{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 1 1}{FONT 0 "-adobe-helve tica-bold-r-normal--*-180-*-*-*-*-*-*" "helvetica" "Helvetica-Bol d" 8 18 0 "Helvetica-Bold" 18}{FONT 1 "-adobe-times-medium-r-norm al--*-180-*-*-*-*-*-*" "times" "Times-Roman" 4 18 64 "Times-Roman " 18}{FONT 2 "-adobe-courier-medium-r-normal--*-140-*" "courier" "Courier" 4 14 192 "Courier" 12}{FONT 3 "-b&h-lucida-bold-r-norma l-sans-*-240-*-*-*-*-*-*" "lucida" "Times-Bold" 8 24 64 "Times-Bo ld" 24}{FONT 4 "-adobe-courier-bold-o-normal--*-140-*-*-*-*-*-*" "courier" "Courier-BoldOblique" 8 14 224 "Courier-BoldOblique" 14 }{FONT 5 "-adobe-times-medium-r-normal--*-120-*-*-*-*-*-*" "times " "Times-Roman" 4 12 64 "Times-Roman" 12}{SCP_R 1 0 42{COM_R 2 0 {TEXT 3 49 " MAT 331 - A Glider"}} {COM_R 3 0{TEXT 1 107 "\015First, we have to teach maple about t he special routines we will need, namely phaseplot and rungekutta hf."}}{INP_R 4 0 "> "{TEXT 0 33 "with(share):readshare(ODE,plots) :"}}{OUT_R 5 0 0{TEXT 2 71 "See ?share and ?share,contents for in formation about the share library\012"}}{SEP_R 6 0}{COM_R 7 0 {TEXT 1 138 "Next, we define the differential equations which des cribe the glider's motion. To start, we use R=0, that is, we ig nore air resistance.\012"}}{INP_R 8 0 "> "{TEXT 0 5 "R:=0:"}} {COM_R 9 0{TEXT 5 110 "The routines we use need a pair of functio ns taking (t,v,theta) to the components of the vector at that poi nt."}}{INP_R 10 0 "> "{TEXT 0 90 "vdot := (t,v,theta) -> -sin(th eta) - R*v^2;\012thdot := (t,v,theta) -> (v^2 - cos(theta))/v;"}} {COM_R 11 0{TEXT 1 0 ""}}{OUT_R 12 0 10{DAG :3n4\`vdot`@8,4n3\`t` n3\`v`n4\`theta`,1,3n5\`operator`n4\`arrow`pD+5(3n3\`sin`,2a2x000 3i2x0001*5n3\`R`j2x0001a2x0002j2x0002p1EpDpD}}{OUT_R 13 0 10{DAG :3n4\`thdot`@8,4n3\`t`n3\`v`n4\`theta`,1,3n5\`operator`n4\`arrow` pD*5+5*3a2x0002j2x0002j2x0001(3n3\`cos`,2a2x0003i2x0001p1Ep1Ap26p DpD}}{SEP_R 14 0}{COM_R 15 0{TEXT 1 146 " We can use the phaseplo t command to produce a phase portrait of the system, together wit h trajectories passing through given initial conditions. "}} {INP_R 16 0 "> "{TEXT 0 50 "phaseplot([vdot,thdot], 0..3,-Pi..Pi, \{[0,1.5,0]\});"}}{GRH_R 17 0{RASTER 609 300 1 77 000000000000000 00000C00000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000C00000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000C00000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000C0000000080000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000C00000001E0000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000C0000 0002B000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000C000008048000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C000000008000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00C00000000800004000000000000000000000000000000000000000000000000 00000000000000000000000000000000004000060000000030000000000000000 00000000000000000000000000C0000000080000F000000000000000000000000 0000000000000000000000000000000000000020000300000800100001E0000F8 0100C00F000000000000000000000000000000000000000000C00000000800005 801000003000018000080000000040000700000800300001C0000C00000000F00 00FC0000E00700003500002403006012000000000000000000000000000000000 000000000C0000000080000440200C00F00007E0000E00100000F0000FC0100E0 0F00007F0000F00300801A0000920100900C00804400002000000002000000000 000000000000000000000000000000000C0000000080000400000601200009300 00B002008015000026030030190080C9000048060040220000100000800000000 400002000000002000000000000000000000000000000000000000000C0000000 08000040000000020000100000880400402400002000000001000008000040000 00002000010000080000000040000200000000200000000000000000000000000 0000000000000000C000000008000040000000020000100000800000000400002 00000000100000800004000000002000010000080000000040000200000000200 0000000000000000000000000000000000000000C000000008000040000000020 00010000080000000040000200000000100000800004000000002000010000080 0000000400002000000002000000000000000000000000000000000000000000C 00000000800004000000002000010000080000000040000200000000100000800 00400000000200001000008000000004000020000000020000000000000000000 00000000000000000000000C00000000800004000000002000010000080000000 04000020000000010000080000400000000200001000008000000004000020000 00002000000000000000000000000000000000000000000C00000000800004000 00000200001000008000000004000020000000010000080000400000000200001 00000800000000400002000000002000000000000000000000000000000000000 000000C0000000080000400000000200001000008000000004000020000000010 00008000040000000020000100000800000000400002000000002000000000000 000000000000000000000000000000C0000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000C0000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000E0C100000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000030C30000C000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000018F607 00E00300000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000018F60700900600000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000C60000880000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000C3000080000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000600000000300007000000000000000000 0000000000000000000000000C0C1000000010000070000000000000000000000 000000000000000000000000000000000000300000800300001C0000B00100800 D0000DC01000000000000000000000000000000000000000000C3000000010080 3A000038000000000000000000000000000000001C0000E00000000E0000E8000 0401D0000EA000050060080320000220000000000000000000000000000000000 0000000000C6000000010080020000D40100C00100000E000070000080030000E A0000500700003D0000A80100400100000A000048000040020000200000000000 0000000000000000000000000000000018C6000000020040040000140000A00E0 000750000A80300401D00000A0000500000800400004400002002000011000080 0000000400004000000000000000000000000000000000000000000018C600000 00200000800002200002001000009000048000020020000110000880000400800 00400000000200001000008000000004000040000000000000000000000000000 00000000000000030C30000000400000800004000001002008010000084000000 04000020000000010000080000800000000400002000000001000008000080000 000000000000000000000000000000000000000E0C10000000400001000008000 00000200001000008000000004000040000000020000100000800000000400002 00000000100000800008000000000000000000000000000000000000000000000 C0000000040000200000800000000400002000000001000008000040000000020 00020000000010000080000400000000200001000000001000000000000000000 000000000000000000000000C0000000080000200000000100000800004000000 00200001000008000000004000020000000010000080000400000000200001000 000001000000000000000000000000000000000000000000C0000000080000400 00000020000100000800000000400002000000001000008000040000000020000 10000080000000040000200000000200000000000000000000000000000000000 0000000C000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000C000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000C000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000C00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000C00000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000C00 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000C0000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000C000001C000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000C00000EA00000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000E0000000070000000000000000 0000000000000000000000000000C000001200000000000000000000000000000 0000000000000000000000000000000000000000000000000C00100000E000050 0700803A00000000000000000000000000000000000000000000C000001100000 00000000000000000000000000000000000000000000000000000F00000000700 00F80100C00E00007600009000008004000000000000000000000000000000000 00000000000C00000200000F003000000000000000000000000000000380000C0 0F00007E0000B00700003B0000180000200100000900008800004008000000000 00000000000000000000000000000000000C00000400000700000C00F00007E00 00F00300803F0000F80100C00100000E0000D0000080040000240000200200001 10000000100001000000000000000000000000000000000000000000000C00000 800000880000C00100000E0000700000800300004C00004002000012000010010 08008000044000000040000200000000200001000000000000000000000000000 000000000000000000C0000000010008030040060000320000900100800C00008 40100400C00006200000002000030000080010000080000400000000400002000 000000000000000000000000000000000000000000C0000000020000040040180 000C2000010060080300000040200001000008000000004000040000000020000 10000080000000080000400000000000000000000000000000000000000000000 0C000000002000008000060000000030000180000C00000000400002000000001 00001800008000000004000020000000010000080000800000000000000000000 0000000000000000000000000C0000000040000300000800100000C0000600000 00030000180000C00000000600002000000001000008000040000000020000100 0000001000000000000000000000000000000000000000000C000000008000040 00000002000010000080000000040000200000000100000800004000000002000 01000008000000004000020000000020000000000000000000000000000000000 00000000C00000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000C00000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000C00000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000C0000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000C0000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000C0 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000E0C100000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000030C300000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00018F60700000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000C001000000000000000 00000000000000000000000000018F60700000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000080030000F 80100C00E00000000000000000000000000000000000000000000C60000000000 00000000000000000000000000000000000000000000000000000000000000000 0007E0000F00300801D0000180000200100000000000000000000000000000000 000000000000C6000000000000000000000000000000000000000000000000000 00000801F0000FC0000C00F00000E000070000080060000240000200200000000 000000000000000000000000000000000000C300000E000000000000000000000 000000000000700003F0000F00300800300001C0000C001000012000090000080 0800004400000004000000000000000000000000000000000000000000C0C100C 0010000380000C00100000E0000FC0000E00000000D0000D00000800C00006400 00200200002200001001000010000080010000180000000000000000000000000 0000000000000000060C0004003000007000038000080030000340000A0010000 33000010030080300000840100200C0000C000000006000020000000020000200 0000000000000000000000000000000000000000030C000801C00003E0000F001 00800E0000C80100400E0000C20000100C0080400000000200003000000001000 00800004000000004000040000000000000000000000000000000000000000000 18C00080E00000C20100100E0000F10000080E004070000002030000300000800 100000C0000400000000200001000008001000008000080000000000000000000 00000000000000000000000018C00000000300041E0020F000000107000030000 0800100000C0000C0000000060000300000800100000C00006000000002000010 000000010000000000000000000000000000000000000000F8C70000000C00006 0000000030000180000C000000006000030000000010000080000400000000200 