser Argumentationsprozess iteriert -werden (formal, unter Verwendung von Induktion auf die Anzahl der -losen Kanten), bis entweder ein erweiternder Pfad in $G_y$ oder ein -losender Pfad in $G$ gefunden wird. +Die Ungarische Methode wurde 1955 von Harold Kuhn entwickelt und veröffentlicht. +Der Name ``Ungarische Methode'' ergab sich, weil der Algorithmus +weitestgehend auf den früheren Arbeiten zweier ungarischer Mathematiker +basierte: Dénes Kőnig und Jenő Egerváry. +James Munkres überprüfte den Algorithmus im Jahr 1957 und stellte fest, +dass der Algorithmus (stark) polynomiell ist. +Seitdem ist der Algorithmus auch als Kuhn-Munkres oder +Munkres-Zuordnungsalgorithmus bekannt. +Die Zeitkomplexität des ursprünglichen Algorithmus war $O(n^4)$, +später wurde zudem festgestellt, dass er modifiziert werden kann, +um eine $O(n^3)$-Laufzeit zu erreichen. -\subsection{Beweis, dass die Anpassung des Potentials $y$ $M$ unverändert lässt +\subsection{Besondere Leistung der Ungarischen Methode \label{munkres:subsection:malorum}} -Um zu zeigen, dass jede Kante in $M$ nach der Anpassung von $y$ -erhalten bleibt, genügt es zu zeigen, dass für eine beliebige Kante -in $M$ entweder beide Endpunkte oder keiner von ihnen in $Z$ liegen. -Zu diesem Zweck sei $vu$ eine Kante in $M$ von $T$ nach $S$. -Es ist leicht zu sehen, dass wenn $v$ in $Z$ ist, dann muss auch -$u$ in $Z$ sein, da jede Kante in $M$ dicht ist. -Nehmen wir nun an, dass $u$ kein Element von $Z$ und auch $v$ kein -Element von $Z$ ist. -$u$ selbst kann nicht in $R_{S}$ sein, da es der Endpunkt einer -angepassten Kante ist, also muss es einen gerichteten Pfad von engen -Kanten von einem Knoten in $R_{S}$ zu $u$ geben. -Dieser Pfad muss $v$ vermeiden, da es per Annahme nicht in $Z$ ist, -also ist der Knoten, der $u$ in diesem Pfad unmittelbar vorausgeht, -ein anderer Knoten $v$ (ein Element von $T$) und $v$ ein Element -von $u$ ist eine enge Kante von $T$ nach $S$ und ist somit in $M$. -Aber dann enthält $M$ zwei Kanten, die den Knoten $u$ teilen, was -der Tatsache widerspricht, dass $M$ ein Matching ist. -Jede Kante in $M$ hat also entweder beide Endpunkte oder keinen -Endpunkt in $Z$. +Es ist ein kombinatorischer Optimierungsalgorithmus, der das Zuordnungsproblem +in polynomieller Zeit löst. +Der Begriff polynomielle Laufzeit bedeutet, dass die Laufzeit des Programms +wie $n^2$, $n^3$, $n^4$, etc.~wächst und vernünftig skaliert. + -\subsection{Beweis, dass $y$ ein Potential bleibt +\subsection{Beispiel eines händischen Verfahrens \label{munkres:subsection:malorum}} -Um zu zeigen, dass y nach der Anpassung ein Potenzial bleibt, genügt -es zu zeigen, dass keine Kante ihr Gesamtpotenzial über ihre Kosten -hinaus erhöht. -Dies ist für Kanten in $M$ bereits durch den vorangegangenen Absatz -bewiesen. -Man betrachtet also eine beliebige Kante $uv$ von $S$ nach $T$. -Wenn $y(u)$ erhöht wird um $\Delta$, dann wird entweder $v\in -\mathbb{Z}_n$ in diesem Fall wird $y(v)$ verringert um $\Delta$, -wobei das Gesamtpotenzial der Kante unverändert bleibt, oder $v\in -T\setminus Z$, wobei die Definition von $\Delta$ garantiert, dass -$y(u)+y(v)+\Delta \le c(u,v)$ -Also $y$ bleibt ein Potential. +\begin{figure} +\centering +\includegraphics[width=14cm]{papers/munkres/figures/beispiel_munkres} +\caption{Händisches Beispiel des Munkres Algorithmus.} +\label{munkres:Vr2} +\end{figure} diff --git a/buch/papers/munkres/teil4.tex b/buch/papers/munkres/teil4.tex index 3d76743..9a27227 100644 --- a/buch/papers/munkres/teil4.tex +++ b/buch/papers/munkres/teil4.tex @@ -3,34 +3,7 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Matrix-Interpretation +\section{- \label{munkres:section:teil4}} -\rhead{Matrix-Interpretation} -Gegeben ist die quadratische Matrix $C=(c_{ij})$ der Grösse $n\times n$. -Ohne Beschränkung der Allgemeinheit werden eine Zuordnung $j -\rightarrow s_j$, $j = 1, \dots, n$ mit minimaler Gesamtsumme -$\sum_{j=1}^{n}c_{s_j,j}$ gesucht, wobei die $s_j$ eine Permutation -von $\{1,\ldots ,n\}$ sind. -Soll die Summe maximiert werden, dann kann $C$ durch $-C$ ersetzt werden. -Die Grundlage dieses Verfahrens ist, dass sich die optimale Zuordnung -unter bestimmten Änderungen der Matrix nicht ändert, sondern nur -der Optimalwert. -Diese Änderungen sind durch Knotenpotentiale bzw.~duale Variablen -\begin{equation} -u_1 u_2,{\dots}, u_n -\end{equation} +\rhead{-} -für die Zeilen und - -\begin{equation}v_1,v_2,\dots,v_n \end{equation} fuer die Spalten angegeben. -Die modifizierte Matrix hat dann die Komponenten $\tilde{c}_{i,j} -= c_{ij} - u_j - v_j$. - -In der Summe über jede kantenmaximale Zuordnung kommt jedes -Knotenpotential genau einmal vor, so dass die Änderung der Zielfunktion -eine Konstante ist. -Sind die Einträge von $C$ nichtnegativ, und sind alle Knotenpotentiale -ebenfalls nichtnegativ, so nennt man die modifizierte Matrix \~{C} -auch eine Reduktion. -Ziel ist, in der reduzierten Matrix möglichst viele Komponenten auf -den Wert Null zu bringen und unter diesen die Zuordnung zu konstruieren. diff --git a/buch/papers/munkres/teil5.tex b/buch/papers/munkres/teil5.tex index f8138f4..b938c50 100644 --- a/buch/papers/munkres/teil5.tex +++ b/buch/papers/munkres/teil5.tex @@ -3,12 +3,6 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Ungarische Methode anhand eines Beispiels +\section{- \label{munkres:section:teil5}} -\rhead{Ungarische Methode anhand eines Beispiels} -\begin{figure} -\centering -\includegraphics[width=14cm]{papers/munkres/figures/beispiel_munkres} -\caption{Händisches Beispiel des Munkres Algorithmus.} -\label{munkres:Vr2} -\end{figure} +\rhead{-} diff --git a/buch/papers/reedsolomon/Makefile b/buch/papers/reedsolomon/Makefile index 9c96e88..25fd98b 100644 --- a/buch/papers/reedsolomon/Makefile +++ b/buch/papers/reedsolomon/Makefile @@ -4,6 +4,52 @@ # (c) 2020 Prof Dr Andreas Mueller # -images: - @echo "no images to be created in reedsolomon" +SOURCES := \ + anwendungen.tex \ + codebsp.tex \ + decmitfehler.tex \ + decohnefehler.tex \ + dtf.tex \ + einleitung.tex \ + endlichekoerper.tex \ + hilfstabellen.tex \ + idee.tex \ + main.tex \ + packages.tex \ + rekonstruktion.tex \ + restetabelle1.tex \ + restetabelle2.tex \ + standalone.tex \ + zusammenfassung.tex + +TIKZFIGURES := \ + tikz/polynom2.tex \ + tikz/plotfft.tex + +FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) + + +all: images standalone + + +.PHONY: images +images: $(FIGURES) + +figures/%.pdf: tikz/%.tex + mkdir -p figures + pdflatex --output-directory=figures $< + +.PHONY: standalone +standalone: standalone.tex $(SOURCES) $(FIGURES) + mkdir -p standalone + cd ../..; \ + pdflatex \ + --halt-on-error \ + --shell-escape \ + --output-directory=papers/reedsolomon/standalone \ + papers/reedsolomon/standalone.tex; + cd standalone; \ + bibtex standalone; \ + makeindex standalone; + diff --git a/buch/papers/reedsolomon/dtf.tex b/buch/papers/reedsolomon/dtf.tex index a111527..e9aacfb 100644 --- a/buch/papers/reedsolomon/dtf.tex +++ b/buch/papers/reedsolomon/dtf.tex @@ -3,52 +3,71 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Diskrete Fourier Transformation +\section{Übertragung mit hilfe der Diskrete Fourier Transformation \label{reedsolomon:section:dtf}} \rhead{Umwandlung mit DTF} Um die Polynominterpolation zu umgehen, gehen wir nun über in die Fourientransformation. -Dies wird weder eine erklärung der Forientransorfmation noch ein genauer gebrauch -für den Reed-Solomon-Code. Dieser Abschnitt zeigt nur wie die Fourientransformation auf Fehler reagiert. +Dies wird weder eine Erklärung der Forientransorfmation, noch ein genauer gebrauch für den Reed-Solomon-Code. +Dieser Abschnitt zeigt nur wie die Fourientransformation auf Fehler reagiert. wobei sie dann bei späteren Berchnungen ganz nützlich ist. -\subsection{Diskrete Fourientransformation Zusamenhang +\subsection{Diskrete Fourietransformation Zusamenhang \label{reedsolomon:subsection:dtfzusamenhang}} -Die Diskrete Fourientransformation ist definiert als - \[ - \label{ft_discrete} +Mit hilfe der Fourietransformation werden die \textcolor{blue}{blauen Datenpunkte} transformiert, +zu den \textcolor{darkgreen}{grünen Übertragungspunkten}. +Durch eine Rücktransformation könnnen die \textcolor{blue}{blauen Datenpunkte} wieder rekonstruiert werden. +Nun zur definition der Diskrete Fourietransformation, diese ist definiert als +\begin{equation} \hat{c}_{k} = \frac{1}{N} \sum_{n=0}^{N-1} {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn} - \] -, wenn man nun - \[ - w = e^{-\frac{2\pi j}{N} k} - \] + ,\label{reedsolomon:DFT} +\end{equation} +wenn man nun +\begin{equation} + w = + e^{-\frac{2\pi j}{N} k} + \label{reedsolomon:DFT_summand} +\end{equation} ersetzte, und $N$ konstantbleibt, erhält man - \[ - \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) - \] +\begin{equation} + \hat{c}_{k}= + \frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) + \label{reedsolomon:DFT_polynom} +\end{equation} was überaust ähnlich zu unserem Polynomidee ist. -\subsection{Übertragungsabfolge + +\subsection{Beispiel \label{reedsolomon:subsection:Übertragungsabfolge}} +Der Auftrag ist nun 64 Daten zu übertragen und nach 32 Fehler abzusicheren, +16 Fehler erkennen und rekonstruieren. -\begin{enumerate}[1)] +Dieser Auftrag soll mittels Fouriertransformation bewerkstelligt werden. +In der Abbildung \ref{reedsolomon:subsection:Übertragungsabfolge} sieht man dies Schritt für schritt, +und hier werden die einzelne Schritte erklärt: +\begin{enumerate}[(1)] \item Das Signal hat 64 die Daten, Zahlen welche übertragen werden sollen. Dabei zusätzlich nach 16 Fehler abgesichert, macht insgesamt 96 Übertragungszahlen. -\item Nun wurde mittels der schnellen diskreten Fourientransformation diese 96 codiert. -Das heisst alle information ist in alle Zahlenvorhanden. -\item Nun kommen drei Fehler dazu an den Übertragungsstellen 7, 21 und 75. -\item Dieses wird nun Empfangen und mittels inversen diskreten Fourientransormation, wieder rücktransformiert. -\item Nun sieht man den Fehler im Decodieren in den Übertragungsstellen 64 bis 96. -\item Nimmt man nun nur diese Stellen 64 bis 96, auch Syndrom genannt, und Transformiert diese. -\item Bekommt man die Fehlerstellen im Locator wieder, zwar nichtso genau, dennoch erkkent man wo die Fehler stattgefunden haben. +(siehe Abschnitt \externaldocument{papers/reedsolomon/idee}\ref{reedsolomon:section:Fehlerkorrekturstellen}) +Die 32 Fehlerkorrekturstellen werden als Null Übertragen +\item Nun wurde mittels der diskreten Fourientransformation diese 96 codiert. +Das heisst alle Informationen ist in alle Zahlenvorhanden. (Auch die Fehlerkorrekturstellen Null) +\item Nun kommen drei Fehler dazu an den Übertragungsstellen 7, 21 und 75.(die Skala ist Rechts) +Die Fehler können auf den ganzen 96 Übertragungswerten liegen, wie die 75 zeigt. +\item Dieses wird nun Empfangen und mittels inversen diskreten Fourientransormation, wieder rücktransformiert.(Iklusive der Fehler) +\item Nun sieht man den Fehler im Decodieren in den Übertragungsstellen 64 bis 96, da es dort nicht mehr Null ist. +\item Nimmt man nun nur diese Stellen 64 bis 96, dies definieren wir als Syndrom, und transformiert nur dieses Syndrom. +\item Bekommt man die Fehlerstellen wieder, zwar nichtso genau, dennoch erkennt man wo die Fehler stattgefunden haben. +Dies definieren wir als Locator. \end{enumerate} +Nun haben wir mit Hilfe der Fourietransformation die 3 Fehlerstellen durch das Syndrom lokalisiert, +jetzt gilt es nur noch diese zu korrigieren und wir haben unser originales Signal wieder. \begin{figure} \centering - \resizebox{0.9\textwidth}{!}{ - %\includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/plot.pdf} - \input{papers/reedsolomon/images/plotfft.tex} + \resizebox{\textwidth}{!}{ + \includegraphics[width=\textwidth]{papers/reedsolomon/figures/plotfft} + %\input{papers/reedsolomon/images/plotfft.tex} } \caption{Übertragungsabfolge \ref{reedsolomon:subsection:Übertragungsabfolge}} \label{fig:sendorder} diff --git a/buch/papers/reedsolomon/einleitung.tex b/buch/papers/reedsolomon/einleitung.tex index 2b1d878..074df05 100644 --- a/buch/papers/reedsolomon/einleitung.tex +++ b/buch/papers/reedsolomon/einleitung.tex @@ -7,13 +7,11 @@ \label{reedsolomon:section:einleitung}} \rhead{Einleitung} Der Reed-Solomon-Code ist entstanden um, -das Problem der Fehler, bei der Datenübertragung, zu lösen. -In diesem Abschnitt wird möglichst verständlich die mathematische Abfolge, Funktion oder Algorithmus erklärt. +das Problem der Fehler bei der Datenübertragung, zu lösen. +In diesem Abschnitt wird möglichst verständlich die mathematische Abfolge, +Funktion oder Algorithmus des Reed-Solomon-Code erklärt. Es wird jedoch nicht auf die technische Umsetzung oder Implementierung eingegangen. -Um beim Datenübertragen Fehler zu erkennen, könnte man die Daten jeweils doppelt senden, -und so jeweilige Fehler zu erkennen. -Doch nur schon um weinige Fehler zu erkennen werden überproportional viele Daten doppelt und dreifach gesendet. -Der Reed-Solomon-Code macht dies auf eine andere, clevere Weise. + diff --git a/buch/papers/reedsolomon/experiments/plot.tex b/buch/papers/reedsolomon/experiments/plot.tex index 2196c82..4b156bb 100644 --- a/buch/papers/reedsolomon/experiments/plot.tex +++ b/buch/papers/reedsolomon/experiments/plot.tex @@ -90,7 +90,7 @@ \draw[ultra thick, ->] (zoom) to[out=180, in=90] (syndrom.north); %item - \node[circle, draw, fill =lightgray] at (signal.north west)+(1,0) {1}; + \node[circle, draw, fill =lightgray] at (signal.north west) {1}; \node[circle, draw, fill =lightgray] at (codiert.north west) {2}; \node[circle, draw, fill =lightgray] at (fehler.north west) {3}; \node[circle, draw, fill =lightgray] at (empfangen.north west) {4}; diff --git a/buch/papers/reedsolomon/figures/plotfft.pdf b/buch/papers/reedsolomon/figures/plotfft.pdf Binary files differnew file mode 100644 index 0000000..c5e21e3 --- /dev/null +++ b/buch/papers/reedsolomon/figures/plotfft.pdf diff --git a/buch/papers/reedsolomon/figures/polynom2.pdf b/buch/papers/reedsolomon/figures/polynom2.pdf Binary files differnew file mode 100644 index 0000000..55a50ac --- /dev/null +++ b/buch/papers/reedsolomon/figures/polynom2.pdf diff --git a/buch/papers/reedsolomon/idee.tex b/buch/papers/reedsolomon/idee.tex index 39adbbf..8ad3d27 100644 --- a/buch/papers/reedsolomon/idee.tex +++ b/buch/papers/reedsolomon/idee.tex @@ -1,21 +1,32 @@ % -% teil1.tex -- Beispiel-File für das Paper +% idee.tex -- Polynom Idee % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Idee \label{reedsolomon:section:idee}} \rhead{Problemstellung} +Um beim Datenübertragen Fehler zu erkennen, könnte man die Daten jeweils doppelt senden, +und so jeweilige Fehler zu erkennen. +Doch nur schon um Fehler zu erkennen werden überproportional viele Daten doppelt und dreifach gesendet. +Der Reed-Solomon-Code macht dies auf eine andere, clevere Weise. Das Problem liegt darin Informationen, Zahlen, zu Übertragen und Fehler zu erkennen. Beim Reed-Solomon-Code kann man nicht nur Fehler erkennen, man kann sogar einige Fehler korrigieren. +Der unterschied des Fehler erkennen und korrigiren, ist das beim Erkennen nur die Frage beantwortet wird mit: Ist die Übertragung fehlerhaft oder nicht? +Beim Korrigieren werden Fehler erkennt und dann zusätzlich noch den original Wert rekonstruieren. +Auch eine Variante wäre es die Daten nach einem Fehler nachdem Fehlerhaften senden, nochmals versenden(auch hier wieder doppelt und dreifach Sendung), +was bei Reed-Solomon-Code-Anwendungen nicht immer sinnvoll ist. +\externaldocument{papers/reedsolomon/anwendungen} +\ref{reedsolomon:section:anwendung} +\subsection{Polynom-Ansatz +\label{reedsolomon:section:polynomansatz}} \rhead{Polynom-Ansatz} -Eine Idee ist aus den Daten -ein Polynom zu bilden. +Eine Idee ist aus den Daten ein Polynom zu bilden. Diese Polynomfunktion bei bestimmten Werten, ausrechnet und diese Punkte dann überträgt. -Nehmen wir als beisbiel die Zahlen \textcolor{blue}{2}, \textcolor{blue}{1}, \textcolor{blue}{5}, +\begin{beispiel} Nehmen wir die Zahlen \textcolor{blue}{2}, \textcolor{blue}{1}, \textcolor{blue}{5}, welche uns dann das Polynom \begin{equation} p(x) @@ -24,49 +35,63 @@ p(x) \label{reedsolomon:equation1} \end{equation} ergeben. -Übertragen werden nun die Werte an den stellen 1, 2, 3\dots 7 dieses Polynomes. +Übertragen werden nun die \textcolor{darkgreen}{grünen Werte} +dieses \textcolor{blue}{blauen Polynomes} an den Stellen 1, 2, 3\dots 7 dieses Polynomes. Grafisch sieht man dies dann in Abbildung \ref{fig:polynom}, -mit den Punkten, $p(1),p(2),...,p(7) = (\textcolor{green}{8}, -\textcolor{green}{15}, \textcolor{green}{26}, -\textcolor{green}{41}, \textcolor{green}{60}, -\textcolor{green}{83}, \textcolor{green}{110})$ -Wenn ein Fehler sich in die Übertragung eingeschlichen hatt, muss der Leser/Empfänger diesen erkennen und das Polynom rekonstruieren. +mit den Punkten, $p(1),p(2),...,p(7) = (\textcolor{darkgreen}{8}, +\textcolor{darkgreen}{15}, \textcolor{darkgreen}{26}, +\textcolor{darkgreen}{41}, \textcolor{darkgreen}{60}, +\textcolor{darkgreen}{83}, \textcolor{darkgreen}{110})$ +Wenn ein Fehler sich in die Übertragung eingeschlichen hat, muss der Leser/Empfänger diesen erkennen und das Polynom rekonstruieren. Der Leser/Empfänger weiss, den Grad des Polynoms und dessen Werte übermittelt wurden. +Die Farbe blau brauchen wir für die \textcolor{blue}{Daten} welche wir mit der Farbe grün \textcolor{darkgreen}{Übermitteln}. +\end{beispiel} -\subsection{Beispiel} -Für das Beispeil aus der Gleichung \eqref{reedsolomon:equation1}, +\begin{beispiel} +Aus der Gleichung \eqref{reedsolomon:equation1}, ist ein Polynome zweiten Grades durch drei Punkte eindeutig bestimmbar. Hat es Fehler in der Übertragunge gegeben,(Bei Abbildung \ref{fig:polynom}\textcolor{red}{roten Punkte}) kann man diese erkennen, da alle Punkte, die korrekt sind, auf dem Polynom liegen müssen. -(Bei Abbildung \ref{fig:polynom}\textcolor{green}{grünen Punkte}) +(Bei Abbildung \ref{fig:polynom}\textcolor{darkgreen}{grünen Punkte}) Ab wie vielen Fehler ist das Polynom nicht mehr erkennbar beim Übertragen von 7 Punkten? Bei 2 Fehlern kann man noch eindeutig bestimmen, dass das Polynom mit 4 Punkten, gegenüber dem mit 5 Punkten falsch liegt.