diff --git a/PS2/doc.aux b/PS2/doc.aux
new file mode 100644
index 0000000..83d3ccd
--- /dev/null
+++ b/PS2/doc.aux
@@ -0,0 +1,5 @@
+\relax 
+\newlabel{LastPage}{{}{2}}
+\xdef\lastpage@lastpage{2}
+\gdef\lastpage@lastpageHy{}
+\gdef \@abspage@last{2}
diff --git a/PS2/doc.fdb_latexmk b/PS2/doc.fdb_latexmk
new file mode 100644
index 0000000..0a6283d
--- /dev/null
+++ b/PS2/doc.fdb_latexmk
@@ -0,0 +1,75 @@
+# Fdb version 3
+["pdflatex"] 1614622332 "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf" "doc" 1614622334
+  "C:/Users/speed/AppData/Local/MiKTeX/miktex/data/le/pdftex/pdflatex.fmt" 1612675286 9293900 83195ab665706b6f706823352908aa95 ""
+  "C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map" 1614621894 80909 eab91d9745dd2edfd62a31d53cd5fe15 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1233951848 1004 54797486969f23fa377b128694d548df ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1233951848 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1233951854 916 f87d7c45f9c908e672703b83b72241a3 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1233951854 928 2dc8d444221b7a635bb58038579b861a ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1233951854 908 2921f8a10601f252058503cc6570e581 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1233951854 940 228d6584342e91276bf566bcf9716b83 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmex10.tfm" 1136765053 992 662f679a0b3d2d53c1b94050fdaa3f50 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmmi12.tfm" 1136765053 1524 4414a8315f39513458b80dfc63bff03a ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmmi6.tfm" 1136765053 1512 f21f83efb36853c0b70002322c1ab3ad ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmmi8.tfm" 1136765053 1520 eccf95517727cb11801f4f1aee3a21b4 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmr12.tfm" 1136765053 1288 655e228510b4c2a1abe905c368440826 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmr17.tfm" 1136765053 1292 296a67155bdbfc32aa9c636f21e91433 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmr6.tfm" 1136765053 1300 b62933e007d01cfd073f79b963c01526 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmr8.tfm" 1136765053 1292 21c1c5bfeaebccffdb478fd231a0997d ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmsy10.tfm" 1136765053 1124 6c73e740cf17375f03eec0ee63599741 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmsy6.tfm" 1136765053 1116 933a60c408fc0a863a92debe84b2d294 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/cm/cmsy8.tfm" 1136765053 1120 8b7d695260f3cff42e636090a8002094 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1247593067 35752 024fb6c41858982481f6968b5fc26508 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1247593067 32722 d7379af29a190c3f453aba36302ff5a9 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr17.pfb" 1247593066 32362 bc3f3eec7ab7d65fe700963d4017d32c ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/context/base/mkii/supp-pdf.mkii" 1580390158 71627 94eb9990bed73c364d7f53f960cc8c5b ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/iftex/iftex.sty" 1583523400 6501 4011d89d9621e0b0901138815ba5ff29 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/iftex/ifvtex.sty" 1583523400 1057 525c2192b5febbd8c1f662c9468335bb ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/kvsetkeys/kvsetkeys.sty" 1576433820 13807 952b0226d4efca026f0e19dd266dcc22 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/ltxcmds/ltxcmds.sty" 1601732009 18568 4409f8f50cd365c68e684407e5350b1b ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsfonts/amsfonts.sty" 1358197772 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsfonts/amssymb.sty" 1358197772 13829 94730e64147574077f8ecfea9bb69af4 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsfonts/umsa.fd" 1358197772 961 6518c6525a34feb5e8250ffa91731cff ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsfonts/umsb.fd" 1358197772 961 d02606146ba5601b5645f987c92e6193 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsmath/amsbsy.sty" 1601804949 2283 ca7ce284ab93c8eecdc6029dc5ccbd73 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsmath/amsgen.sty" 1601804951 4297 7f6eb9092061a11f87d08ed13515b48d ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsmath/amsmath.sty" 1601804952 90280 2c21ff5f2e32e1bf714e600924d810db ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsmath/amsopn.sty" 1601804953 4233 32e6abd27229755a83a8b7f18e583890 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/amsmath/amstext.sty" 1601804953 2508 8ff93b1137020e8f21930562a874ae66 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/article.cls" 1610120746 20145 aad8c3dd3bc36e260347b84002182bc2 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/size10.clo" 1610120746 8449 a72d5d4e612221b46000c3d71724e0ef ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/caption.sty" 1603736996 51746 e89c4da670ba533e6ab38e045ce6d1d9 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/caption3.sty" 1603736996 67929 d50ae850e1d9604065e8337a75a41029 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/subcaption.sty" 1603736996 6133 46bea384e36e9b74bd53a238fc2d0654 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1580041542 14411 d1306dcf79a944f6988e688c1785f9ce ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/etoolbox/etoolbox.sty" 1601894156 46845 3b58f70c6e861a13d927bff09d35ecbc ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/fancyhdr/fancyhdr.sty" 1612001844 17086 