00100000800000000400002000000002000000000000000000000000000000000 000000000C0000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000C0000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000C0000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000C000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000C000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000C 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000C00000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000C00000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000C0000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000C00100000000000000 000000000000000000000000000000C0000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000080030000 FC0100C00E00000000000000000000000000000000000000000000C0000000000 00000000000000000000000000000000000000000000000000000000000000000 00007E0000F00300801D00000C000020010000000000000000000000000000000 0000000000000C000000000000000000000000000000000000000000000000000 00000000000000FC0000E00700000E00007000008006000034000020020000000 0000000000000000000000000000000000000C000000000000000000000000000 000000000000000000000000C00100801F00001C0000E00000001100009000008 0080000440000000400000000000000000000000000000000000000000000C000 0000000000000000000000000000000000800300003F000038000080060000640 00020030000210000100100001000008000000018000000000000000000000000 00000000000000000000C0000000000000000000000000060000700000E000000 00D000068000080180000840100200C0000C00000000600002000000001000020 00000000000000000000000000000000000000000000C00000000000000000C00 000800300000E0000A00300007200009003008060000004020000100000000100 00080000400000000200004000000000000000000000000000000000000000000 000C00000000000080000700000C0030000F40100403C0000820300101C000080 0100000C000060000000020000100000800100000C00008000000000000000000 000000000000000000000000000C00000000000040000F8070080FC0100081E00 40C00100000C000060000000060000300000800100000C0000600000000200001 000000001000000000000000000000000000000000000000000C00000000C0002 7F0030F80300011E0010E00000000600003000008001000008000040000000020 00010000080000000040000200000000200000000000000000000000000000000 0000000000C00080C00300FF00004000000002000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000C000403800000E00000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000C000C00 70000180000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000C000E0000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000C00000070000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 C0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000C0000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000C0000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000C000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000070000000000000 0000000000000000000000000000000C000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000E000 0F00300801E000000000000000000000000000000000000000000C0C000000000 00000000000000000000000000000000000000000000000000000000000000000 000001C0000C00F00007600003000008004000000000000000000000000000000 000000000000E0C00000000000000000000000000000000000000000000000000 000000000000000F00300801F0000FC0000C00000000900004800004008000000 000000000000000000000000000000000000F0F00700000000000000000000000 0000000000000000000000000000700003F000070000080030000240000200300 001100008800000010000000000000000000000000000000000000000000D8F00 7000000000000000000000000000000000000000000700000E00000000D000090 0100800C0000C4000020040000600000000300002000000000000000000000000 0000000000000000000C0C0000000000000000000000000000000600000000700 000E0000A00300003200001002008010000000010000080000800000000400004 0000000000000000000000000000000000000000000C0C0000000000000000000 000000000000380000C0030000F40000400C0000C20000100C000060000000020 00030000000010000080000800000000000000000000000000000000000000000 00C0C00000000000000000000000000C0000FC010080FC0000040F00407000000 0030000300000800100000C000040000000020000100000000100000000000000 00000000000000000000000000C0C0000000080000400080800300C71F0008FE0 08000070008300000800100000C00004000000002000010000080000000040000 20000000020000000000000000000000000000000000000000C0C000000004000 03000407800803F00001000000001000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000C0C00000000200000C00A00700000700002000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000C0C00000000200080300700000000C00 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000C0C00000 000100C800008003000000F8FFFFFF07000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000F8C7000080000038000000000000FE0F000000F8070000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000C00000400000F8010000000 0FC010000000000FC000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0C0000020000000000000008003000000000000807F0000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000C000001100000000000000780000000000000000 803F0000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000C000001200000000 0000000E000000000000000000C00300000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000C00000EA0000000000008001000000000000000000003C00000000000 00000000000000000000000000000000000000000000003000038000000000000 00000000000000000000000000000000C000001C0000000000006000000000000 00000000000C00100000000000000000000000000000000000000000E0000E000 00800E0000D401000000000000000000000000000000000000000000C00000000 00000000000180000000000000000000000000E00000000000000000000000000 380000C0010000760000D00300803200001400000000000000000000000000000 000000000000000C000000000000000000006000000000000000000000000F800 0000000000000000801F0000D40100A00E0000050000500000400400002200000 000000000000000000000000000000000000000C0000000000000000080010000 00000000000000000000800F00003F0000F003008001000024000020010000090 000880000000400004000000000000000000000000000000000000000000000C0 00000000000000004000000000000000000000000000807B00000700007000004 00200004200001002000010000080000000080000400000000000000000000000 0000000000000000000000C000000000000000003000000000000000000000380 00070C00100190000880000400C00004000000002000020000000010000080000 8000000000000000000000000000000000000000000000C000000000000000001 C00000000000000010000070000D0010700210000080100001000008000000004 00002000000002000010000000010000000000000000000000000000000000000 00000C0000000000000000006000000000000C0000000FA0000200E3C00C00000 00060000200000000100000800004000000002000010000000010000000000000 00000000000000000000000000000C0000000080000400003000200101800E0FF 00000207002030E00000010000080000400000000200001000008000000004000 02000000002000000000000000000000000000000000000000000C00000000800 00200001000100080700400000000400000000800300000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000C0000000040000108000C00000F80000800000000000000000000 60000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000C000000004000010C0002200001C0 000000100000000000000001C0000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000C0000 000040000086000120000E0000000000000000000000000700000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000C00000000200400420007E000000000000000000000000 000000C0000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C00000000200800210000E 00000000000000000000000000000080010000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00C00000000100801E10000000000000000000000000000000000000030000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000C00000000100000708000000000000000000000 00000000000000004000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000C00000000100000 00800000000000000000000000000000000000008000000000000000000000000 00000000000000000000000000000002000000000000000000000000000000000 000000000C0000080000000000C00000000000000000000000000000000000010 00000000000000000000000000000000000000000C00006000008007000000000 000000000000000000000000000000000C0000088000000000400000000000000 00000000000000000000002000000000000000000000020000300000800100003 F0000F80100C00A000000000000000000000000000000000000000000C0000090 060000000400000000000000000000000000000000000040000000080000C0000 0000F0000FC0000E0070080640000240300201200000000000000000000000000 0000000000000000C00000E003000000060000000000000000000000000000000 00000C00300003E0000F00300801A0000920100900C0000040000200000000200 0000000000000000000000000000000000000000C00000C000000000020000000 00000000000000000060000700000E00F00006B00004806004022000010000080 0000000400002000000002000000000000000000000000000000000000000000C 000000000000000020000000000000000000000801F0000FC0100B01900808800 00400000000200001000008000000004000020000000020000000000000000000 00000000000000000000000C000000000000000020000000000000000000000C0 24000026030080010000080000400000000200001000008000000004000020000 00002000000000000000000000000000000000000000000C00000000000000002 00000000000000000080010004000020000080010000080000400080010200001 00000800000000400002000000003000000000000000000000000000000000000 F0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0F000000 000000000000000000000000F0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF0F000000000000000000000000000000000000C0000000080 00040020000020000100000808001000000000000000001000000000000008001 00000000000000000000000000000000000300000000000000000000000000000 00000000000C0C000000008000040020000020000100000880400000000000000 00800100000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000E0C100000008000040020000020000 910000B0020000000000000000800000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000030C330 000008000040020000020000560000E0810100000000000000800000000000000 000C0030000000000000000000000000000000080070000000000000000000000 00000000000000000030C3780000080000400200601200003C000080C00100000 000000000800000000000000000600600000000000000000000000000000000C0 0C000000000000000000000000000000000000000018C6CC0000080000400600C 00F000010000000E00100000000000000400000000000000000300C0000000000 00000000000000000000006018000000000000000000000000000000000000000 018C6CC00000800004C06000003000000000000B0010000000000000040000000 0000000000300C000000000000000000000000000000006018000000000000000 000000000000000000000000018C6860100080000F80500000000000000000080 0100000000000000200000000000000000000C000000000000000000000000000 000000018000000000000000000000000000000000000000018C6860100080000 6008000000000000000000800100000000000000100000000000000000000C000 00000000000000000000000000000006C00000000000000000000000000000000 0000000018C686010008000000080000000000000000008001000000000000000 80000000000000000000600000000000000000000C00100000E0000DF00000000 0000000000000000000000000000000030C386010008000000080000000000000 00000800100000000000000060000000000000000800300000000070000380000 B80200C0150000AE000000000000000000000000000000000000000030C386018 04800000010000000000000000000800100000000000000030000000000000038 C000C00100C00B000057000080020000140000380100000000000000000000000 