\ref{fig:polynom} Werden es mehr Fehler kann nur erkennt werden, dass das Polynom nicht stimmt. Das orginale Polynom kann aber nicht mehr gefunden werden. -Dafür sind mehr übertragene Werte nötig. +Da das Konkurenzpolynom, grau gestrichelt in Abbildung \ref{fig:polynom}, das orginal fehlleited. +Um das Konkurenzpolynom auszuschliessen, währen mehr \textcolor{darkgreen}{Übertragungspunkte} nötig. +\end{beispiel} \begin{figure} \centering - %\includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/polynom2} - \input{papers/reedsolomon/images/polynom2.tex} - \caption{Polynom $p(x)$ \eqref{reedsolomon:equation1}} + \includegraphics[width=\textwidth]{papers/reedsolomon/figures/polynom2} + %\input{papers/reedsolomon/tikz/polynom2.tex} + \caption{Polynom $p(x)$ von der Gleichung\eqref{reedsolomon:equation1}} \label{fig:polynom} \end{figure} -\section{Fehlerbestimmung -\label{reedsolomon:section:Fehlerbestimmmung}} -So wird ein Muster indentifiziert, welches genau vorherbestimmen kann, -wie gross das Polynom sein muss und wie viele Übertragungspunkte gegeben werden müssen. -Um zu bestimmen wie viel Fehler erkennt und korriegiert werden können. -Die Anzahl Zahlen (Daten, ab hier verwenden wir das Wort Nutzlast), -die Entschlüsselt werden sollen, brauchen die gleiche Anzahl an Polynomgraden, beginnend bei Grad 0. ( \( k-1 \) ) -Für die Anzahl an Übertragungspunkte, muss bestimmt werden wieviel Fehler erkennt und korrigiert werden sollen. -Mit Hilfe der Tabelle, sieht man das es bei $t$ Fehlern und $k$ Nutzlast Zahlen, -$k+2t$ Punkte übertragen werden müssen. +\section{Fehlerkorekturstellen bestimmen +\label{reedsolomon:section:Fehlerkorrekturstellen}} +Um zu bestimmen wieviel zusätzliche \textcolor{darkgreen}{Übertragungspunkte} notwendig sind, die dann Fehler korrigieren, +muss man zuerst Wissen wieviel \textcolor{blue}{Daten} gesendet und wieviel \textcolor{red}{Fehler} erkennt werden sollen. +Die Anzahl \textcolor{blue}{Daten} (ab hier verwenden wir das Wort Nutzlast), die als Polynomkoeffizente $k$ übergeben werden, +brauchen die gleiche Anzahl an Polynomgraden, beginnend bei Grad 0 somit ergibt sich der Polynomgrad mit $k-1$. +Für die Anzahl der Fehler $t$, welche korrigiert werden können, gehen wir zum Beispiel. +\begin{beispiel} von den Polynom \ref{reedsolomon:equation1} in, welchem wir 7 \textcolor{darkgreen}{Übertragungspunkte} senden. +Durch 3 Punkte wird das Polyom eindeutig bestimmt, nun haben wir mehrere Konkurenzpolynome, doch mit maximal 2 Fehler liegen auf einem Konkurenzpolynom, +maximal 4 Punkte und auf unserem orginal 5 Punkte. Ansonsten hatt es mehr Fehler oder unser Konkurenzpolynom ist das gleiche wie das Original. +Somit können wir nun bestimmen, dass von den \textcolor{darkgreen}{7 Übertragungspunkten$u$} bis zu 2 Fehler korrigiert werden können und 4 Übertragungspunkte zusätzlich gesendet werden müssen. +\end{beispiel} +Durch das erkennen des Schemas in der Tabelle\ref{tabel:fehlerkorrekturstellen} +\begin{equation} + \frac{\textcolor{darkgreen}{u}-\textcolor{blue}{k}}{\textcolor{red}{t}} + =2 + \label{reedsolomon:equation2} +\end{equation} +zeigt sich das es $k+2t$ Übertragungspunkte braucht. \begin{center} - \begin{tabular}{ c c c } + \begin{tabular}{ c c | c} \hline Nutzlas & Fehler & Übertragen \\ \hline @@ -77,12 +102,11 @@ $k+2t$ Punkte übertragen werden müssen. $k$ & $t$ & $k+2t$ Werte eines Polynoms vom Grad $k-1$ \\ \hline \end{tabular} + Fehlerkorrekturstellen Bestimmung TODO: Tabellenreferenz + \label{tabel:fehlerkorrekturstellen} \end{center} -Ein toller Nebeneffekt ist das dadurch auch $2t$ Fehler erkannt werden. -Um zurück auf unser Beispiel zu kommen, -können von den 7 Übertragungspunkten bis zu $2t = 2\cdot2 = 4 $ Punkten falsch liegen -und es wird kein eindeutiges Polynom zweiten Grades erkannt, und somit die Nutzlast Daten als fehlerhaft deklariert. +Ein Nebeneffekt ist das dadurch auch $2t$ Fehler erkannt werden können, nicht aber korrigiert. Um aus den Übertragenen Zahlen wieder die Nutzlastzahlen zu bekommen könnte man eine Polynominterpolation anwenden, doch die Punkte mit Polynominterpolation zu einem Polynom zu rekonstruieren ist schwierig und Fehleranfällig. diff --git a/buch/papers/reedsolomon/images/codiert.txt b/buch/papers/reedsolomon/images/codiert.txt deleted file mode 100644 index 4a481d8..0000000 --- a/buch/papers/reedsolomon/images/codiert.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,284 -1,131.570790435043 -2,41.9840308053375 -3,12.1189172092243 -4,23.8408857476069 -5,69.1793197789512 -6,24.0186013379153 -7,37.3066577242559 -8,18.2010889773887 -9,12.3214904922455 -10,15.6627133315015 -11,24.5237955316204 -12,32.1114345314062 -13,44.9845039238714 -14,13.5324640263625 -15,10.1736266929292 -16,4.58257569495584 -17,23.217268502288 -18,16.5769107917917 -19,6.89948680823017 -20,4.84567134895776 -21,10.4219666223433 -22,43.6179140616243 -23,35.9073375743642 -24,15.0332963783729 -25,21.7594021268945 -26,23.2496572716993 -27,17.9815599423852 -28,11.3577742151117 -29,38.467599433197 -30,28.3035029562577 -31,9.54321919833388 -32,21.377558326432 -33,17.6292439561917 -34,12.6951848921471 -35,20.0667752354841 -36,22.9097309529208 -37,8.78894645948548 -38,13.360682005498 -39,25.1757616314718 -40,38.0357773686457 -41,18.4633287776253 -42,19.0584505869806 -43,10.8631093309173 -44,12.6147770818983 -45,12.5398140021274 -46,34.901983501949 -47,22.3480442021702 -48,6 -49,22.3480442021702 -50,34.901983501949 -51,12.5398140021274 -52,12.6147770818983 -53,10.8631093309173 -54,19.0584505869806 -55,18.4633287776253 -56,38.0357773686457 -57,25.1757616314718 -58,13.360682005498 -59,8.78894645948548 -60,22.9097309529208 -61,20.0667752354841 -62,12.6951848921471 -63,17.6292439561917 -64,21.377558326432 -65,9.54321919833388 -66,28.3035029562577 -67,38.467599433197 -68,11.3577742151117 -69,17.9815599423852 -70,23.2496572716993 -71,21.7594021268945 -72,15.0332963783729 -73,35.9073375743642 -74,43.6179140616243 -75,10.4219666223433 -76,4.84567134895776 -77,6.89948680823017 -78,16.5769107917917 -79,23.217268502288 -80,4.58257569495584 -81,10.1736266929292 -82,13.5324640263625 -83,44.9845039238714 -84,32.1114345314062 -85,24.5237955316204 -86,15.6627133315015 -87,12.3214904922455 -88,18.2010889773887 -89,37.3066577242559 -90,24.0186013379153 -91,69.1793197789512 -92,23.8408857476069 -93,12.1189172092243 -94,41.9840308053375 -95,131.570790435043 diff --git a/buch/papers/reedsolomon/images/decodiert.txt b/buch/papers/reedsolomon/images/decodiert.txt deleted file mode 100644 index f6221e6..0000000 --- a/buch/papers/reedsolomon/images/decodiert.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,6.05208333333333 -1,6.02602539785853 -2,0.0261327016093151 -3,5.98927158561317 -4,4.019445724874 -5,0.0247005083663722 -6,4.97798278395618 -7,1.95246440445439 -8,0.974000110512201 -9,2.00528527696027 -10,1.00071804528155 -11,1.97630907888264 -12,0.0232923747656228 -13,6.01302820392331 -14,3.03567381915226 -15,5.02435590137329 -16,7.00526061008995 -17,5.00739608089369 -18,5.02211514480064 -19,4.02175864806658 -20,1.00236543833726 -21,4.98147315261261 -22,8.97728828610336 -23,8.98481304394618 -24,2.98958333333333 -25,1.98491220960989 -26,5.97728835934715 -27,5.98144124907561 -28,4.00163839998525 -29,2.02176249296313 -30,9.02210713874162 -31,1.00742763919872 -32,1.00557258081044 -33,1.02435888848794 -34,2.03577412756745 -35,6.01302820392331 -36,5.97917574041123 -37,0.976310374034338 -38,9.00062625447998 -39,7.00515849238528 -40,6.97396416790894 -41,0.95256880864368 -42,8.97794719866783 -43,9.01850701506487 -44,10.0194409579917 -45,8.98926601525997 -46,7.9866590265379 -47,5.02603060999077 -48,2.05208333333333 -49,4.02603841132848 -50,0.986882897867895 -51,0.0177592928994285 -52,9.01944131204563 -53,3.0185365665612 -54,2.97803642439316 -55,2.95243072164649 -56,4.97396651395488 -57,6.00516695947321 -58,0.0143895905726619 -59,7.97630812771393 -60,5.97917574041123 -61,9.01298821331865 -62,3.03567381915226 -63,4.02435609145793 -64,0.0275599094902563 -65,0.0115837187254191 -66,0.025877761014238 -67,0.0224618032819697 -68,0.04410594689944 -69,0.0474504002669341 -70,0.0227694695500626 -71,0.0271436638090525 -72,0.0104166666666667 -73,0.0271436638090523 -74,0.0227694695500608 -75,0.0474504002669343 -76,0.0441059468994397 -77,0.0224618032819701 -78,0.0258777610142379 -79,0.0115837187254183 -80,0.027559909490256 -81,0.0245124379481793 -82,0.0499782237195209 -83,0.0401432022864265 -84,0.0232923747656228 -85,0.0237974288564099 -86,0.0143895905726624 -87,0.0271745729691685 -88,0.0275599094902567 -89,0.0515501672184983 -90,0.0358255004834542 -91,0.024700508366373 -92,0.0210194725405171 -93,0.0177592928994296 -94,0.0261327016093158 -95,0.0314909067039411 diff --git a/buch/papers/reedsolomon/images/empfangen.txt b/buch/papers/reedsolomon/images/empfangen.txt deleted file mode 100644 index 38c13b0..0000000 --- a/buch/papers/reedsolomon/images/empfangen.