7ed8cbc4d361ec87392817e0dd4f65ec ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/float/float.sty" 1469020353 6916 16d2656a1984957e674b149555f1ea1d ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/geometry/geometry.cfg" 1578053545 1104 7ac475a4e3466b0b43e138e9356bda83 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/geometry/geometry.sty" 1578053545 42759 9cf6c5257b1bc7af01a58859749dd37a ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics-cfg/color.cfg" 1465890692 1213 620bba36b25224fa9b7e1ccb4ecb76fd ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics-cfg/graphics.cfg" 1465890692 1224 978390e9c2234eab29404bc21b268d1e ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics-def/pdftex.def" 1601874598 19103 48d29b6e2a64cb717117ef65f107b404 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics/color.sty" 1601741526 7300 5b27b7e61091c6128cd6300e21704e4b ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics/graphics.sty" 1601741526 18881 a8c6a275b34ab6717ceeb8fa04b104e2 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics/graphicx.sty" 1601741526 8167 20fdfdd783821971c55bc8ee918cbe63 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics/keyval.sty" 1601741526 2677 e3b24ff953e5b58d924f163d25380312 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/graphics/trig.sty" 1601741526 4093 d7fa7d81d2870d509d25b17d0245e735 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/kvoptions/kvoptions.sty" 1602224496 22521 d2fceb764a442a2001d257ef11db7618 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/l3backend/l3backend-pdftex.def" 1611916124 27097 58278863d97b10ab86e334b8da33df7a ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/lastpage/lastpage.sty" 1427648580 9922 eb7d00b99f0f5207f71a5cdcbafceac1 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/listings/listings.cfg" 1585216535 1879 e31effa752c61538383451ae21332364 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/listings/listings.sty" 1585216535 83225 64e57373f36316e4a09b517cbf1aba2e ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/listings/lstmisc.sty" 1585216535 79106 ee25ce086f4a79d8cf73bac6f94c02a5 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/parskip/parskip.sty" 1592833306 4414 25631f9679adf750bac898538ededd61 ""
+  "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/setspace/setspace.sty" 1324294077 22913 a27d7908fc6f0385466454a966a316eb ""
+  "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.aux" 1614622334 114 6e1e809bbf8828c6eb46a14c07135d2a ""
+  "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" 1614622331 782 25436f76e2a26f13ca483eaacdb52b38 ""
+  "doc.aux" 1614622334 114 6e1e809bbf8828c6eb46a14c07135d2a "pdflatex"
+  "doc.tex" 1614622331 782 25436f76e2a26f13ca483eaacdb52b38 ""
+  (generated)
+  "doc.log"
+  "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.log"
+  "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf"
+  "doc.pdf"
+  "doc.aux"
diff --git a/PS2/doc.fls b/PS2/doc.fls
new file mode 100644
index 0000000..11f7047
--- /dev/null
+++ b/PS2/doc.fls
@@ -0,0 +1,425 @@
+PWD d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2
+INPUT C:\Users\speed\AppData\Local\MiKTeX\miktex\data\le\pdftex\pdflatex.fmt
+INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.tex
+OUTPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.log
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\article.cls
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\size10.clo
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\size10.clo
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\size10.clo
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\base\size10.clo
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphicx.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\graphics.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\trig.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\graphics.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\graphics.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\graphics.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\graphics.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-def\pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-def\pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-def\pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-def\pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\setspace\setspace.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstmisc.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstmisc.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstmisc.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstmisc.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\listings.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\color.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\color.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\color.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\color.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics-cfg\color.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsmath.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amstext.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsbsy.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsopn.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsmath\amsgen.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amssymb.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\amsfonts.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\float\float.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption3.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\subcaption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\caption\caption.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\graphics\keyval.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\ifvtex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\iftex\iftex.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\geometry\geometry.cfg