000000000000000E0C1CC00002B00000010000000000000000000800100000000 00008001000000E00F0000376000B80100000A000050000040040000220060180 000000000000000000000000000000000000000C0C0CC00001E00000020000000 000000000000800100000000000EC000F80100000E00004830004002000011000 08800002000000001006018000000000000000000000000000000000000000000 C0780000080000006000000000000000000080010080010000703000C00100000 9000044300020020080000000040000200000000100C00C000000000000000000 000000000000000000000000C030000000000000C0000000000000000000F00F0 000060000580C003001008008000002F00F100000400000000200001000008000 00800F000000000000000000000000000000000000000000C0000000000000008 0000000000000000000600000001C000026070008010060000000010000080000 40000000020000080000400000000400000000000000000000000000000000000 0000000C00000000000000000010000000000000000C00100E00F0080E1010006 00001000008000000004000020000000010000080000400000000400000000000 0000000000000000000000000000000C000000008000040000300020000301000 80FF03001C0200607000000100000800004000000002000010000080000000040 0002000000002000000000000000000000000000000000000000000C000000008 0000800006000C0000C0110000C00100000000001C00000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000C000000010000000011C00100200002E0000600000000000000 70000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000C00000001000000001300020020 000380000000000000000C0010000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000C00 0000010000000026000C00100000700000000000000007C000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000C000000020000000248001F801000000000000000000 00C00700000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000C0000000200000002800 06000000000000000000000000780000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000C0000000200000801B001C0000000000000000000000000F0000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000C0000000200000001C0070000000000000000 0000000C001000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000C000000040000 0000000C001000000000000000000003C00000000000000000000000000000000 00000000000000000000000000000000000700000000000000000000000000000 00000000000C0000000400000000000000F000000000000000000C00300000000 000000000000000000000000000000000000000000001C0000FC0000E00600000 00000000000000000000000000000000000C00000005804000000000078000000 0000000000C03F0000000000000000000000000000000000000000700000F0030 0801B0000C0000000090000000000000000000000000000000000000000C00000 00F0030000000000C003000000000000807F0000000000000000000000000000F 00300C00F00007E00008003000026000030010080080000000000000000000000 000000000000000000C0000000C000000000000000FC010000000000FC0000000 000000000C00100007E0000800300000E00008800004004000021000008010040 000000000000000000000000000000000000000000C0000000000000000000000 000FF07000000FC070000000000700000000E0000580000600200801100008600 00300400800000000400002000000000000000000000000000000000000000000 0C000000000000000000000000000F8FFFFFF870100000E0000800300800B0000 26000018020040100000010000080000400000000200001000000000000000000 0000000000000000000000000C000000000000000000000000000000000000007 00007800007801006004008021000006020030000080000000040000300000800 1000008000000000000000000000000000000000000000000C000000000000000 00000000000000200000E00F00E02700800701001C0400600000800100000C000 06000000003000008000040000000040000000000000000000000000000000000 00000000C000000008000040000000060800F0C300801F04001C2000608000000 30000180000400000000200001000008000000004000020000000020000000000 00000000000000000000000000000000C00000001000008001000078100000FC0 10000020000100000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000C0C00000001 000000006000080170000C0000000010000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000E0C0000000200000001801000038000020000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000F0F0070000400000006001000007 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000D8F0 07000080000000800300000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000C0C000000080000000F00300000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000C0C000000000010000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0FEC1C00000000022000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000C0C00000000014000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000C0C0000000C015 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000C00100C00F0000000000000000000000000000 0000000000C0C0000000000E00000000000000000000000000000000000000000 0000000000000000000000000000000000000000E00007E0000B80100000C0000 0000000000000000000000000000000000C0C0000000000000000000000000000 00000000000000000000000000000000000000000000000003F0000F80100C00F 0000700000600200001200000000000000000000000000000000000000C0C0000 000000000000000000000000000000000000000000000000000000000001C0000 E0070000380000C00100000900004800001002000011000000000000000000000 00000000000000000F8C700000000000000000000000000000000000000000000 0000E00000003F0000E0000080050000260000300100C0080000460000080000C 0000000000000000000000000000000000000000000C000000000000000000000 00000000000000000700001C0000000700002C0000B00000600400802100000C0 10020000000010000040000200000000000000000000000000000000000000000 00C00000000000000000000000000000E00000001C0000E00000C005008013000 08E000018040040000000020000180000C0000000020000100000000000000000 00000000000000000000000000C00000000000000000000000180000C00300C00 B00005E00003C0200701000808100000600003000008001000004000020000080 01000008000000000000000000000000000000000000000000C00000000000000 0000100007000003F01003C0800E04100800302000C0000600000800100000C00 00600000000300001800004000000004000000000000000000000000000000000 000000000C0000000180000C01F0600FEFF00F00001800304001C200060000000 03000018000040000000020000100000800000000400002000000002000000000 000000000000000000000000000000000C0000000E0400000E00F000070000080 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000C0000000 008F0000000700001800000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000C000000000F00000800100000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000C000000000C00100000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000C 00000000038000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000C00000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000C00000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000C0000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000C0000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000E0000000000000000000000000000000000000000C0000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000380000F80100C00D000000000000000000000000000 0000000000000C000000000000000000000000000000000000000000000000000 00000000000000000000000000000000F80100E00F00003700008001000012000 0000000000000000000000000000000000000C000000000000000000000000000 000000000000000000000000000000000000FC0000E00700003F0000C00100000 E00004C000060020000110000000000000000000000000000000000000000C000 0000001C000000000000000000000000000000001C0000F00300801F0000E0000 00007000038000020010000090000420000100200800000000000000000000000 00000000000000000000C000000000E00000C00100000E0000700000801F0000E 00000C0020000160000980000C0040000260000180100C0080000010000080000 40000000000000000000000000000000000000000000C000000000B00000000E0 000700000800300000E0000B00000300200801100008600003004008021000004 00002000008000000004000020000000000000000000000000000000000000000 000C0000000004E0000800700003C0000E00100C00900004E00000C0200601000 00810000080000400000000300001800004000000002000010000000000000000 000000000000000000000000000C000000080410000780400C02300001E010038 0400C0410000030200180000C0000000060000300000800000000400003000008 001000008000000000000000000000000000000000000000000C0000000600000 00070200381000C0810000060000300000C0000000060000300000800100000C0 00060000000030000080000400000000400000000000000000000000000000000 0000000000C0000000180000C0000000060000300000800100000C00002000000 00100000800004000000002000010000080000000040000200000000200000000 0000000000000000000000000000000000C000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000C000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000C00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000C00000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 C0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000E0C1000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000030C3000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000018F6070000000E0000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000008003000000000 0000000000000000000000000000018F6070000C0150000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 E000070000070050000000000000000000000000000000000000000C600000000 14000000000000000000000000000000000000000000000000000000000000000 0000E0000700000F80100C0150000AE0000000500000000000000000000000000 00000000000000C600000000220000E0000000000000000000000000000000000 0000000000000380000F80100C00D00006E000080020000120000900000800800 0000000000000000000000000000000000FE01C300000000010000DC0000C00F0 000000000700000801F0000FC0000E0070000370000800100001A000090000040 020000210000080100400000000000000000000000000000000000000000C0C10 0000080000000200100000E00007E0000800300001C0000E00000000700002C00 00600200001100008800002004008000000004000020000000000000000000000 000000000000000000060C0000000800000001001000009000070000080030000 12000090000080040000220000100200C01000000600001000008000000004000 020000000000000000000000000000000000000000030C0000000400000000C00 00C00800004C0000600200801100008C000060040000010000080000200000000 10000080000400000000200001000000000000000000000000000000000000000 0018C000000020000000020000200000004200001002004000000002000010000 08000000004000010000080000000040000200000000100000800000000000000 0000000000000000000000000018C000000010000000010000100000800100000 C0000200000000100000800006000000003000008000040000000020000100000 80000000040000000000000000000000000000000000000000F8C700000010000 0800000000C000060000000030000180000C00000000600001000008000000004 00002000000001000008000040000000040000000000000000000000000000000 00000000000C00000000800004000000002000010000080000000040000200000 00010000080000400000000200001000008000000004000020000000020000000 00000000000000000000000000000000000C00000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000C00000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000C0000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000C0000000C00000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0C0000000F0010000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000C000000058020000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000C000000040040000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000C00000004000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000C0000000060000380000000000 00000000000000000000000000000000C0000000400000000E000000000000000 0000000000000000000000000000000000000000000C0000000070000380000F0 