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,284 -1,131.570790435043 -2,41.9840308053375 -3,12.1189172092243 -4,23.8408857476069 -5,69.1793197789512 -6,23.6290258699579 -7,37.3066577242559 -8,18.2010889773887 -9,12.3214904922455 -10,15.6627133315015 -11,24.5237955316204 -12,32.1114345314062 -13,44.9845039238714 -14,13.5324640263625 -15,10.1736266929292 -16,4.58257569495584 -17,23.217268502288 -18,16.5769107917917 -19,6.89948680823017 -20,5.55320238736303 -21,10.4219666223433 -22,43.6179140616243 -23,35.9073375743642 -24,15.0332963783729 -25,21.7594021268945 -26,23.2496572716993 -27,17.9815599423852 -28,11.3577742151117 -29,38.467599433197 -30,28.3035029562577 -31,9.54321919833388 -32,21.377558326432 -33,17.6292439561917 -34,12.6951848921471 -35,20.0667752354841 -36,22.9097309529208 -37,8.78894645948548 -38,13.360682005498 -39,25.1757616314718 -40,38.0357773686457 -41,18.4633287776253 -42,19.0584505869806 -43,10.8631093309173 -44,12.6147770818983 -45,12.5398140021274 -46,34.901983501949 -47,22.3480442021702 -48,6 -49,22.3480442021702 -50,34.901983501949 -51,12.5398140021274 -52,12.6147770818983 -53,10.8631093309173 -54,19.0584505869806 -55,18.4633287776253 -56,38.0357773686457 -57,25.1757616314718 -58,13.360682005498 -59,8.78894645948548 -60,22.9097309529208 -61,20.0667752354841 -62,12.6951848921471 -63,17.6292439561917 -64,21.377558326432 -65,9.54321919833388 -66,28.3035029562577 -67,38.467599433197 -68,11.3577742151117 -69,17.9815599423852 -70,23.2496572716993 -71,21.7594021268945 -72,15.0332963783729 -73,35.9073375743642 -74,44.6135417384784 -75,10.4219666223433 -76,4.84567134895776 -77,6.89948680823017 -78,16.5769107917917 -79,23.217268502288 -80,4.58257569495584 -81,10.1736266929292 -82,13.5324640263625 -83,44.9845039238714 -84,32.1114345314062 -85,24.5237955316204 -86,15.6627133315015 -87,12.3214904922455 -88,18.2010889773887 -89,37.3066577242559 -90,24.0186013379153 -91,69.1793197789512 -92,23.8408857476069 -93,12.1189172092243 -94,41.9840308053375 -95,131.570790435043 diff --git a/buch/papers/reedsolomon/images/fehler.txt b/buch/papers/reedsolomon/images/fehler.txt deleted file mode 100644 index 23f1a83..0000000 --- a/buch/papers/reedsolomon/images/fehler.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,0 -1,0 -2,0 -3,0 -4,0 -5,0 -6,2 -7,0 -8,0 -9,0 -10,0 -11,0 -12,0 -13,0 -14,0 -15,0 -16,0 -17,0 -18,0 -19,0 -20,2 -21,0 -22,0 -23,0 -24,0 -25,0 -26,0 -27,0 -28,0 -29,0 -30,0 -31,0 -32,0 -33,0 -34,0 -35,0 -36,0 -37,0 -38,0 -39,0 -40,0 -41,0 -42,0 -43,0 -44,0 -45,0 -46,0 -47,0 -48,0 -49,0 -50,0 -51,0 -52,0 -53,0 -54,0 -55,0 -56,0 -57,0 -58,0 -59,0 -60,0 -61,0 -62,0 -63,0 -64,0 -65,0 -66,0 -67,0 -68,0 -69,0 -70,0 -71,0 -72,0 -73,0 -74,1 -75,0 -76,0 -77,0 -78,0 -79,0 -80,0 -81,0 -82,0 -83,0 -84,0 -85,0 -86,0 -87,0 -88,0 -89,0 -90,0 -91,0 -92,0 -93,0 -94,0 -95,0 diff --git a/buch/papers/reedsolomon/images/locator.txt b/buch/papers/reedsolomon/images/locator.txt deleted file mode 100644 index b28988c..0000000 --- a/buch/papers/reedsolomon/images/locator.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,0.0301224340567056 -1,0.141653026854885 -2,0.138226631799377 -3,0.0339903276086929 -4,0.310585462557496 -5,0.551427312631385 -6,0.628514858396814 -7,0.51102386251559 -8,0.275861355940449 -9,0.0502396354182268 -10,0.090185502547573 -11,0.110759344849756 -12,0.0684618905063001 -13,0.0362855426992259 -14,0.0697096919781468 -15,0.109288539370248 -16,0.0923187999496653 -17,0.0512198536768088 -18,0.274192386987782 -19,0.51349614953654 -20,0.633154426602466 -21,0.553283743533942 -22,0.307840573214514 -23,0.0341664350328392 -24,0.140270857957 -25,0.138527177682831 -26,0.029637547736156 -27,0.0816962563186052 -28,0.0944383203811073 -29,0.0263932110686261 -30,0.0585881348402056 -31,0.0737117341599984 -32,0.0239973937701886 -33,0.0464215468420038 -34,0.0616218854220964 -35,0.0221963086695009 -36,0.0390764778127646 -37,0.0537637218396934 -38,0.0208333333333332 -39,0.0343107696069045 -40,0.0483441215964552 -41,0.0198077862118806 -42,0.0311207395968725 -43,0.0444955089373458 -44,0.0190533549944159 -45,0.0290049795038723 -46,0.0417536642697558 -47,0.0185261550443084 -48,0.0277059929762261 -49,0.0398606084144816 -50,0.0181978813094817 -51,0.0271098219177584 -52,0.0386836665079729 -53,0.0180518611046889 -54,0.0272138992557141 -55,0.0381891287148314 -56,0.0180809085252469 -57,0.0281418959420061 -58,0.0384596362516637 -59,0.0182864418432272 -60,0.0302250788423173 -61,0.0397874837986351 -62,0.0186786556701694 -63,0.0342489348284216 -64,0.0429932815348666 -65,0.0192777878591759 -66,0.0422808966931999 -67,0.0506815964680563 -68,0.0201167847752226 -69,0.0615048274405271 -70,0.0744953894508454 -71,0.021246054596492 -72,0.142602265816215 -73,0.273502052865436 -74,0.325309673287599 -75,0.272705389655349 -76,0.149074257381345 -77,0.0247199397628712 -78,0.0680137859566976 -79,0.075388270873485 -80,0.0273637831604903 -81,0.0407867704453274 -82,0.0632964886441949 -83,0.0309749128751093 -84,0.0315202035072035 -85,0.0627625211892184 -86,0.0360843918243497 -87,0.02794920551495 -88,0.0677921493367236 -89,0.0437167157553067 -90,0.0270640150996317 -91,0.0783380025231622 -92,0.0561293738314281 -93,0.0278742033265809 -94,0.0981443889498639 -95,0.0794543457386548 diff --git a/buch/papers/reedsolomon/images/plotfft.tex b/buch/papers/reedsolomon/images/plotfft.tex deleted file mode 100644 index 83a89eb..0000000 --- a/buch/papers/reedsolomon/images/plotfft.tex +++ /dev/null @@ -1,89 +0,0 @@ -% -% Plot der Übertrangungsabfolge ins FFT und zurück mit IFFT -% -\begin{tikzpicture}[] - -%--------------------------------------------------------------- - %Knote -\matrix[draw = none, column sep=25mm, row sep=2mm]{ - \node(signal) [] { - \begin{tikzpicture} - \begin{axis} - [title = {\Large {Signal}}, - xlabel={Anzahl Übertragene Zahlen}, - xtick={0,20,40,64,80,98},] - \addplot[blue] table[col sep=comma] {papers/reedsolomon/images/signal.txt}; - \end{axis} - \end{tikzpicture}}; & - - \node(codiert) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Codiert}}] - \addplot[] table[col sep=comma] {papers/reedsolomon/images/codiert.txt}; - \end{axis} - \end{tikzpicture}}; \\ - - &\node(fehler) [] { - \begin{tikzpicture} - \begin{axis}[scale=0.6, title = {\Large {Fehler}}, - xtick={7,21,75}] - \addplot[red] table[col sep=comma] {papers/reedsolomon/images/fehler.txt}; - \end{axis} - \end{tikzpicture}};\\ - - \node(decodiert) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Decodiert}}] - \addplot[blue] table[col sep=comma] {papers/reedsolomon/images/decodiert.txt}; - \end{axis} - \end{tikzpicture}}; & - - \node(empfangen) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Empfangen}}] - \addplot[] table[col sep=comma] {papers/reedsolomon/images/empfangen.txt}; - \end{axis} - \end{tikzpicture}};\\ - - \node(syndrom) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Syndrom}}] - \addplot[blue] table[col sep=comma] {papers/reedsolomon/images/syndrom.txt}; - \end{axis} - \end{tikzpicture}}; & - - \node(locator) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Locator}}] - \addplot[] table[col sep=comma] {papers/reedsolomon/images/locator.txt}; - \end{axis} - \end{tikzpicture}};\\ -}; -%------------------------------------------------------------- - %FFT & IFFT deskription - -\draw[thin,gray,dashed] (0,12) to (0,-12); -\node(IFFT) [scale=0.7] at (0,12.3) {IFFT}; -\draw[<-](IFFT.south west)--(IFFT.south east); -\node(FFT) [scale=0.7, above of=IFFT] {FFT}; -\draw[->](FFT.north west)--(FFT.north east); - -\draw[thick, ->,] (fehler.west)++(-1,0) +(0.05,0.5) -- +(-0.1,-0.1) -- +(0.1,0.1) -- +(0,-0.5); -%Arrows -\draw[ultra thick, ->] (signal.east) to (codiert.west); -\draw[ultra thick, ->] (codiert.south) to (fehler.north); -\draw[ultra thick, ->] (fehler.south) to (empfangen.north); -\draw[ultra thick, ->] (empfangen.west) to (decodiert.east); -\draw[ultra thick, ->] (syndrom.east) to (locator.west); -\draw(decodiert.south east)++(-1.8,1) ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ; -\draw[ultra thick, ->] (zoom) to[out=180, in=90] (syndrom.north); - -%item -\node[circle, draw, fill =lightgray] at (signal.north west) {1}; -\node[circle, draw, fill =lightgray] at (codiert.north west) {2}; -\node[circle, draw, fill =lightgray] at (fehler.north west) {3}; -\node[circle, draw, fill =lightgray] at (empfangen.north west) {4}; -\node[circle, draw, fill =lightgray] at (decodiert.north west) {5}; -\node[circle, draw, fill =lightgray] at (syndrom.north west) {6}; -\node[circle, draw, fill =lightgray] at (locator.north west) {7}; -\end{tikzpicture}