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\parskip\parskip.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\kvoptions\kvoptions.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\ltxcmds\ltxcmds.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\generic\kvsetkeys\kvsetkeys.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\etoolbox\etoolbox.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\fancyhdr\fancyhdr.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\lastpage\lastpage.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\l3backend\l3backend-pdftex.def
+INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux
+INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux
+INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux
+OUTPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\context\base\mkii\supp-pdf.mkii
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\context\base\mkii\supp-pdf.mkii
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\context\base\mkii\supp-pdf.mkii
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\context\base\mkii\supp-pdf.mkii
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\epstopdf-pkg\epstopdf-base.sty
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmr17.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmr12.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmr8.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmr6.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmmi12.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmmi8.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmmi6.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmsy10.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmsy8.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmsy6.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmex10.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex8.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex7.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsa.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsa.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsa.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsa.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam10.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam10.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam7.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsb.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsb.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsb.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\amsfonts\umsb.fd
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm10.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm10.tfm
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm7.tfm
+OUTPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf
+INPUT C:\Users\speed\AppData\Local\MiKTeX\pdftex\config\pdftex.map
+INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr10.pfb
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr10.pfb
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr12.pfb
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr12.pfb
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr17.pfb
+INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr17.pfb
diff --git a/PS2/doc.log b/PS2/doc.log
new file mode 100644
index 0000000..a581002
--- /dev/null
+++ b/PS2/doc.log
@@ -0,0 +1,309 @@
+This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6)  1 MAR 2021 11:12
+entering extended mode
+**d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
+(d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
+LaTeX2e <2020-10-01> patch level 4
+L3 programming layer <2021-01-09> xparse <2020-03-03> (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/base\article.cls
+Document Class: article 2020/04/10 v1.4m Standard LaTeX document class
+(C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/base\size10.clo
+File: size10.clo 2020/04/10 v1.4m Standard LaTeX file (size option)
+)
+\c@part=\count177
+\c@section=\count178
+\c@subsection=\count179
+\c@subsubsection=\count180
+\c@paragraph=\count181
+\c@subparagraph=\count182
+\c@figure=\count183
+\c@table=\count184
+\abovecaptionskip=\skip47
+\belowcaptionskip=\skip48
+\bibindent=\dimen138
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics\graphicx.sty
+Package: graphicx 2020/09/09 v1.2b Enhanced LaTeX Graphics (DPC,SPQR)
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics\keyval.sty
+Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
+\KV@toks@=\toks15
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics\graphics.sty
+Package: graphics 2020/08/30 v1.4c Standard LaTeX Graphics (DPC,SPQR)
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics\trig.sty
+Package: trig 2016/01/03 v1.10 sin cos tan (DPC)
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics-cfg\graphics.cfg
+File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
+)
+Package graphics Info: Driver file: pdftex.def on input line 105.