0100800F0000EE000000000000000000000000000000000000000000C00000002 00000C01500007000000000000000000000000000000000700000800300001C00 00700100E00A0000570000580200C012000010010000000000000000000000000 000000000000000C000000020000000140000BC000000070000380000C0010000 0E0000AE0000700500802B00004C0100000A00005000004004000022000010000 000000000000000000000000000000000000000C000000020000000220000A000 00E0060000570000B80200C0150000A0000000050000280000200200001100008 800002000000001000008000000000000000000000000000000000000000000C0 00000010000000020000100100000900004800004002000022000010010080080 00044000010000080000000040000200000000100000800000000000000000000 0000000000000000000000C000000010000000010000100000800800008400002 00400000100000800004000000002000010000080000000040000100000800000 0008000000000000000000000000000000000000000000C000000010000000010 00008000080000000040000200000000100000400002000000001000008000040 00000002000010000080000000040000000000000000000000000000000000000 00000C00000001000008000000004000040000000020000100000800000000400 00200000000100000400002000000001000008000040000000040000000000000 00000000000000000000000000000C00000000800008000000004000020000000 01000008000040000000020000100000800000000400002000000001000008000 04000000002000000000000000000000000000000000000000000C00000000800 00400000000200001000008000000004000020000000010000080000400000000 20000100000800000000400002000000002000000000000000000000000000000 000000000000C0000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000C0000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000C0000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000C00000000C000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C00000003F000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00C00000804900000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000C00000000800000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000C00000000800000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000003000000000000000000000000000000000 000000000C0000000080000600000000000000000000000000000000000000000 00000000000000000000000000000000800100000C0000600000C00F000000000 0000000000000000000000000000000E0C1000000080000F80100000300000000 000000000000000000000000000000080000C0000000060000300000E00700003 F0000F801006012000000000000000000000000000000000000000030C3000000 0800004C0200C00F0000180000C0000000060000700000800300003E0000F0030 0801F0000FC0000900C0080640000240300000200000000000000000000000000 0000000000000018F6070000080000400000601200007E0000F00300801F0000F C0100E00F00006B00004806004032000092010080000000040000200000000200 0000000000000000000000000000000000000018F607000008000040000000020 000930000980400C0240000260300301900808800004000000002000010000080 0000000400002000000002000000000000000000000000000000000000000000C 60000000800004000000002000010000080000000040000200000000100000800 00400000000200001000008000000004000020000000020000000000000000000 00000000000000000000000C30000000800004000000002000010000080000000 04000020000000010000080000400000000200001000008000000004000020000 0000200000000000000000000000000000000000000FEC1C10000000800004000 00000200001000008000000004000020000000010000080000400000000200001 00000800000000400002000000002000000000000000000000000000000000000 000000C3000000080000400000000200001000008000000004000020000000010 00008000040000000020000100000800000000400002000000002000000000000 000000000000000000000000000000C6000000080000400000000200001000008 00000000400002000000001000008000040000000020000100000800000000400 002000000002000000000000000000000000000000000000000018C6000000080 00040000000020000100000800000000400002000000001000008000040000000 02000010000080000000040000200000000200000000000000000000000000000 0000000000018C600000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000030C300000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000E0C100 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000C00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000C00000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000C0000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000C0000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000C0000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000C000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000C000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000C000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000C00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000C00000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 C0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000C0000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000C0000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000C000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000C000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000}}{COM_R 18 0{TEXT 1 357 "Or, \+ if we want to see a whole range of initial conditions, we can use the seq command to generate a whole list of them. In this case, we build conditions starting out with an initial angle of 0 and \+ eleven different initial velocities between 1 and 3. Note that t he trajectories plotted show not only where the solution goes (t> 0), but where it came from.\015"}}{INP_R 19 0 "> "{TEXT 0 66 "pha seplot([vdot,thdot], 0..3,-Pi..Pi,\{seq([0,1+.2*i,0],i=0..10)\}); "}}{GRH_R 20 0{RASTER 605 296 1 76 00000000000000000000C000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000C0000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000C000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000C00000000 60000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000C00000801F000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000C00000C02400000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000C0000000 04000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000C00000100400000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000060000000 000000000000000000000000000000000000C0000010040000300000000000000 00000000000000000000000000000000000000000000000000000000000300000 800100000C0000F8010000000000000000000000000000000000000000C000001 0040000FC00008001000000000000000000000000000000000000000200001800 00C0000000060000FC0000E00700003F000024030000000000000000000000000 000000000000000C0000010040000260100E00700000C00006000000003000018 1000E00000800700007E0000F00300801F0000920100900C00806400002000000 0000000000000000000000000000000000000C000001004000020000030090000 3F0000F80100C00F00007E1000F80300C00A0000930000980400C024000010000 08000000004000020000000000000000000000000000000000000000000C00000 100400002000000001008064000024030120190000C910004C060020130000100 00080000000040000100000800000000400002000000000000000000000000000 0000000000000000C000001004000020000000010000040000200001000100000 80800400000000300001000008000000004000010000080000000040000200000 00000000000000000000000000000000000000C00000100400002000000001000 00400002000010001000008080040000000030000100000800000000400001000 008000000004000020000000000000000000000000000000000000000000C0000 01004000020000000010000040000200001000100000808004000000003000010 00008000000004000010000080000000040000200000000000000000000000000 00000000000000000C00000100400002000000011000004000020000100010000 08080040000000030000100000800000000400001000008000000004000020000 000000000000000000000000000000000000000C0000010040000200000001100 00040000200001000100000804004000000003000010000080000000050000100 0008000000004000020000000000000000000000000000000000000000000C000 00100400002000000011000004000020000100010000080400400000000300001 00002800000000500001000008000000004000020000000000000000000000000 000000000000000000C0000010000000000000001000000000000000010000000 00004000000000001000000000200000000010000000000000000000000000000 0000000000000000000000000000000000000000C000001000000000000000100 00000000000000100000000000400000000000100000000020000000002000000 000000000000000000000000000000000000000000000000000000000000F0C00 00010000000000000001000000000000000010000000000040000000000010000 00000400000000020000000000000000000000000000000000000000000000000 0000000000000000098C100002000000000000000200000000000000001000000 00000800000000000100000000040000000002000000000000000000000000000 0000000000000000000000000000000000000000CFB0700E00100000000000020 00000000000000020000000000080000000000020000000004000000000200000 00000000000000000000000000000000000000000000000000000000000000CFB 07007007000000000000200000000000000002000000000008000000000002000 00000040000000002000000000000000000000000000000000000000000000000 00000000000000000000C30000A80000000000000020000000000000000200000 00000080000000000020000000004000000000200000000000000000000000000 000000000000000000000000000000000000000080C10000A0000000000000002 00000000000000002000000000010000000000002000000000800000000040000 00000000000060000000030000000000000000000000000000000000000000E0C 00000A00000800100000040000000000000000400000000001000000000000400 00000008000000300400800300001C0000B00100800D000000000000000000000 000000000000000000080C10000A00000400700000C4000000000000000040000 0000002000000000180400C00100080E0000E80400C01C0000E60000500600803 2000000000000000000000000000000000000000000C30000200100401900003A 8000700000800300081C0000E0002000070000740400A00E00087500002807004 0010000090000480000400200000000000000000000000000000000000000000C C3000020010020020000CA8000B00300801D0008EA0000500740803A000094090 0A000001005000044080020010000080000800000000400000000000000000000 000000000000000000000CC3000020010000020000110001280000400100100A0 00050004040020000220800100100900800004008000002000010000080000000 04000000000000000000000000000000000000000098C10000200200000400002 00001480000400200101100008800800004000040100000020020100000801000 0002000010000000010000080000000000000000000000000000000000000000F 0C000002002000008000020000280000000040020200000000180000800004010 00000200201000000011000004000020000000010000080000000000000000000 00000000000000000000000C00000200200000800004000020001000008004040 00000002000110000080200000040040200000002100000400002000000002000 010000000000000000000000000000000000000000000C0000020020000100000 80000400010000080040400000000200011000000021000008004040000000220 00008000040000000020000100000000000000000000000000000000000000000 00C00000200400001000008000080002000010008080000000040002200000004 10000080080400000004200000800004000000004000020000000000000000000 000000000000000000000000C0000040040000200000000108000400002000000 10100000800044000000042000010008080000000440000100000800000000400 0020000000000000000000000000000000000000000000C000004000000000000 00000100000000000000002000000000008000000008000000000000100000080 00000000000000000000000000000000000000000000000000000000000000000 000C0000080000000000000000020000000000000000400000000001000000000 80000000000002000000800000000000000000000000000000000000000000000 0000000000000000000000000C000008000000000000000004000000000000000 04000000000010000000000001000000000400000000010000000000000000000 