\ No newline at end of file diff --git a/buch/papers/reedsolomon/images/signal.txt b/buch/papers/reedsolomon/images/signal.txt deleted file mode 100644 index c4fa5f8..0000000 --- a/buch/papers/reedsolomon/images/signal.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,6 -1,6 -2,0 -3,6 -4,4 -5,0 -6,5 -7,2 -8,1 -9,2 -10,1 -11,2 -12,0 -13,6 -14,3 -15,5 -16,7 -17,5 -18,5 -19,4 -20,1 -21,5 -22,9 -23,9 -24,3 -25,2 -26,6 -27,6 -28,4 -29,2 -30,9 -31,1 -32,1 -33,1 -34,2 -35,6 -36,6 -37,1 -38,9 -39,7 -40,7 -41,1 -42,9 -43,9 -44,10 -45,9 -46,8 -47,5 -48,2 -49,4 -50,1 -51,0 -52,9 -53,3 -54,3 -55,3 -56,5 -57,6 -58,0 -59,8 -60,6 -61,9 -62,3 -63,4 -64,0 -65,0 -66,0 -67,0 -68,0 -69,0 -70,0 -71,0 -72,0 -73,0 -74,0 -75,0 -76,0 -77,0 -78,0 -79,0 -80,0 -81,0 -82,0 -83,0 -84,0 -85,0 -86,0 -87,0 -88,0 -89,0 -90,0 -91,0 -92,0 -93,0 -94,0 -95,0 diff --git a/buch/papers/reedsolomon/images/syndrom.txt b/buch/papers/reedsolomon/images/syndrom.txt deleted file mode 100644 index 8ca9eed..0000000 --- a/buch/papers/reedsolomon/images/syndrom.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,0 -1,0 -2,0 -3,0 -4,0 -5,0 -6,0 -7,0 -8,0 -9,0 -10,0 -11,0 -12,0 -13,0 -14,0 -15,0 -16,0 -17,0 -18,0 -19,0 -20,0 -21,0 -22,0 -23,0 -24,0 -25,0 -26,0 -27,0 -28,0 -29,0 -30,0 -31,0 -32,0 -33,0 -34,0 -35,0 -36,0 -37,0 -38,0 -39,0 -40,0 -41,0 -42,0 -43,0 -44,0 -45,0 -46,0 -47,0 -48,0 -49,0 -50,0 -51,0 -52,0 -53,0 -54,0 -55,0 -56,0 -57,0 -58,0 -59,0 -60,0 -61,0 -62,0 -63,0 -64,0.0275599094902563 -65,0.0115837187254191 -66,0.025877761014238 -67,0.0224618032819697 -68,0.04410594689944 -69,0.0474504002669341 -70,0.0227694695500626 -71,0.0271436638090525 -72,0.0104166666666667 -73,0.0271436638090523 -74,0.0227694695500608 -75,0.0474504002669343 -76,0.0441059468994397 -77,0.0224618032819701 -78,0.0258777610142379 -79,0.0115837187254183 -80,0.027559909490256 -81,0.0245124379481793 -82,0.0499782237195209 -83,0.0401432022864265 -84,0.0232923747656228 -85,0.0237974288564099 -86,0.0143895905726624 -87,0.0271745729691685 -88,0.0275599094902567 -89,0.0515501672184983 -90,0.0358255004834542 -91,0.024700508366373 -92,0.0210194725405171 -93,0.0177592928994296 -94,0.0261327016093158 -95,0.0314909067039411 diff --git a/buch/papers/reedsolomon/main.tex b/buch/papers/reedsolomon/main.tex index ab4e4be..017fe94 100644 --- a/buch/papers/reedsolomon/main.tex +++ b/buch/papers/reedsolomon/main.tex @@ -8,29 +8,9 @@ \begin{refsection} \chapterauthor{Joshua Bär und Michael Steiner} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} - % Joshua \input{papers/reedsolomon/einleitung.tex} \input{papers/reedsolomon/idee.tex} -%\input{papers/reedsolomon/teil2.tex} \input{papers/reedsolomon/dtf.tex} % Michael diff --git a/buch/papers/reedsolomon/packages.tex b/buch/papers/reedsolomon/packages.tex index b84e228..40c6ea3 100644 --- a/buch/papers/reedsolomon/packages.tex +++ b/buch/papers/reedsolomon/packages.tex @@ -10,3 +10,5 @@ \usepackage{pgfplots} \usepackage{filecontents} +\usepackage{xr} + diff --git a/buch/papers/reedsolomon/standalone.tex b/buch/papers/reedsolomon/standalone.tex new file mode 100644 index 0000000..c850d1f --- /dev/null +++ b/buch/papers/reedsolomon/standalone.tex @@ -0,0 +1,30 @@ +\documentclass{book} + +\input{common/packages.tex} + +% additional packages used by the individual papers, add a line for +% each paper +\input{papers/common/addpackages.tex} + +% workaround for biblatex bug +\makeatletter +\def\blx@maxline{77} +\makeatother +\addbibresource{chapters/references.bib} + +% Bibresources for each article +\input{papers/common/addbibresources.tex} + +% make sure the last index starts on an odd page +\AtEndDocument{\clearpage\ifodd\value{page}\else\null\clearpage\fi} +\makeindex + +%\pgfplotsset{compat=1.12} +\setlength{\headheight}{15pt} % fix headheight warning +\DeclareGraphicsRule{*}{mps}{*}{} + +\begin{document} + \input{common/macros.tex} + \def\chapterauthor#1{{\large #1}\bigskip\bigskip} + \input{papers/reedsolomon/main.tex} +\end{document} diff --git a/buch/papers/reedsolomon/standalone/standalone.pdf b/buch/papers/reedsolomon/standalone/standalone.pdf Binary files differnew file mode 100644 index 0000000..1f2f0b9 --- /dev/null +++ b/buch/papers/reedsolomon/standalone/standalone.pdf diff --git a/buch/papers/reedsolomon/experiments/codiert.txt b/buch/papers/reedsolomon/tikz/codiert.txt index 4a481d8..4a481d8 100644 --- a/buch/papers/reedsolomon/experiments/codiert.txt +++ b/buch/papers/reedsolomon/tikz/codiert.txt diff --git a/buch/papers/reedsolomon/experiments/decodiert.txt b/buch/papers/reedsolomon/tikz/decodiert.txt index f6221e6..f6221e6 100644 --- a/buch/papers/reedsolomon/experiments/decodiert.txt +++ b/buch/papers/reedsolomon/tikz/decodiert.txt diff --git a/buch/papers/reedsolomon/experiments/empfangen.txt b/buch/papers/reedsolomon/tikz/empfangen.txt index 38c13b0..38c13b0 100644 --- a/buch/papers/reedsolomon/experiments/empfangen.txt +++ b/buch/papers/reedsolomon/tikz/empfangen.txt diff --git a/buch/papers/reedsolomon/experiments/fehler.txt b/buch/papers/reedsolomon/tikz/fehler.txt index 23f1a83..23f1a83 100644 --- a/buch/papers/reedsolomon/experiments/fehler.txt +++ b/buch/papers/reedsolomon/tikz/fehler.txt diff --git a/buch/papers/reedsolomon/experiments/locator.txt b/buch/papers/reedsolomon/tikz/locator.txt index b28988c..b28988c 100644 --- a/buch/papers/reedsolomon/experiments/locator.txt +++ b/buch/papers/reedsolomon/tikz/locator.txt diff --git a/buch/papers/reedsolomon/tikz/plotfft.tex b/buch/papers/reedsolomon/tikz/plotfft.tex new file mode 100644 index 0000000..14af683 --- /dev/null +++ b/buch/papers/reedsolomon/tikz/plotfft.tex @@ -0,0 +1,94 @@ +% +% Plot der Übertrangungsabfolge ins FFT und zurück mit IFFT +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{pgfplots} +\usepackage{pgfplotstable} +\usepackage{csvsimple} +\usepackage{filecontents} + + +\begin{document} +\begin{tikzpicture}[] + + %--------------------------------------------------------------- + %Knote + \matrix(m) [draw = none, column sep=25mm, row sep=2mm]{ + + \node(signal) [] { + \begin{tikzpicture} + \begin{axis} + [title = {\Large {Signal}}, + xtick={0,20,40,64,80,98}] + \addplot[blue] table[col sep=comma] {tikz/signal.txt}; + \end{axis} + \end{tikzpicture}}; & + + \node(codiert) [] { + \begin{tikzpicture}[] + \begin{axis}[ title = {\Large {Codiert \space + \space Fehler}}, + xtick={0,40,60,100}, axis y line*=left] + \addplot[green] table[col sep=comma] {tikz/codiert.txt}; + \end{axis} + \begin{axis}[xtick={7,21,75}, axis y line*=right] + \addplot[red] table[col sep=comma] {tikz/fehler.txt}; + \end{axis} + \end{tikzpicture}}; \\ + + \node(decodiert) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Decodiert}}] + \addplot[blue] table[col sep=comma] {tikz/decodiert.txt}; + \end{axis} + \end{tikzpicture}}; & + + \node(empfangen) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Empfangen}}] + \addplot[green] table[col sep=comma] {tikz/empfangen.txt}; + \end{axis} + \end{tikzpicture}};\\ + + \node(syndrom) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Syndrom}}] + \addplot[black] table[col sep=comma] {tikz/syndrom.txt}; + \end{axis} + \end{tikzpicture}}; & + + \node(locator) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Locator}}] + \addplot[gray] table[col sep=comma] {tikz/locator.txt}; + \end{axis} + \end{tikzpicture}};\\ + }; + %------------------------------------------------------------- + %FFT & IFFT deskription + + \draw[thin,gray,dashed] (0,9) to (0,-9); + \node(IFFT) [scale=0.8] at (0,9.3) {IFFT}; + \draw[stealth-](IFFT.south west)--(IFFT.south east); + \node(FFT) [scale=0.8, above of=IFFT] {FFT}; + \draw[-stealth](FFT.north west)--(FFT.north east); + + \draw[thick, ->,] (codiert)++(-1,0) +(0.05,0.5) -- +(-0.1,-0.1) -- +(0.1,0.1) -- +(0,-0.5); + %Arrows + \draw[thick, ->] (signal.east) to (codiert.west); + \draw[thick, ->] (codiert.south) to (empfangen.north); + \draw[thick, ->] (empfangen.west) to (decodiert.east); + \draw[thick, ->] (syndrom.east) to (locator.west); + \draw[thick](decodiert.south east)++(-1.8,1) ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ; + \draw[thick, ->] (zoom) to[out=180, in=90] (syndrom.north); + + %item + \node[circle, draw, fill =lightgray] at (signal.north west) {1}; + \node[circle, draw, fill =lightgray] at (codiert.north west) {2+3}; + \node[circle, draw, fill =lightgray] at (empfangen.north west) {4}; + \node[circle, draw, fill =lightgray] at (decodiert.north west) {5}; + \node[circle, draw, fill =lightgray] at (syndrom.north west) {6}; + \node[circle, draw, fill =lightgray] at (locator.north west) {7}; +\end{tikzpicture} +\end{document}