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics-def\pdftex.def
+File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex
+))
+\Gin@req@height=\dimen139
+\Gin@req@width=\dimen140
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/setspace\setspace.sty
+Package: setspace 2011/12/19 v6.7a set line spacing
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/listings\listings.sty
+\lst@mode=\count185
+\lst@gtempboxa=\box47
+\lst@token=\toks16
+\lst@length=\count186
+\lst@currlwidth=\dimen141
+\lst@column=\count187
+\lst@pos=\count188
+\lst@lostspace=\dimen142
+\lst@width=\dimen143
+\lst@newlines=\count189
+\lst@lineno=\count190
+\lst@maxwidth=\dimen144
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/listings\lstmisc.sty
+File: lstmisc.sty 2020/03/24 1.8d (Carsten Heinz)
+\c@lstnumber=\count191
+\lst@skipnumbers=\count192
+\lst@framebox=\box48
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/listings\listings.cfg
+File: listings.cfg 2020/03/24 1.8d listings configuration
+))
+Package: listings 2020/03/24 1.8d (Carsten Heinz)
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics\color.sty
+Package: color 2020/02/24 v1.2b Standard LaTeX Color (DPC)
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/graphics-cfg\color.cfg
+File: color.cfg 2016/01/02 v1.6 sample color configuration
+)
+Package color Info: Driver file: pdftex.def on input line 147.
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsmath\amsmath.sty
+Package: amsmath 2020/09/23 v2.17i AMS math features
+\@mathmargin=\skip49
+
+For additional information on amsmath, use the `?' option.
+(C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsmath\amstext.sty
+Package: amstext 2000/06/29 v2.01 AMS text
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsmath\amsgen.sty
+File: amsgen.sty 1999/11/30 v2.0 generic functions
+\@emptytoks=\toks17
+\ex@=\dimen145
+)) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsmath\amsbsy.sty
+Package: amsbsy 1999/11/29 v1.2d Bold Symbols
+\pmbraise@=\dimen146
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsmath\amsopn.sty
+Package: amsopn 2016/03/08 v2.02 operator names
+)
+\inf@bad=\count193
+LaTeX Info: Redefining \frac on input line 234.
+\uproot@=\count194
+\leftroot@=\count195
+LaTeX Info: Redefining \overline on input line 399.
+\classnum@=\count196
+\DOTSCASE@=\count197
+LaTeX Info: Redefining \ldots on input line 496.
+LaTeX Info: Redefining \dots on input line 499.
+LaTeX Info: Redefining \cdots on input line 620.
+\Mathstrutbox@=\box49
+\strutbox@=\box50
+\big@size=\dimen147
+LaTeX Font Info:    Redeclaring font encoding OML on input line 743.
+LaTeX Font Info:    Redeclaring font encoding OMS on input line 744.
+\macc@depth=\count198
+\c@MaxMatrixCols=\count199
+\dotsspace@=\muskip16
+\c@parentequation=\count266
+\dspbrk@lvl=\count267
+\tag@help=\toks18
+\row@=\count268
+\column@=\count269
+\maxfields@=\count270
+\andhelp@=\toks19
+\eqnshift@=\dimen148
+\alignsep@=\dimen149
+\tagshift@=\dimen150
+\tagwidth@=\dimen151
+\totwidth@=\dimen152
+\lineht@=\dimen153
+\@envbody=\toks20
+\multlinegap=\skip50
+\multlinetaggap=\skip51
+\mathdisplay@stack=\toks21
+LaTeX Info: Redefining \[ on input line 2923.
+LaTeX Info: Redefining \] on input line 2924.
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\amssymb.sty
+Package: amssymb 2013/01/14 v3.01 AMS font symbols
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\amsfonts.sty
+Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
+\symAMSa=\mathgroup4
+\symAMSb=\mathgroup5
+LaTeX Font Info:    Redeclaring math symbol \hbar on input line 98.
+LaTeX Font Info:    Overwriting math alphabet `\mathfrak' in version `bold'
+(Font)                  U/euf/m/n --> U/euf/b/n on input line 106.