00000000000000000000000000000000000000000000000C00000000100000000 00000040000000000000000800000000002000000000000200000000040000000 00100000000000000000000000000000000000000000000000000000000000000 0000C000000001000000000000008000000000000000100000000000400000000 00004000000000800000000020000000000000000000000000000000000000000 00000000000000000000000000C00000000200000000000000000100000000000 02000000000008000000000000800000000100000000004000000000000000000 000000000000000000000000000000000000000000000000C000000E020000000 00000000006000000000000400000000000000100000000100000000020000000 00080000000000000000000000000000000000000000000000000000000000000 00000C00000760400000000000000000800000000000080000000000000020000 00002000000000400000000008000000000000001C0000E000000000000000000 000000000000000000000000000C0000009040000000000000000300000000000 000001000000000004000000004000000000400000000010380000C00100007A0 000D003000000000000000000000000000000000000000000C000000908000000 000000000040000000000000000200000000000800000000801C0000E08000003 F0020D80100C00E00001200009000000000000000000000000000000000000000 000000C00000100800F801000000000080000000000000000C00000000F033008 01F0000ED00006007010003004024000020010000110000880000000000000000 0000000000000000000000000000C00000201000380000E00700003F0300F8010 0C00F10007E000070400080030000320000900102800C00404400002002000020 00000001000000000000000000000000000000000000000000C00000401000440 000E0000000070400380000C00120000E00009080008004000046000010020480 10008080000000040000400000000200000000000000000000000000000000000 0000000C0000080200084010020030000191800C8000040064000320000100301 80180000980000000408002000000101000008000080000000040000000000000 00000000000000000000000000000C00000002100000200200C00002120000801 00400880004200000004020020000020010000081000400000020200001000000 001000008000000000000000000000000000000000000000000C0000000410000 040000300000C0C00000060000300003800100000804004000004006000030600 08001000404000020000000010000080000000000000000000000000000000000 00000000C0000000420000180000C0000000030100180000C0000400060000301 80080010080080000408000000200080800004000000002000010000000000000 000000000000000000000000000000C0000000840000200000000100000402002 00000000118000800004020000002000011000080000100040030100000800000 0004000020000000000000000000000000000000000000000000C000000000030 000000000000000000C0000000000006000000000004000000000000600000000 02000000400000000000000000000000000000000000000000000000000000000 000000000C0000000000400000000000000000030000000000000800000000000 80010000000008000000000400000080000000000000000000000000000000000 0000000000000000000000000000000C00000000008000000000000000000C000 00000000000003000000000002000000001000000000080000000001000000000 00000000000000000000000000000000000000000000000000000C00000000010 00000000000000000000030000000000000400000000000400000000600000000 01000000000020000000000000000000000000000000000000000000000000000 0000000000C00000000020000000000000000000000C000000000000180000000 00018000000008000000000600000000004000000000000000000000000000000 00000000000000000000000000000000C000000000C0000000000000000000003 00000000000006000000000002000000000000300000080000000000800000000 0000000000000000000000000000000000000000000000000000F0C0000000000 001000000000000000000C0000000000000800100000000C00000000000040000 00000100000010000000000000000000000000000000000000000000000000000 00000000098C10000000000020000000000000000000007000000000000060000 00000003000000000800000000060000002000000000000000000000000000000 00000000000000000000000000000000CFB07000000000C000000000000000000 00180000000000001800000000000C00000000300000000008000000C00000000 000000000380000000000000000000000000000000000000000000CFB07000000 00300000000000000000000060000000000000600000000000300000000040000 000001000000E0001F00300801F0000F800000000000000000000000000000000 000000000000C30000000000C0000000000000000000008001000000000080010 0000000C00000000080F90100C06F000076000230000080010000240000000000 0000000000000000000000000000000000C300000000000003000000000000000 000000600000000000006000000E00703003F00003A0000C08100001A0004D000 00800600004400000000000000000000000000000000000000000080C10000070 000000C0000000000000000000018800300801F0018FC0000E00004000700004C 00004002010022000810010080080000800000000000000000000000000000000 00000000000E0C000E00000001C3000E00000000700003F00E0700000800600E0 34000020031800190000980100400C06004200300002000010000000010000000 00000000000000000000000000000000030C000A001000007C0011C0000E00000 000E0000D7000080180000C70000200C600061000060020000100800800040000 400002000000002000000000000000000000000000000000000000018C000400E 00001D001EF80000C0030000720000380700806000000C0300001080018000008 00C00006010000001800008000040000000040000000000000000000000000000 0000000000000CC00040700000E201E0080700403C0000840300E018000080010 0700C000060000200030000110000806000000600013000008001000008000000 00000000000000000000000000000000000CC00000800100020E001F780080C00 100000C00006700000006008031000080010C000C000066000000830000080006 40000000020000100000000000000000000000000000000000000000FCC300000 006000030007080010000060000300000B8010000080000460000000230001000 00880000000403001000088000000004000020000000000000000000000000000 000000000000000C000000000000000008007000000000000000000C001000000 00001800000000C00000000030000000000400000010000000000000000000000 0000000000000000000000000000000000000C000000000000000000038000000 000000000000000E0000000000600000000000010000004000000000080000006 00000000000000000000000000000000000000000000000000000000000C00000 00000000000000C00300000000000000000030000000000080010000000006000 00080010000003000000080000000000000000000000000000000000000000000 0000000000000000C0000000000000000000003C000000000000000000C001000 00000000600000000180000000006000000400000000003000000000000000000 00000000000000000000000000000000000000C000000000000000000000C0070 000000000000000000E0000000000180000000060000000000800000080010000 000400000000000000000000000000000000000000000000000000000000C0000 00000000000000000007800000000000000000030000000000060000000008000 00000030000000000200000008000000000000000000000000000000000000000 00000000000000000C00000000000000000000000800F0000000000000000C000 0000000080010000000003000000C000000000040000003000000000000000000 000000000000000000000000000000000000000C0000000000000000000000000 F001000000000000000007000000000006000000000C000000000100000018000 0004000000000000000000000000000000000000000000000000000000000C000 0000000000000000000000003E000000000000000018000000000018000000003 00000000006000000200000008000000000001C00000000000000000000000000 000000000000000000C000000000000000000000000000C007000000000000006 000000000006000000000400000000018000000CE0000F00303801F0000EC0000 0000000000000000000000000000000000000000C000000000000000000000000 00000F80000000000000080030000000080010000008001C00100E00F00007E01 00700004800300003200000000000000000000000000000000000000000000C00 000000000000000000000000000000F000000000000001C00000000000700003F 0006380000C001000012020090000880040000420000000000000000000000000 0000000000000000000C0000000000000000000000000000000F0010000000000 0EE0007E0000E01800000D001868000040070000220C001001308008000080000 00000000000000000000000000000000000000000C00000000000000000000000 00000000183E00C00100C00100031A0000A0610000310020880100401E0000C21 000000640003000000001000000000000000000000000000000000000000000C0 0000000000000000000000000300000EC0033800008007001CE40000208E0300C 100C0080600003800000061000008800040000000020000000000000000000000 00000000000000000000C00000000000000000600000C00100000F003CD003008 07800E004070020300C0000030003180000E0000000820000100001800000000C 000000000000000000000000000000000000000000C0000000000004000038000 0E00F0000F203C0133C000081030007180000C03000000C000C600000C0030000 0C01006000060003000010000000000000000000000000000000000000000000C 00000000600833F00FCFF01C0F00700043C003CC00100000C003860000000C301 00100010800000000500001006008000080004000020000000000000000000000 000000000000000000000C00040C001807F000018000000010000000000E00100 00000000C00000000000060000006000000000060000000800000010000000000 0000000000000000000000000000000000000000000C000403C00000700002000 0000000000000000001E000000000000070000000018000000800100000008000 00030000000200000000000000000000000000000000000000000000000000000 C000A00300000C00000000000000000000000000E003000000000038000000006 00000000006000000300000004000000040000000000000000000000000000000 0000000000000000000000C000E00000000000000000000000000000000000003 C0000000000C00000000080010000000800000040000000800000008001000000 00000000000000000000000000000000000000000000C00000070000000000000 000000000000000000000C0030000000000030000000006000000300000008001 00000003000000020000000000000000000000000000000000000000000000000 0C00000000000000000000000000000000000000000001C00000000001C000000 0018000000C000000000020000000400000004000000000000000000000000000 00000000000000000000000C00000000000000000000000000000000000000000 00E00100000000600000000020000000000300000004000000080000000800000 000000000000000000000000000000000000000000000C0000000000000000000 000000000000000000000000000E000000008001000000C000000000040000001 80000003000000010000000000000000000000000000000000000000000000000 00C0000000000000000000000000000000000000000000007000000000000E000 00000030000001800000020000000400000006000000000000000000000000000 000000000000000000000000C0000000000000000000000000000000000000000 0000080030000000030000000000C00000020000000C0000000800000008E0000 F003000000000000000000000000000000000000000000C000000000000000000 000000000000000000000000000003C00000000C00100000030000000C0000000 00390000C00F00007601003000000000000000000000000000000000000000000 060C00000000000000000000000000000000000000000000000C0010000000006 000000C000F00700013F0000DE0100C0040000090200480000000000000000000 0000000000000000000000070C000000000000000000000FEFFFFFFFF1F000000 00000000000E000000001E00007E0003700000060700002C00002009000011040 08800000000000000000000000000000000000000000078F80700000000000000 00F8FF00000000F03F00000000001C0070F80100C0E100000E000490000088080 00054000020320000200800000100000000000000000000000000000000000000 006CF80700000000000000C07F000000000000FC0F800300800300806B0000400 30300320018100300B0300000E00100004C000040100000020000000000000000 00000000000000000000000060C00000000000000000FC0100000000003000F87 F0000000F00009C0100800C0C00C20060000C0040400000800200009000008020 000004000000000000000000000000000000000000000060C000000000000000C 00F0000000200001C0000FC070000710000F00600803030000003800110008081 00000005000020010000C10000080000000000000000000000000000000000000 00060C000000000000000F800000080010000FE0000207F0000820300001B0000 C0C000000C0006600000060300000E00004002000002010010000000000000000 000000000000000000000000060C0000000040000300E40E001C0FF07000C3F00 40E00700000C00006C00000003030010001880000018040000180000800400000 4020020000000000000000000000000000000000000000060C00000000200008C 