\ No newline at end of file diff --git a/buch/papers/reedsolomon/images/polynom2.tex b/buch/papers/reedsolomon/tikz/polynom2.tex index 288b51c..47dc679 100644 --- a/buch/papers/reedsolomon/images/polynom2.tex +++ b/buch/papers/reedsolomon/tikz/polynom2.tex @@ -1,5 +1,13 @@ % polynome %------------------- + +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{pgfplots} + + +\begin{document} % Teiler für das Skalieren der Grafik /40 \newcommand{\teiler}{40} @@ -21,9 +29,14 @@ \def\hellpunkt#1{ \fill[color=lightgray] #1 circle[radius=0.08]; - \draw #1 circle[radius=0.07]; + \draw[gray] #1 circle[ radius=0.07]; } + \draw[color=gray,line width=1pt,dashed] + plot[domain=0.5:7, samples=100] + ({\x},{(7.832*\x^2-51.5*\x+121.668)/\teiler}); + + \punkt{(1,8/\teiler)} \hellpunkt{(2,15/\teiler)} \hellpunkt{(3,26/\teiler)} @@ -32,9 +45,7 @@ \punkt{(6,83/\teiler)} \punkt{(7,110/\teiler)} - \draw[color=gray,line width=1pt,dashed] - plot[domain=0.5:7, samples=100] - ({\x},{(7.832*\x^2-51.5*\x+121.668)/\teiler}); + \def\erpunkt#1{ \fill[color=red] #1 circle[radius=0.08]; @@ -46,4 +57,4 @@ \draw(0,100/\teiler) -- (-0.1,100/\teiler) coordinate[label={left:$100$}]; \draw(1,0) -- (1,-0.1) coordinate[label={below:$1$}]; \end{tikzpicture} -%\end{document} +\end{document} diff --git a/buch/papers/reedsolomon/experiments/signal.txt b/buch/papers/reedsolomon/tikz/signal.txt index c4fa5f8..c4fa5f8 100644 --- a/buch/papers/reedsolomon/experiments/signal.txt +++ b/buch/papers/reedsolomon/tikz/signal.txt diff --git a/buch/papers/reedsolomon/experiments/syndrom.txt b/buch/papers/reedsolomon/tikz/syndrom.txt index 8ca9eed..8ca9eed 100644 --- a/buch/papers/reedsolomon/experiments/syndrom.txt +++ b/buch/papers/reedsolomon/tikz/syndrom.txt diff --git a/buch/papers/spannung/Einleitung.tex b/buch/papers/spannung/Einleitung.tex index b1588ff..8e0d36d 100644 --- a/buch/papers/spannung/Einleitung.tex +++ b/buch/papers/spannung/Einleitung.tex @@ -1,17 +1,18 @@ \section{Einleitung\label{spannung:section:Einleitung}} \rhead{Einleitung} Das Hook'sche Gesetz beschreibt die Beziehung von Spannung und Dehnung von linear-elastischen Materialien im Eindimensionalen. -In diesem Kapitel geht es darum das Hook'sche Gesetz im Dreidimensionalen zu beschreiben. +In diesem Kapitel geht es darum, das Hook'sche Gesetz im Dreidimensionalen zu beschreiben. Durch variable Krafteinwirkungen entstehen in jedem Punkt des Materials eine Vielzahl an unterschiedlichen Spannungen. In jedem erdenklichen Punkt im Dreidimensionalen herrscht daher ein entsprechender individueller Spannungszustand. Um das Hook'sche Gesetz für den 3D Spannungszustand formulieren zu können, reichen Skalare nicht aus. -Darum werden Vektoren, Matrizen und Tensoren zur Hilfe gezogen. +Darum werden Vektoren, Matrizen und Tensoren zu Hilfe gezogen. Mit diesen lässt sich eine Spannungsformel für den 3D Spannungszustand bilden. Diese Spannungsformel ist Grundlage für Computerprogramme und geotechnische Versuche, wie der Oedometer-Versuch. -Um die mathematische Untersuchung vorzunehmen, beschäftigt man sich zuerst mit den spezifischen Gegebenheiten und Voraussetzungen. -Ebenfalls gilt es ein paar wichtige Begriffe und deren mathematischen Zeichen einzuführen. -In diesem Kapitel gehen wir auch auf die Zusammenhänge von Spannung, Dehnungen und Verformungen an elastischen Materialien ein, +Um die mathematischen und physikalischen Berechnungen anwenden zu können, +müssen vorerst ein paar spezifische Bedingungen vorausgesetzt und Annahmen getroffen werden. +Ebenfalls gilt es, ein paar wichtige Begriffe und deren mathematischen Zeichen einzuführen. +In diesem Kapitel gehen wir auch auf die Zusammenhänge von Spannungen, Dehnungen und Verformungen an elastischen Materialien ein, wie sie in gängigen Lehrbüchern der Mechanik oder der Geotechnik behandelt werden, z.~B.~\cite{spannung:Grundlagen-der-Geotechnik}. \section{Spannungsausbreitung\label{spannung:section:Spannungsausbreitung}} @@ -29,7 +30,7 @@ Belastet man den Boden mit einer Spannung so wird diese in den Boden geleitet und von diesem kompensiert. Im Boden entstehen unterschiedlich hohe Zusatzspannungen. Diese Zusatzspannung breitet sich räumlich im Boden aus. -Im Falle einer konstanten Flächenlast $\sigma$ siehe Abbildung~\ref{spannung:Bild4} breitet sich die Zusatzspannung zwiebelartig aus. +Im Falle einer konstanten Flächenlast $\sigma$ siehe Abbildung~\ref{fig:Bild4} breitet sich die Zusatzspannung zwiebelartig aus. \begin{figure} \centering @@ -38,11 +39,11 @@ Im Falle einer konstanten Flächenlast $\sigma$ siehe Abbildung~\ref{spannung:Bi \label{fig:Bild4} \end{figure} -Mit der Tiefe $t$ nimmt diese permanent ab (siehe Abbildung~\ref{spannung:Bild5}). -Wie diese Geometrie der Ausbreitung ist, kann durch viele Modelle und Ansätze näherungsweise beschrieben werden. +Mit der Tiefe $t$ nimmt diese permanent ab (siehe Abbildung~\ref{fig:Bild5}). +Wie diese Geometrie der Ausbreitung aussieht, kann durch viele Modelle und Ansätze näherungsweise beschrieben werden. Diese Zusatzspannung $\sigma$ ist im Wesentlichen abhängig von $(x,y,t)$. Je nach Modell werden noch andere Parameter berücksichtigt. -Das können beispielsweise jenste Bodenkennwerte oder auch der Wassergehalt sein. +Das können beispielsweise verschiedene Bodenkennwerte oder auch der Wassergehalt sein. \begin{figure} \centering @@ -72,18 +73,18 @@ berechnet werden mit: t &= \text{Tiefe [\si{\meter}]} \\ s &= \text{Setzung, Absenkung [m].} \end{align*} -Diese Zusammenhänge sind wie erwähnt unter anderem im Lehrbuch [\cite{spannung:Grundlagen-der-Geotechnik}] beschrieben. +Diese Zusammenhänge sind wie erwähnt unter anderem im Lehrbuch \cite{spannung:Grundlagen-der-Geotechnik} beschrieben. In der praktischen Geotechnik wird man allerdings weitaus schwierigere Situationen antreffen. -Ein Beispiel wäre eine Baugrube mit einem Baugrubenabschluss, wo ein Teil des Bodens abgetragen ist (siehe Abbildung~\ref{spannung:Bild3}). +Ein Beispiel wäre eine Baugrube mit einem Baugrubenabschluss, wo ein Teil des Bodens abgetragen ist (siehe Abbildung~\ref{fig:Bild3}). Die Ausbreitung der Zusatzspannung $\sigma(x,y,t)$ würde hier deutlich komplizierter ausfallen. Dies bedeutet auch eine komplexere Setzung der Bodenoberfläche infolge einer Flächenlast $\sigma$. Aus allen zusätzlichen Spannungen müssen die adäquaten Dehnungen mit Hilfe einer Spannungsgleichung berechnet werden. Diese beruht auf Annahmen nach Hooke auf einem linear-elastischen Boden. -Generell wird im Ingenieurwesen versucht Phänomene möglichst nach dem Hook'schen Gesetz abbilden zu können. +Generell wird im Bauingenieurwesen oder auch im Maschinenbau versucht, manche Phänomene möglichst nach dem Hook'schen Gesetz abbilden zu können. \begin{figure} \centering \includegraphics[width=0.45\linewidth,keepaspectratio]{papers/spannung/Grafiken/Bild3.png} - \caption{Beispiel eines Lastauftrags auf den Boden bei einer komplexeren Situation, welches kompliziertere Spannungsausbreitung zur Folge hat} + \caption{Beispiel eines Lastauftrags auf den Boden bei einer komplexeren Situation, welche kompliziertere Spannungsausbreitung zur Folge hat} \label{fig:Bild3} \end{figure} diff --git a/buch/papers/spannung/main.tex b/buch/papers/spannung/main.tex index bbdf730..d2aeda9 100644 --- a/buch/papers/spannung/main.tex +++ b/buch/papers/spannung/main.tex @@ -3,7 +3,7 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:spannung}} +\chapter{Dreidimensionaler Spannungszustand\label{chapter:spannung}} \lhead{Dreiachsiger Spannungszustand} \begin{refsection} \chapterauthor{Adrian Schuler und Thomas Reichlin} diff --git a/buch/papers/spannung/teil0.tex b/buch/papers/spannung/teil0.tex index 7647252..089c28e 100644 --- a/buch/papers/spannung/teil0.tex +++ b/buch/papers/spannung/teil0.tex @@ -1,9 +1,10 @@ \section{Der Spannungszustand\label{spannung:section:Der Spannungsustand}} \rhead{Der Spannungszustand} -Ein Spannungszustand ist durch alle Spannungen, welche in einem beliebigen Punkt im Körper wirken, definiert (siehe Abbildung~\ref{spannung:Bild2}). +Ein Spannungszustand ist durch alle Spannungen, welche in einem beliebigen Punkt im Körper wirken, definiert (siehe Abbildung~\ref{fig:Bild2}). Änderungen der äusseren Kräfte verändern die inneren Spannungszustände im Material. -Um alle Spannungen eines Punktes darstellen zu können, wird ein infinitesimales Bodenelement in Form eines Würfels modellhaft vorgestellt. -Man spricht auch von einem Elementarwürfel, da