+)) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/float\float.sty
+Package: float 2001/11/08 v1.3d Float enhancements (AL)
+\c@float@type=\count271
+\float@exts=\toks22
+\float@box=\box51
+\@float@everytoks=\toks23
+\@floatcapt=\box52
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/caption\caption.sty
+Package: caption 2020/10/26 v3.5g Customizing captions (AR)
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/caption\caption3.sty
+Package: caption3 2020/10/21 v2.2e caption3 kernel (AR)
+\captionmargin=\dimen154
+\captionmargin@=\dimen155
+\captionwidth=\dimen156
+\caption@tempdima=\dimen157
+\caption@indent=\dimen158
+\caption@parindent=\dimen159
+\caption@hangindent=\dimen160
+Package caption Info: Standard document class detected.
+)
+\c@caption@flags=\count272
+\c@continuedfloat=\count273
+Package caption Info: float package is loaded.
+Package caption Info: listings package is loaded.
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/caption\subcaption.sty
+Package: subcaption 2020/10/07 v1.3j Sub-captions (AR)
+\c@subfigure=\count274
+\c@subtable=\count275
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/geometry\geometry.sty
+Package: geometry 2020/01/02 v5.9 Page Geometry
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/generic/iftex\ifvtex.sty
+Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. Use iftex instead.
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/generic/iftex\iftex.sty
+Package: iftex 2020/03/06 v1.0d TeX engine tests
+))
+\Gm@cnth=\count276
+\Gm@cntv=\count277
+\c@Gm@tempcnt=\count278
+\Gm@bindingoffset=\dimen161
+\Gm@wd@mp=\dimen162
+\Gm@odd@mp=\dimen163
+\Gm@even@mp=\dimen164
+\Gm@layoutwidth=\dimen165
+\Gm@layoutheight=\dimen166
+\Gm@layouthoffset=\dimen167
+\Gm@layoutvoffset=\dimen168
+\Gm@dimlist=\toks24
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/geometry\geometry.cfg)) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/parskip\parskip.sty
+Package: parskip 2020-06-15 v2.0f non-zero parskip adjustments
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/kvoptions\kvoptions.sty
+Package: kvoptions 2020-10-07 v3.14 Key value format for package options (HO)
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/generic/ltxcmds\ltxcmds.sty
+Package: ltxcmds 2020-05-10 v1.25 LaTeX kernel commands for general use (HO)
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/generic/kvsetkeys\kvsetkeys.sty
+Package: kvsetkeys 2019/12/15 v1.18 Key value parser (HO)
+)) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/etoolbox\etoolbox.sty
+Package: etoolbox 2020/10/05 v2.5k e-TeX tools for LaTeX (JAW)
+\etb@tempcnta=\count279
+)) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/fancyhdr\fancyhdr.sty
+Package: fancyhdr 2021/01/28 v4.0.1 Extensive control of page headers and footers
+\f@nch@headwidth=\skip52
+\f@nch@O@elh=\skip53
+\f@nch@O@erh=\skip54
+\f@nch@O@olh=\skip55
+\f@nch@O@orh=\skip56
+\f@nch@O@elf=\skip57
+\f@nch@O@erf=\skip58
+\f@nch@O@olf=\skip59
+\f@nch@O@orf=\skip60
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/lastpage\lastpage.sty
+Package: lastpage 2015/03/29 v1.2m Refers to last page's name (HMM; JPG)
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/l3backend\l3backend-pdftex.def
+File: l3backend-pdftex.def 2020-01-29 L3 backend support: PDF output (pdfTeX)
+\l__color_backend_stack_int=\count280
+\l__pdf_internal_box=\box53
+) (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux)
+\openout1 = `doc.aux'.
+
+LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 29.
+LaTeX Font Info:    ... okay on input line 29.
+LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 29.
+LaTeX Font Info:    ... okay on input line 29.
+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 29.
+LaTeX Font Info:    ... okay on input line 29.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 29.
+LaTeX Font Info:    ... okay on input line 29.
+LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 29.
+LaTeX Font Info:    ... okay on input line 29.
+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 29.
+LaTeX Font Info:    ... okay on input line 29.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 29.
+LaTeX Font Info:    ... okay on input line 29.
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/context/base/mkii\supp-pdf.mkii
+[Loading MPS to PDF converter (version 2006.09.02).]
+\scratchcounter=\count281
+\scratchdimen=\dimen169
+\scratchbox=\box54
+\nofMPsegments=\count282
+\nofMParguments=\count283
+\everyMPshowfont=\toks25
+\MPscratchCnt=\count284
+\MPscratchDim=\dimen170
+\MPnumerator=\count285
+\makeMPintoPDFobject=\count286
+\everyMPtoPDFconversion=\toks26
+) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/epstopdf-pkg\epstopdf-base.sty
+Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
+Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 485.
+)
+\c@lstlisting=\count287
+Package caption Info: Begin \AtBeginDocument code.
+Package caption Info: End \AtBeginDocument code.
+
+*geometry* driver: auto-detecting
+*geometry* detected driver: pdftex
+*geometry* verbose mode - [ preamble ] result:
+* driver: pdftex
+* paper: <default>
+* layout: <same size as paper>
+* layoutoffset:(h,v)=(0.0pt,0.0pt)
+* modes: 
+* h-part:(L,W,R)=(54.2025pt, 505.89pt, 54.2025pt)
+* v-part:(T,H,B)=(54.2025pt, 686.56499pt, 54.2025pt)
+* \paperwidth=614.295pt
+* \paperheight=794.96999pt
+* \textwidth=505.89pt
+* \textheight=686.56499pt
+* \oddsidemargin=-18.06749pt
+* \evensidemargin=-18.06749pt
+* \topmargin=-55.06749pt
+* \headheight=12.0pt
+* \headsep=25.0pt
+* \topskip=10.0pt
+* \footskip=30.0pt
+* \marginparwidth=65.0pt
+* \marginparsep=11.0pt
+* \columnsep=10.0pt
+* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
+* \hoffset=0.0pt
+* \voffset=0.0pt
+* \mag=1000
+* \@twocolumnfalse
+* \@twosidefalse
+* \@mparswitchfalse
+* \@reversemarginfalse
+* (1in=72.27pt=25.4mm, 1cm=28.453pt)
+
+Package lastpage Info: Please have a look at the pageslts package at
+(lastpage)             https://www.ctan.org/pkg/pageslts
+(lastpage)             ! on input line 29.
+LaTeX Font Info:    Trying to load font information for U+msa on input line 31.
+(C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\umsa.fd
+File: umsa.fd 2013/01/14 v3.01 AMS symbols A
+)
+LaTeX Font Info:    Trying to load font information for U+msb on input line 31.
+ (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\umsb.fd
+File: umsb.fd 2013/01/14 v3.01 AMS symbols B
+) [1
+
+{C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map}] 
+AED: lastpage setting LastPage
+[2] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) ) 
+Here is how much of TeX's memory you used:
+ 6514 strings out of 479618
+ 99594 string characters out of 2865027
+ 381395 words of memory out of 3000000
+ 23620 multiletter control sequences out of 15000+200000
+ 408374 words of font info for 46 fonts, out of 3000000 for 9000
+ 1141 hyphenation exceptions out of 8191
+ 68i,11n,74p,603b,263s stack positions out of 5000i,500n,10000p,200000b,50000s
+<C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr17.pfb>
+Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (2 pages, 41934 bytes).
+PDF statistics:
+ 21 PDF objects out of 1000 (max. 8388607)
+ 0 named destinations out of 1000 (max. 500000)
+ 1 words of extra memory for PDF output out of 10000 (max. 10000000)
+
diff --git a/PS2/doc.synctex.gz b/PS2/doc.synctex.gz
new file mode 100644
index 0000000..44f1f6b
Binary files /dev/null and b/PS2/doc.synctex.gz differ