01B01F008003000010000000007C0000000000300000000004000000200000002 00000001000000008000000040000000000000000000000000000000000000000 000060C00000000100044300780000000600000000000000C00700000000C0000 0000018000000C0000000C0000000200000001000000008000000000000000000 0000000000000000000000000060C00000800000C430006000000000000000000 0000000FC00000000000700000060000000000100000003000040000000200000 00100000000000000000000000000000000000000000000060C00000400000341 C0080010000000000000000000000800F00000000180000008000000000060000 00040000800000004000000020000000000000000000000000000000000000000 00000FCC30000200000FC060000000000000000000000000000007C00000000E0 00000000030000000800000008000000030000800000004000000000000000000 00000000000000000000000000000C00000200000000300000000000000000000 0000000000C00300000000030000000C000000100000001000000004000000010 000800000000000000000000000000000000000000000000000C0000011000080 00000000000000000000000000000000001E000000000C0000001000000060000 00020000000080000000200008000000000000000000000000000000000000000 00000000C00000090000400000000000000000000000000000000000700000000 03000000060000000800000004000000010000000040000000100000000000000 000000000000000000000000000000C0000076000020000000000000000000000 00000000000008003000000C00000008000000000010000800000002000000008 6000000207000000000000000000000000000000000000000000C000000E00001 00000000000000000000000000000000000001E00000000030000000300000002 00000001800140001C0010D00100841E000000000000000000000000000000000 000000000C00000000000080000000000000000F0FFFF07000000000000F80000 00000C000000040000070C00380002400780007A0020500300880200000000000 0000000000000000000000000000000C00000000000040000000000000000FF00 00FE7F0000000000C003000000100000E01800003B1000D80104400D00010A002 08800005004000000000000000000000000000000000000000000C00000000000 0200000000000000FC00000000F80700000000000E000000FC000060270080042 00024000820020002110040800000100400000000000000000000000000000000 0000000000C0000000000001000000000000F0030000000000F80300E00000F80 F00009C0000904000800840004400100002000410008000010020080000000000 00000000000000000000000000000000C00000000080010000000000003C00000 00000000E7E001C0000C003000022010010830000108000800010000400042000 000101004008000000000000000000000000000000000000000000C000000000C 0000000000000C00300008000008003C007740000400F00004206000004030020 00010001200008000840000002020040100000000000000000000000000000000 00000000000C000000000C0000000000000F0000000600000003D003C88030040 3C000080090000080400400001000240000800104000000402008010000000000 000000000000000000000000000000000C000000004600020000000011C080600 303E0000C101E0090C00007000000012000010080080000200048000100020800 0000404008020000000000000000000000000000000000000000000C000000004 6000100000800006C40100F80100000200000F000000C00000006000000010000 00004000080000000400000000800000001000000000000000000000000000000 000000000000C00000000220000800006080013C0000700000000000003800000 08001000080000000200000000800000001000040000000080000000100000000 0000000000000000000000000000000000C00000000220000800001140000E000 0C0000000000000C0010000000200000001000040000000080000000200008000 00001000000002000000000000000000000000000000000000000000C00000000 210000400000930007000000000000000000000070000000C0000000200004000 00001000000004000080000000100000000200000000000000000000000000000 0000000000000C000000001100002000007180000000000000000000000001C00 00001800000004000080000000200000000400000001000020000000040000000 00000000000000000000000000000000000C00000000118200100003F04000000 00000000000000000070000000300000000800000001000040000000080000000 100002000000004000000000000000000000000000000000000000000C0000080 0008401D000000020000000000FCFF7F00000000C000000040000000080000000 20000400000000800000002000040000000080000000000000000000000000000 00000000000000C0000080000C80030000000100000000E00F00E00F000000000 30000800000001000000004000080000000100000000200004000000008000000 000000000000000000000000000000000000C0000080000C00000000800100000 0007C0000007C0000000006000000010000200000000400008000000020000000 0400008000000028000000000000000000000000000000000000000000C000004 0000C00000000C0000000000007000000C0030000000C00000003000040000000 0800000001000020000000840100800C0000F8000000000000000000000000000 000000000000000C0000048000400000000C000000000C000000000001E000000 18000000060000400000001000000001060040300000E40700803F0000B801000 0000000000000000000000000000000000000C000005006040000000060000000 0030000000000070000000300000000400008000180010C00000821F0040FC000 0940C008064000034020000000000000000000000000000000000000000C00000 B00104000000006000000000080000000000C00000006000E0000C000380007E0 020F00300C2240040920100880000800400003000000000000000000000000000 0000000000000000C000006000040000000020000000000400000000000301001 84000F80308C00F00019300209804000204004010000088000080040000300000 00000000000000000000000000000000000000C00000000004000000003000000 0000200000000C00F02007EC0004C061860120001100020800000020400401000 008800000005000030000000000000000000000000000000000000000000C0000 0000004000000001000000000030000000020190600C980004000180002000110 00208000000404008010000088000000050000300000000000000000000000000 00000000000000000C00000000004000000001000000000010000600000010C00 08800040001000020002100060800000040400801000009000000005000030000 000000000000000000000000000000000F0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000000000000F0FFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000 000000000000000000C0000000040400200000100100000401002060000000080 00080010000100000000200006000000004000080000000100000000100003000 0000000000000000000000000000000000000060C000000004040020000010010 00004030024020000000C00008001000010000000020000400000000400008000 000010000000010000200000000000000000000000000000000000000000F0C00 0000004040020000010010080640300A801000000040000800000001000000001 00004000000004000080000000080000000100001000000000000000000000000 0000000000000000098C1300000040400200000300100003F0600F06000000002 0000C000000018000000010000F00000000200008000000008000000010000780 00000000000000000000000000000000000000098C17800000404002000003009 00000C040020700000800100004000000018000000010000B8010000020000400 0000008000000010000DC00000000000000000000000000000000000000000CC3 CC0000040400200000E007000000080000780000C000000060000000080000800 000002C0300000200004000000008000080000000960100000000000000000000 0000000000000000000CC3CC0000040400260100E0010000003000006C0000700 00000300000000C0000800000001C030000020000400000000400008000000096 01000000000000000000000000000000000000000CC3860100040400FC0000C00 0000000C000006000001E00000018000000060000400000001003000001000040 000000040000800000009001000000000000000000000000000000000000000CC 3860100040C00300000C0000000008003006000E0030000000C00000002000040 000000080300000100002000000004000080000000C8060000000000000000000 00000000000000000000CC3860100040C000000008001000000003C0060007C00 0000000600000001000020000000840100800000002000000004380080C00100F 80F0000000000000000000000000000000000000098C1860100040C0000000000 0100000000F00760F00F000000800100008000000010000000E400008000C0011 000070002570080B80200C8120000000000000000000000000000000000000098 C18601C024080000000000020000000000FCFF3F00000000C0000000400000000 800000E32003F4000B80110C00B00025000408004008823000000000000000000 00000000000000000000F0C0CC00801F180000000000040000000000006000000 0000030000000300000F80900C00D190030400080020800120001880040400000 86010000000000000000000000000000000000000060C0CC00000610000000000 0180000000000006000000000009C0300007E000080050000920C004820004002 04000100010400202000008601000000000000000000000000000000000000000 0C07800000010000000000030000000000000600000E00080071C00007C000040 020000910C0044100020000480008000040020200000CE0000000000000000000 00000000000000000000000C03000000020000000000040000000000000FC0300 0007E0011600004E00003003008040FC030410001000024000800002001010000 0FA000000000000000000000000000000000000000000C0000000002000000000 0080010000000000200000E0033880090080430000C8000040200000020800100 00140004000010010080000410000000000000000000000000000000000000000 00C000000000600000000000000600000400004000001C0207600800E00100002 40000201000000104000800012000400001000808000041000000000000000000 000000000000000000000000C000000004600020000000011C001C0800E0FF000 003E1011800007800000012000010080080000200048000100020800000080400 8020000000000000000000000000000000000000000000C000000004C00040000 00006F000E00B0000600000003C000000000C0000000800000004000000020000 40000000100000000400008000000000000000000000000000000000000000000 000C000000008C0008000000008C103001C0000100000C0070000000003000000 06000000030000000100002000000008000000020000400000000000000000000 0000000000000000000000000C00000000880010001000010011C800300000000 007F00000000C0000000000100008000000080000000200000000400000001000 04000000000000000000000000000000000000000000000C00000000800010001 0000E000F0010000000000FC03000000003800000080000000400000004000000 01000000004000080000000200000000000000000000000000000000000000000 0000C000000010000200120000FC00007E00000000FC0300000000000F0000006 00000002000000020000000080000000200004000000010000000000000000000 00000000000000000000000000C0000000100004C01D0000000000807F0000FF3 F0000000000C00300000010000000180000001800000004000000010000400000 001000000000000000000000000000000000000000000000C0000000100008000 E000000000000F8FFFF0300000000000078000000000C00000004000000040000 00020000800000002000000008000000000000000000000000000000000000000 00000C00000001000100000000000000000000000000000000000001E00000000 03000000030000000200000001000040000000100000000400000000000000000 000000000000000000000000000C0000000200020000000000000000000000000 00000000008003000000C00000008000000000010000800000002000000008000 00E0200700000000000000000000000000000000000000000C000000020024000 00000000000000000000000000000000700000000030000000600000008000000 040000000700000F00700C00D01006E0000000000000000000000000000000000 000000C00000002C018000000000000000000000000000000000001E000000000 C0000001000000060800300E00F00006E00000003000092000090000000000000 0000000000000000000000000000C0000000F8000003000000000000000000000 000000000E00300000000030080030C007E0010F00300100C00009E0000C00500 00910000880000000000000000000000000000000000000000C00000006000000 60000000000000000000000000000007C00000000F00000001C030070000C4002 0008130000850000A004008040000004000000000000000000000000000000000 0000000C00000000000000C0000000000000000000000000000830F00FC000098 0300009600004C000230020084100080020000500000402000000200000000000 00000000000000000000000000000C00000000000003000000000000000000000 C0000000FE0000780000E70200806900004200010802004300004001000028000 020100000010000000000000000000000000000000000000000C0000000000000 4000000000000000100000800300C01F00004700C01801006018008001C000040 0C0300000E0000000160000100800800000000000000000000000000000000000 00000000C00000000000008001000000000000600000F00700FC0900E02000300 