dieser elementar klein ist. +Um alle Spannungen eines Punktes darstellen zu können, +stellt man sich modellhaft ein infinitesimales Bodenelement in Form eines Würfels vor. +Man spricht auch von einem Elementarwürfel. \begin{figure} \centering @@ -15,19 +16,19 @@ Man spricht auch von einem Elementarwürfel, da dieser elementar klein ist. Es werden jeweils drei Seiten dieses Würfels betrachtet, wobei die drei gegenüberliegenden Seiten im Betrag die selben Spannungen aufweisen, sodass der Elementarwürfel im Gleichgewicht ist. Wäre dieses Gleichgewicht nicht vorhanden, käme es zu Verschiebungen und Drehungen. -Das infinitesimale Bodenteilchen hat die Koordinaten $1$, $2$, $3$. +Das infinitesimale Bodenteilchen hat die Koordinatenachsen $1$, $2$, $3$. Veränderungen der Normalspannungen können durch Schubspannungen kompensiert werden und umgekehrt. -So sind insgesamt neun verschiedene Spannungen möglich, wobei drei Normal- und sechs Schubspannungen sind. +So sind insgesamt neun verschiedene Spannungen möglich, konkret sind dies drei Normal- und sechs Schubspannungen. Normalspannungen wirken normal (mit rechtem Winkel) zur angreifenden Fläche und Schubspannungen parallel zur angreifenden Fläche. Alle Beträge dieser neun Spannungen am Elementarwürfel bilden den Spannungszustand. -Daraus können die äquivalenten Dehnungen $\varepsilon$ mit Hilfe des Hook'schen Gesetz berechnet werden. +Daraus können die äquivalenten Dehnungen $\varepsilon$ mit Hilfe des Hook'schen Gesetzes berechnet werden. Daher gibt es auch den entsprechenden Dehnungszustand. \section{Spannungszustand\label{spannung:section:Spannungsustand}} \rhead{Spannungszustand} -Im einachsigen Spannungszustand herrscht nur die Normalspannung $\sigma_{11}$ (siehe Abbildung~\ref{spannung:Bild1}). +Im einachsigen Spannungszustand herrscht nur die Normalspannung $\sigma_{11}$ (siehe Abbildung~\ref{fig:Bild1}). Das Hook'sche Gesetz beschreibt genau diesen 1D Spannungszustand. Nach Hooke gilt: \[ @@ -59,7 +60,7 @@ mit A &= \text{Fläche [\si{\meter\squared}].} \end{align*} Diese Beziehung gilt bei linear-elastischen Materialien, welche reversible Verformungen zulassen. -Es ist praktisch die relative Dehnung $\varepsilon$ anzugeben und nicht eine absolute Längenänderung $\Delta l$. +Es ist praktisch, die relative Dehnung $\varepsilon$ anzugeben und nicht eine absolute Längenänderung $\Delta l$. \begin{figure} \centering \includegraphics[width=0.35\linewidth,keepaspectratio]{papers/spannung/Grafiken/Bild1.png} @@ -73,10 +74,10 @@ Mithilfe vom Elastizitätsmodul $E$ als Proportionalitätskonstante lässt sich E\cdot\varepsilon \] beschreiben. -Im Falle, dass $E$ nicht konstant ist, kann dieser näherungsweise durch +Im Falle, dass $E$ nicht konstant ist, wird dieser durch \[ E = -\frac{\Delta\sigma}{\Delta\varepsilon} +\frac{\text{d}\sigma}{\text{d}\varepsilon} \] -ausgedrückt werden.
\ No newline at end of file +ausgedrückt.
\ No newline at end of file diff --git a/buch/papers/spannung/teil1.tex b/buch/papers/spannung/teil1.tex index 74516c1..647b452 100644 --- a/buch/papers/spannung/teil1.tex +++ b/buch/papers/spannung/teil1.tex @@ -1,8 +1,8 @@ \section{Skalare, Vektoren, Matrizen und Tensoren\label{spannung:section:Skalare,_Vektoren,_Matrizen_und_Tensoren}} \rhead{Skalare, Vektoren, Matrizen und Tensoren} -Der Begriff Tensor kann als Überbegriff, der mathematischen Objekte Skalar, Vektor und Matrix, betrachtet werden. +Der Begriff Tensor kann als Überbegriff der mathematischen Objekte Skalar, Vektor und Matrix, betrachtet werden. Allerdings sind noch höhere Stufen dieser Objekte beinhaltet. -Ein Skalar, ein Vektor oder eine Matrix ist daher auch ein Tensor. +Skalare, Vektoren oder Matrizen sind daher auch Tensoren. Ein Skalar ist ein Tensor 0. Stufe. Mit einem Vektor können mehrere Skalare auf einmal beschrieben werden. Ein Vektor hat daher die Stufe 1 und ist höherstufig als ein Skalar. @@ -14,11 +14,10 @@ Jede Stufe von Tensoren verlangt andere Rechenregeln. So zeigt sich auch der Nachteil von Tensoren mit Stufen höher als 2. Man ist also bestrebt höherstufige Tensoren mit Skalaren, Vektoren oder Matrizen zu beschreiben. -Der Begriff Tensor wurde 1840 von Rowan Hamilton in die Mathematik eingeführt. +In den 40er Jahren vom 19. Jahrhundert wurde der Begriff Tensor von Rowan Hamilton in die Mathematik eingeführt. James Clerk Maxwell hat bereits mit Tensoren operiert, ohne den Begriff Tensor gekannt zu haben. Erst Woldemar Voigt hat den Begriff in die moderne Bedeutung von Skalar, Matrix und Vektor verallgemeinert. Er hat in der Elastizitätstheorie als erstes Tensoren eingesetzt und beschrieben. Auch Albert Einstein hat solche Tensoren eingesetzt, um in der Relativitätstheorie die Änderung der 4D Raumzeit beschreiben zu können. \cite{spannung:Tensor} -\cite{spannung:Voigtsche-Notation} diff --git a/buch/papers/spannung/teil2.tex b/buch/papers/spannung/teil2.tex index 6326eab..8620afe 100644 --- a/buch/papers/spannung/teil2.tex +++ b/buch/papers/spannung/teil2.tex @@ -3,7 +3,7 @@ Durch komplexe Spannungsausbreitungen im Boden entstehen im 3D Spannungszustand unterschiedliche Normal- und Schubspannungen. \begin{figure} \centering - \includegraphics[width=0.4\linewidth,keepaspectratio]{papers/spannung/Grafiken/infinitesimalerWuerfel.png} + \includegraphics[width=0.30\linewidth,keepaspectratio]{papers/spannung/Grafiken/infinitesimalerWuerfel.png} \caption{Beispiel eines Spannungszustandes; Vergrösserung eines infinitesimalen Bodenteilchen} \label{fig:infinitesimalerWuerfel} \end{figure} @@ -49,7 +49,7 @@ Der Dehnungstensor ist ebenfalls ein Tensor 2. Stufe und kann somit auch als $3\ dargestellt werden und beschreibt den gesamten Dehnungszustand. Der Spannungs- und Dehnungstensor 2. Stufe kann je in einen Tensor 1. Stufe überführt werden, welches ein Spaltenvektor ist. -Gemäss der Hadamard-Algebra dürfen Zeile um Zeile in eine Spalte notiert werden, sodass es einen Spaltenvektor ergibt. +Man darf Zeile um Zeile in eine Spalte notieren, sodass es einen Spaltenvektor ergibt. So ergibt sich der Spannungsvektor \[ @@ -79,7 +79,7 @@ So ergibt sich der Spannungsvektor \sigma_{33} \end{pmatrix} \] -und Dehnungsvektor +und der Dehnungsvektor \[ \overline{\varepsilon} = @@ -140,14 +140,6 @@ C_{3311} & C_{3312} & C_{3313} & C_{3321} & C_{3322} & C_{3323} & C_{3331} & C_{ \end{pmatrix} \] geschrieben werden kann. -Dieser Elastizitätstensor muss für isotrope Materialien zwingend symmetrisch sein. -Folglich gilt: -\[ -\overline{\overline{C}} -= -\overline{\overline{C}}~^{T} -. -\] Die allgemeine Spannungsgleichung lautet nun: \[ \vec\sigma @@ -155,8 +147,7 @@ Die allgemeine Spannungsgleichung lautet nun: \overline{\overline{C}}\cdot\vec{\varepsilon} . \] - -Als Indexnotation +Sie kann ebenfalls als Indexnotation \[ \sigma_{ij} = @@ -164,7 +155,15 @@ Als Indexnotation \sum_{l=1}^3 C_{ijkl}\cdot\varepsilon_{kl} \] -kann dies ebenfalls geschrieben werden. +geschrieben werden. +Der Elastizitätstensor muss für isotrope Materialien zwingend symmetrisch sein. +Folglich gilt: +\[ +\overline{\overline{C}} += +\overline{\overline{C}}~^{T} +. +\] Die Konstanten $C$ werden nun nach dem Hook'schen Gesetz mit Hilfe des Elastizitätsmoduls $E$ definiert. Da dieser Modul durch die eindimensionale Betrachtung definiert ist, @@ -221,7 +220,7 @@ definiert ist. Trägt man die Konstanten in die Matrix ein, ergibt sich \end{pmatrix} . \] -Die Normalspannung $\sigma_{22}$ lässt sich exemplarisch als +Die Normalspannung $\sigma_{22}$ lässt sich zum Beispiel als \[ \sigma_{22} = @@ -229,11 +228,13 @@ Die Normalspannung $\sigma_{22}$ lässt sich exemplarisch als \] berechnen. +Reduzierte Spannungs- und Dehnungsgleichungen + Man betrachte nun die Eigenschaften des Elastizitätstensors. Dieser ist quadratisch und symmetrisch, die verschiedenen Einträge wechseln sich aber miteinander ab. Es ergeben sich keine Blöcke mit einheitlichen Einträgen. -Allerdings weiss man, dass im isotropen Boden der Spannungs-, Dehnungs- und daher auch Elastizitätstensor symmetrisch sind. +Allerdings weiss man, dass im isotropen Boden der Spannungs-, Dehnungs- und daher auch der Elastizitätstensor symmetrisch sind. Wäre dem nicht so, würde sich das Material je nach Richtung unterschiedlich elastisch verhalten. Diese Symmetrie setzt daher voraus, dass \[ @@ -399,7 +400,7 @@ Somit lässt sich die reduzierte allgemeine Spannungsgleichung mit \] beschreiben. Die Konstanten $C$ werden wieder nach dem Hook'schen Gesetz definiert. -Dies ergibt die Spannungsformel, welche weit möglichst vereinfacht ist: +Dies ergibt die Spannungsgleichung, welche weit möglichst vereinfacht ist: \begin{equation} \begin{pmatrix} \sigma_{11}\\ @@ -433,7 +434,7 @@ Dies ergibt die Spannungsformel, welche weit möglichst vereinfacht ist: Im Elastizitätstensor fallen zwei $3\times3$ Blöcke auf, welche