70100180600600020000300300800003000000009000008040040000000000000 000000000000000000000000000000C000000004000060060000030200FCFF00E 00F03E0070400180000CC000000860100100018800000080400001C0000800400 0004020020000000000000000000000000000000000000000060C000000008000 0807900003C04000060000080803F000000000000030000006000000000060000 00060000000200000002000080010000000000000000000000000000000000000 000000070C000000010000000E60700C00B000030000000FE010000000000E000 00000018000000800100008001000000010000000100004000000000000000000 0000000000000000000000000000078F80700001000000098FE00001C00000800 00F8070000000000001C00000000060000006000000040000000C000000080000 0002000000000000000000000000000000000000000000000006CF80700002000 000060E13F800300000000FC07000000000000800300000080010000001800000 03000000020000000400000001000000000000000000000000000000000000000 0000000060C000000040000000C001FC7F00000000F01F0000000000000070000 00000600000000004000000080000001000000030000000080000000000000000 00000000000000000000000000000060C000000080000000380000FFFFFFFFFF0 F00000000000000000E00000000180000000003000000060000000C0000000800 00000400000000000000000000000000000000000000000000FF60C0000000001 1000000000000000000000000000000000000C0010000000007000000C0000000 00010000000200000004000000020000000000000000000000000000000000000 00000000060C000000000090000000000000000000000000000000000003C0000 0000C00000000030000000C000000000010000000300000001000000000000000 000000000000000000000000000000060C0000000C00B00000000000000000000 0000000000000080030000000030000000000C00000020000000C000000080000 0008000000000C00100000000000000000000000000000000000060C000000000 0700000000000000000000000000000000007000000000000E000000000300000 018000000200000004000000760003F0000B80100000000000000000000000000 000000000060C0000000000000000000000000000000000000000000000E00000 0008001000000C000000000040000003F0000F83100E006100030000040020000 0000000000000000000000000000000060C000000000000000000000000000000 0000000000000E0010000000060000000003000F80100E30700003C0000C00900 800908004C00002002000000000000000000000000000000000000FCC30000000 000000000000000000000000000000000001C0000380000DC0100003F0C00C001 C0000700002600002005004008040042000010000000000000000000000000000 0000000000000C00000000000000000000000000000000000000000C00F0000C0 0100030E00002C0300B0003080040080230000180300200002000100000C00000 00000000000000000000000000000000000C00000000000000000000000000000 300000C001003E3800006001C0000B0000E300008C0008600400C001000084000 010800180000000020000000000000000000000000000000000000000C0000000 0000000000000000060000E00000000EE0012E00009C0038E00400C0300000020 00618000070000000430000084000400000000100000000000000000000000000 00000000000000C000000000000000800000001C0000E00100F0051EE01100808 300071C0400300C00800180010400002800008030000006200030000080000000 000000000000000000000000000000000000C000000000000000000100803F00C 0DF00000FE4011C10006000E0000300000C0300600060000300001E0000600800 0001100008000040000000000000000000000000000000000000000000C000000 00C0000E00F02007F18003C2000E0001E00030000180018C0000000C200001000 10800000000500001006008000080004000020000000000000000000000000000 000000000000000C000000070200000F0070000040000000000C0030000000000 00070000000030000000000C000000C0000000000100000006000000000000000 0000000000000000000000000000000000000C000000080470000C00100000000 000000003C000000000000E000000000000C00000000030000003000000080000 00000010000000000000000000000000000000000000000000000000000C00000 0000780000000000000000000000E0030000000000001C000000008003000000C 00000000008000000600000008000000000000000000000000000000000000000 0000000000000000C000000000E000000000000000000000001E0000000000008 00300000000600000000020000000000600000010000000600000000000000000 00000000000000000000000000000000000000C0000000001C000000000000000 00000F00100000000000060000000000018000000001800000000010000000C00 000010000000000000000000000000000000000000000000000000000000C0000 0000000000000000000000000800F000000000000001C00000000000700000000 06000000C00000000002000000080000000000000000000000000000000000000 00000000000000000C00000000000000000000000000000780000000000000080 0300000000C000000000800100000020000000000100000004000000000000000 000000000000000000000000000000000000000C0000000000000000000000000 00C007000000000000006000000000003000000000400000000018000000C0000 0000003000000000000000000000000000000000000000000000000000000C000 0000000000000000000000003E00000000000000001800000000000C000000003 00000000006000000200000008000070000380000F80100000000000000000000 000000000000000000C0000000000000000000000000F00100000000000000000 7000000000003000000000C00000000010000381800F80140E006000037000080 0100000000000000000000000000000000000000C000000000000000000000008 00F0000000000000000C00000000000C0000000000003FC0100E00700003F0400 C00130800900004C0000600200000000000000000000000000000000000000C00 0000000000000000000007C000000000000000000300000380000F00700003F80 00C00100300700002402002001084008000042000010020000000000000000000 0000000000000000000C0000000007E0000E00000C0070000380000E00000003F 0000C001008C0500002C6000B0000088040000A20100180104200000000100000 80000000000000000000000000000000000000000C0000000005800000007003C 380000E00000000700C02D0000600100630400002318008C00006604008041000 004000310000080000000040000000000000000000000000000000000000000C0 00000000270000C003C0031E0000B80000C00500B81300009C00C0180400C0200 60002008019000040300000038000080000400000000200000000000000000000 00000000000000000000C0000000C02000003C0238E01100804700003C0200761 00080830030060000300001800100400400002008008000600006000030000080 010000000000000000000000000000000000000000C0000000300000800381071 C0800704000800302C00D00006000008C0100000CC00060000030030000180400 6000100001000008000040000000000000000000000000000000000000000000C 00000000C0000600070000300000C000060000038030000180000430000000230 00100000880000000403001000088000000004000020000000000000000000000 000000000000000000000C000000000000000000F000000000000000000000700 00000000C000000000000C0000000006000000800000000006000000000000000 0000000000000000000000000000000000000000000C000000000000000E00000 0000000000000000E000000000000030000000000002000000000100000060000 00000010000000000000000000000000000000000000000000000000000000000 C0000000000000001E00000000000000000000180000000000000C00000000800 10000008000000000100000008000000000000000000000000000000000000000 0000000000000000000000C0000000000000C0010000000000000000000007000 00000000003000000006000000000600000000008000000400000000000000000 00000000000000000000000000000000000000000000C00000000000003000000 000000000000000E0000000000000E00000000000180000000010000000000600 0000300000000000000000000000000000000000000000000000000000000000F 0C00000000000000C000000000000000000001800000000000018000000000004 000000000C0000000001000000080000000000000000000000000000000000000 00000000000000000000098C10000000000000300000000000000000000060000 00000000060000000000030000000002000000800000000004000000000000000 00000000000000000000000000000000000000000000CFB0700000007C0000000 0000000000000080010000000000800100000000C000000000800100000060000 00000020000000000000000000000000000000000000000000000000000000000 0CFB070000E00A300000000000000000000060000000000000600000000000300 000000040000000001000000000010000C00100000E0000700000000000000000 000000000000000000000000C3000000000A0C000000000000000000001800000 00000001800000000000C00000000300000000008000E00C03E0000B80200C00D 00006E0000000000000000000000000000000000000000C300000000110200700 0000000000000000700000000000006000000000003000E00003F0000F80106C0 0D00205000004002000012000090000000000000000000000000000000000000F F80C1000000808001006E0000E007000000C000000000E00F80013F0000F8C100 C00D0000340000800101001200104800002004000011000088000000000000000 00000000000000000000000E0C000000040400000900000000700003F3000F801 00000E6000380000C02100000B00004B000040820000110008840000100000800 00000040000000000000000000000000000000000000030C00000004020000088 000080040000380C00C0010000091800240000201900800800804400002062008 00000040200001000008000000004000000000000000000000000000000000000 0018C00000002010000006000060040000260300300100C008040023000018050 04000006003000018100040000002010000080000400000000200000000000000 0000000000000000000000000CC00000001008000001000010000080E100000C0 10030000380000000040200200000900000000408002000008100000004000020 00000001000000000000000000000000000000000000000CC0000000080600800 00000080000603000000300000880004000000082010018000048000000020400 10008040000000020000100000800000000000000000000000000000000000000 000FCC300000008010040000000060000180C00C0000000066000300000804100 00040000260000000102000800602000000001000008000040000000000000000 000000000000000000000000000C0000000840000200000000100000402002000 00000118000800004020000002000011000080000100040010100000800000000 4000020000000000000000000000000000000000000000000C000000040000000 00000000000080010000000000000400000000001800000000800000000080000 00000080000000000000000000000000000000000000000000000000000000000 000000C0000000400000000000000000004000000000000000030000000000040 00000004000000000600000000004000000000000000000000000000000000000 0000000000000000000000000000C000000020000000000000000000200000000 00000800000000000000200000000200000000010000000000200000000000000 00000000000000000000000000000000000000000000000000C00000006000000 00000000000001800000000000040000000000000010000000018000000000800 00000001000000000000000000000000000000000000000000000000000000000 0000000C0000000F8000000000000000000040000000000002000000000008000 00000000040000000004000000800000000000000000000000000000000000000 00000000000000000000000000000C00000003C01000000000000000003000000 00000010000000000060000000000002000000000200000040000000000000000 000000000000000000000000000000000000000000000000000C0000000280200 00000000000080000000000000000C00000000001000000000000100000000010 00000400000000000000000000000000000000000000000000000000000000000 00000000C00000002800000000000000006000000000000000020000000000080 000000080000000008000000000200000000000180000E0000000070000000000 000000000000000000000000000000C0000000240000000700000000100000000 00000000100000000000400000000400000000040180000E01000000700003E00 00B80100C00D0000000000000000000000000000000000000000C000000014000 0E00A000038000800000000000080000000000300021C0000E02000800300402E 00005C0900E00A00004B000040020000120000000000000000000000000000000 000000000C0000000120000001200005E0006C00100000E0040700000C0050081 2B00005C1100E00500A0290000400900001200008800004004000002000000000 0000000000000000000000000000000C000000012000000010000500001F00200 80170020AE0000300580002800004009000009001044000020060000010000040 00020000000010000000000000000000000000000000000000000C00000000900 00000100008880004004000012001010010080084000440000200600800000080 40000200200800000000400002000000001000000000000000000000000000000 0000000000C000000009000080000000088000200000002100080800004000200 00200001002008000000402000010010080000000020000100000800000000000 