nur Einträge mit $0$ haben. Der Tensor besagt also, dass diese jeweiligen Dehnungen keinen Einfluss auf unsere Spannung haben. -Man sieht nun auch ganz gut, dass sich im Vergleich zu der allgemeinen Spannungsgleichung, die Einträge verschoben haben. +Man sieht nun auch ganz gut, dass sich im Vergleich zu der allgemeinen Spannungsgleichung die Einträge verschoben haben. Da nach Voigt zuerst die Normalspannungen und anschliessend die Schubspannungen notiert worden sind, ergeben sich die $3\times3$ Blöcke. Man betrachte als Beispiel die Berechnung von $\sigma_{33}$. @@ -441,8 +442,8 @@ Es ist ersichtlich, dass die Schubdehnungen keinen Einfluss auf $\sigma_{33}$ ha Der Einfluss der zu $\sigma_{33}$ äquivalenten Dehnung $\varepsilon_{33}$ hat den grössten Einfluss. Die anderen Normalspannungen $\sigma_{11}$ und $\sigma_{22}$ haben einen unter anderem mit $\nu$ korrigierten Einfluss. -Von $\overline{\overline{C}}$ bildet man noch die inverse Matrix $\overline{\overline{C}}\mathstrut^{-1}$ um die Gleichung umstellen zu können. -Dadurch erhält man die Dehnungsgleichung: +Von $\overline{\overline{C}}$ bildet man die inverse Matrix $\overline{\overline{C}}\mathstrut^{-1}$, mithilfe des Gauss - Jordan Algorithmus, um die Gleichung umstellen zu können. +Durch einige Berechnungsschritte erhält man die Dehnungsgleichung: \[ \vec{\varepsilon} diff --git a/buch/papers/spannung/teil3.tex b/buch/papers/spannung/teil3.tex index 3e456c3..a9080ea 100644 --- a/buch/papers/spannung/teil3.tex +++ b/buch/papers/spannung/teil3.tex @@ -30,7 +30,7 @@ q \label{spannung:Invariante_q} . \end{equation} -Diese Zusammenhänge werden im Skript [\cite{spannung:Stoffgesetze-und-numerische-Modellierung-in-der-Geotechnik}] aufgezeigt. +Diese Zusammenhänge werden im Skript \cite{spannung:Stoffgesetze-und-numerische-Modellierung-in-der-Geotechnik} aufgezeigt. Die hydrostatische Spannung $p$ kann gemäss Gleichung \eqref{spannung:Invariante_p} als \[ p @@ -38,28 +38,28 @@ p \frac{\sigma_{11}+2\sigma_{33}}{3} \] vereinfacht werden. -Die deviatorische Spannung $q$ wird gemäss Gleichung \eqref{spannung:Invariante_q}als +Die deviatorische Spannung $q$ wird gemäss Gleichung \eqref{spannung:Invariante_q} als \[ q = \sigma_{11}-\sigma_{33} \] -vereinfacht. Man kann $p$ als Isotrop und $q$ als Schub betrachten. +vereinfacht. Man kann $p$ als Druck und $q$ als Schub betrachten. -Die Invarianten können mit der Spannungsformel \eqref{spannung:Spannungsgleichung} berechnet werden. +Die Invarianten $p$ und $q$ können mit der Spannungsgleichung \eqref{spannung:Spannungsgleichung} berechnet werden. Durch geschickte Umformung dieser Gleichung, lassen sich die Module als Faktor separieren. Dabei entstehen spezielle Faktoren mit den Dehnungskomponenten. So ergibt sich \[ -\overbrace{\frac{\sigma_{11}+2\sigma_{33}}{3}}^{p} +\overbrace{\frac{\sigma_{11}+2\sigma_{33}}{3}}^{\displaystyle{p}} = -\frac{E}{3(1-2\nu)} \overbrace{(\varepsilon_{11} - 2\varepsilon_{33})}^{\varepsilon_{v}} +\frac{E}{3(1-2\nu)} \overbrace{(\varepsilon_{11} - 2\varepsilon_{33})}^{\displaystyle{{\varepsilon_{v}}}} \] und \[ -\overbrace{\sigma_{11}-\sigma_{33}}^{q} +\overbrace{\sigma_{11}-\sigma_{33}}^{\displaystyle{q}} = -\frac{3E}{2(1+\nu)} \overbrace{\frac{2}{3}(\varepsilon_{11} - \varepsilon_{33})}^{\varepsilon_{s}} +\frac{3E}{2(1+\nu)} \overbrace{\frac{2}{3}(\varepsilon_{11} - \varepsilon_{33})}^{\displaystyle{\varepsilon_{s}}} . \] Die Faktoren mit den Dehnungskomponenten können so mit @@ -79,8 +79,8 @@ eingeführt werden, mit \varepsilon_{v} &= \text{Hydrostatische Dehnung [-]} \\ \varepsilon_{s} &= \text{Deviatorische Dehnung [-].} \end{align*} -Die hydrostatische Dehnung $\varepsilon_{v}$ kann mit einer Kompression verglichen werden. -Die deviatorische Dehnung $\varepsilon_{s}$ kann mit einer Verzerrung verglichen werden. +Die hydrostatische Dehnung $\varepsilon_{v}$ kann mit einer Kompression und +die deviatorische Dehnung $\varepsilon_{s}$ mit einer Verzerrung verglichen werden. Diese zwei Gleichungen kann man durch die Matrixschreibweise \begin{equation} @@ -90,8 +90,8 @@ Diese zwei Gleichungen kann man durch die Matrixschreibweise \end{pmatrix} = \begin{pmatrix} - \frac{3E}{2(1+\nu)} & 0 \\ - 0 & \frac{E}{3(1-2\nu)} + \displaystyle{\frac{3E}{2(1+\nu)}} & 0 \\ + 0 & \displaystyle{\frac{E}{3(1-2\nu)}} \end{pmatrix} \begin{pmatrix} \varepsilon_{s}\\ @@ -100,9 +100,11 @@ Diese zwei Gleichungen kann man durch die Matrixschreibweise \label{spannung:Matrixschreibweise} \end{equation} vereinfachen. -Man hat so eine Matrix multipliziert mit einem Vektor und erhält einen Vektor. -Änderungen des Spannungszustandes können mit dieser Gleichung vollumfänglich erfasst werden. +Änderungen des Spannungszustandes können mit diesen Gleichungen vollumfänglich erfasst werden. +Diese Spannungsgleichung mit den zwei Einträgen ($p$ und $q$) ist gleichwertig +wie die ursprüngliche Spannungsgleichung mit den neun Einträgen +($\sigma_{11}$, $\sigma_{12}$, $\sigma_{13}$, $\sigma_{21}$, $\sigma_{22}$, $\sigma_{23}$, $\sigma_{31}$, $\sigma_{32}$, $\sigma_{33}$). Mit dieser Formel \eqref{spannung:Matrixschreibweise} lassen sich verschieden Ergebnisse von Versuchen analysieren und berechnen. -Ein solcher Versuch, den oft in der Geotechnik durchgeführt wird, ist der Oedometer-Versuch. +Ein solcher Versuch, der oft in der Geotechnik durchgeführt wird, ist der Oedometer-Versuch. Im nächsten Kapitel wird die Anwendung der Matrix an diesem Versuch beschrieben. diff --git a/buch/papers/spannung/teil4.tex b/buch/papers/spannung/teil4.tex index 2f2e4ce..00b2d4f 100644 --- a/buch/papers/spannung/teil4.tex +++ b/buch/papers/spannung/teil4.tex @@ -1,6 +1,6 @@ -\section{Oedometer-Versuch\label{spannung:section:Oedometer-Versuch}} -\rhead{Oedometer-Versuch} -Mit dem Oedometer-Versuch kann der oedometrische Elastizitätsmodul $E_{OED}$ bestimmt werden. +\section{Oedometrischer Elastizitätsmodul\label{spannung:section:Oedometrischer Elastizitätsmodul}} +\rhead{Oedometrischer Elastizitätsmodul} +Mit dem Oedometer-Versuch kann der oedometrische Elastizitätsmodul $E_{\text{OED}}$ bestimmt werden. Dieser beschreibt ebenfalls das Verhältnis zwischen Spannung und Dehnung, allerdings unter anderen Bedingungen. Diese Bedingung ist das Verhindern der seitlichen Verformung, sprich der Dehnung in Richtung $1$ und $2$. Es wird ein Probeelement mit immer grösseren Gewichten belastet, welche gleichmässig auf das Material drücken. @@ -43,8 +43,8 @@ Diese lautet nun: \end{pmatrix} = \begin{pmatrix} - \frac{E_{OED}}{(1+\nu)} & 0 \\ - 0 & \frac{E_{OED}}{3(1-2\nu)} + \displaystyle{\frac{E_{\text{OED}}}{(1+\nu)}} & 0 \\ + 0 & \displaystyle{\frac{E_{\text{OED}}}{3(1-2\nu)}} \end{pmatrix} \begin{pmatrix} \varepsilon_{11}\\ @@ -52,28 +52,28 @@ Diese lautet nun: \end{pmatrix} . \] -Daraus lässt sich bei jedem Setzungsgrad der oedometrische Elastitzitätsmodul $E_{OED}$ und die seitlichen Spannungen $\sigma_{33}$ mit den 2 Gleichungen +Daraus lässt sich bei jedem Setzungsgrad der oedometrische Elastitzitätsmodul $E_{\text{OED}}$ und die seitlichen Spannungen $\sigma_{33}$ mit den zwei Gleichungen \[ \sigma_{11}-\sigma_{33} = -\frac{E_{OED}}{(1+\nu)}\cdot\varepsilon_{11} +\frac{E_{\text{OED}}}{(1+\nu)}\cdot\varepsilon_{11} \] und \[ \sigma_{11}+2\sigma_{33} = -\frac{E_{OED}}{3(1-2\nu)}\cdot\varepsilon_{11} +\frac{E_{\text{OED}}}{3(1-2\nu)}\cdot\varepsilon_{11} \] berechnen. -Mit diesen Gleichungen hat man das Gleichungssystem um $E_{OED}$ und $\sigma_{33}$ zu berechnen. +Mit diesen Gleichungen hat man das Gleichungssystem um $E_{\text{OED}}$ und $\sigma_{33}$ zu berechnen. Die Poisson-Zahl muss als Kennwert gemäss der Bodenklasse gewählt werden. -Den Versuch kann man auf einem $\sigma$-$\varepsilon$-Diagramm abtragen (siehe Abbildung~\ref{spannung:DiagrammOedometer-Versuch}). +Den Versuch kann man auf einem $\sigma$-$\varepsilon$-Diagramm abtragen (siehe Abbildung~\ref{fig:DiagrammOedometer-Versuch}). Durch die Komprimierung nimmt der Boden mehr Spannung auf, und verformt sich zugleich weniger stark. -Mit diesem ermittelten $E_{OED}$ kann man nun weitere Berechnungen für die Geotechnik durchführen. +Mit diesem ermittelten $E_{\text{OED}}$ kann man nun weitere Berechnungen für die Geotechnik durchführen. \begin{figure} \centering - \includegraphics[width=0.5\linewidth,keepaspectratio]{papers/spannung/Grafiken/DiagrammOedometer-Versuch.png} + \includegraphics[width=0.45\linewidth,keepaspectratio]{papers/spannung/Grafiken/DiagrammOedometer-Versuch.png} \caption{Diagramm Charakteristik verschiedener Elastizitätsmodule bei gleichem Material} \label{fig:DiagrammOedometer-Versuch} \end{figure}
\ No newline at end of file diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf Binary files differdeleted file mode 100644 index e1769f8..0000000 --- a/vorlesungen/punktgruppen/slides.pdf +++ /dev/null |