00000000000000000000000000000000C00000800800008000000004400020000 00001000808000020002000010000080100400000040200001001004000000002 000010000080000000000000000000000000000000000000000000C0000080080 00040000000022000100000800000040400002000100001000088000020000002 01000088000020000000010000080000400000000000000000000000000000000 00000000000C00000400400004000000002100008000040000002020000100008 80000000840000200000010100008800002000000001000008000040000000000 000000000000000000000000000000000C0000040040000200000000110000400 00200000010100000800044000000042000010000081000000440000100000800 0000004000020000000000000000000000000000000000000000000C000002000 00000000000000080000000000008000000000000002000000004000000000800 00000004000000000000000000000000000000000000000000000000000000000 000000000000C0000020000000000000000004000000000000400000000000000 10000000020000000008000000000200000000000000000000000000000000000 0000000000000000000000000000000000C000002000000000000000000200000 00000004000000000000001000000002000000000400000000020000000000000 00000000000000000000000000000000000000000000000000000000C00000200 60000000000000002000000000000200000000000800000000000100000000040 00000000100000000000000000000000000000000000000000000000000000000 0000000000000C00000A01F000000000000000100000000000020000000000080 00000000001000000000200000000010000000000000000000000000000000000 00000000000000000000000000000000000C00000E02400000000000000010000 00000000100000000000400000000000080000000020000000000800000000000 000000000000000000000000000000000000000000000000000000000C0000020 04000000000000800000000000000008000000000040000000000008000000001 00000000008000000000000000000000000000000000000000000000000000000 00000000000000C00000200400000000000080000000000000000800000000002 0000000000004000000001000000000040000000000000000000C000060000000 000000000000000000000000000000000000C0000020040000300000004000000 00000000004000000000020000000000004000000000800000000060000300000 800100003F0000F80100000000000000000000000000000000000000F0C000002 0040000FC00008041000004000000000400000000081000E00000000700001800 08C00000801F0000FC0000E007008064000024030000000000000000000000000 000000000000098C1000020040000260100E02700001E0000600004000300003C 1000F80300C00F00007E0008F00300C0240000920100900C00000400002000000 000000000000000000000000000000000000CFB07002004000020000030290000 350000F80102C00F00006A10004C0600601200009300049804000006000010000 0800000000400002000000000000000000000000000000000000000000CFB0700 20040000200000002100804400002403022019000089080040000000020000100 00480000000060000100000800000000400002000000000000000000000000000 0000000000000000C300002004000020000000210000040000200002000100000 80800400000000200001000048000000006000010000080000000040000200000 00000000000000000000000000000000000080C10000200400002000000021000 00400002000020001000008080040000000030000100004800000000600001000 00800000000400002000000000000000000000000000000000000000FFE0C0000 02004000020000000210000040000200001000100000808004000000003000010 00048000000006000010000080000000040000200000000000000000000000000 00000000000000080C10000100400002000000011000004000020000100010000 08040040000000030000100002800000000600001000008000000004000020000 000000000000000000000000000000000000000C3000010040000200000001100 00040000200001000100000804004000000003000010000280000000050000100 000800000000400002000000000000000000000000000000000000000000CC300 00100400002000000011000004000020000100010000080400400000000300001 00002800000000500001000008000000004000020000000000000000000000000 00000000000000000CC3000010000000000000001000000000000000010000000 00004000000000001000000000000000000010000000000000000000000000000 0000000000000000000000000000000000000098C100001000000000000000100 00000000000000100000000000800000000000100000000000000000000000000 000000000000000000000000000000000000000000000000000000000000F0C00 00010000000000000000000000000000000010000000000080000000000010000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000C000001000000000000000000000000000000001000000 00000800000000000100000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000C00000100000000000000000 00000000000000010000000000080000000000010000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000C0 00001000000000000000000000000000000001000000000010000000000001000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000C00000100000000000000000000000000000000000000 00000100000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000C0000010000000000000000 00000000000000000000000000010000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000C 00000100000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000C0000010000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C000001000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 C0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000C000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000C00000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0C000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000C00000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000C0000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000}}{SEP_R 21 0} {COM_R 22 0{TEXT 1 309 "If we want to look at a graph of v(t) an d theta(t) for a particular solution, we can use rungekuttahf to \+ generate a list of points along the numerical solution. Here we \+ start at the initial condition \{t=0,v=1.2,theta=0\}, and generat e 500 steps with a stepsize of .05 (so our solution goes from t=0 to t=25)."}}{INP_R 23 0 "> "{TEXT 0 54 "MySol := rungekuttahf([v dot,thdot],[0,1.2,0],.05,500):"}}{COM_R 24 0{TEXT 1 180 "we can n ow use makelist to extract the data for (t,v) and (t, theta) from this, and use plot to make a plot of it. Here I add a title to \+ each plot, and adjust the range and domain"}}{INP_R 25 0 "> " {TEXT 0 91 "plot(makelist(MySol,1,2),t=0..25,v=0..1.5,title=`v(t) for R=0 starting at v=1.2, theta=0`);"}}{GRH_R 26 0{RASTER 603 280 1 76 0000000000000000000000000000000000000000000000300C800300 E0070000000000003000000000000000000000000600000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000009819C00000600C000F0030008031000000C00000000CF80030060 00C00000F00000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000008C19C00000600C80190030008001000 000C00000800F8C013003000C0080190000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000C3E633F0796 C300CC018F07C1EFB9B1D6EC0F3611800068C017C3B3C9F07C018000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000C3C63060CC7C3006C018981933DF983373606660180006C0011877 66C60CC0180000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000063C33060C60CF0C37F18181830C398B1 61006660CC1F06E00018636306CC7F18000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000033633030C6 0618066018700C9F61CC9831E0336006000338008C313FC307601800000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000033633030630618E66F0CC08C9961CCD830303360E60F031C008CB 10163E66F0C000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000001A33303063061806600CC6C69831CCD 830181B40030003060086B1813106600C00000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000E3318183 3030C03600666C6CC3066CC1C9819C00180610606C69899310360060000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000066318181E030C03C0033C8CDB60668C1B7033C00080617E06CC 180FE306C00300000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000060C000000000000000000000000 00180000000000000004000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000060600 0000000000000000000000600C000000000000000300000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000C03000000000000000000000000C00700000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000001800000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000180000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000003C00000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000003C0000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000018000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000180000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000018000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000001800000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000003C000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000003C00000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000180000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000001800000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000C0000020180000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000E000003018000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000F0000038FF0000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000D800003CFF000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000C00000361800000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000C000003318000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000C00080311800000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000C0008031180000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000C000807F3C00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000C00000303C0000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000C000073018000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000C0000730180000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000F807073018000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000001800 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000003C000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000003C00000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000180 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000001800000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000180000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000018 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000180000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000003C000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000003 C0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000018000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000001800000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 18000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000001800000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000003C0000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 03C00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000180000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000018000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000C00000 1E180000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000E000003318000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000F0008061FF00000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000D8008 061FF000000000000000000001F000000000000000000C0030000000000000000 00F8000000000000000000003E000000000000000000800F00000000000000000 00000000000000000C000006098010000000000000000C0600000000000000000 00300C0000000000000000000C03000000000000000080C100000000000000000 060300000000000000000000000000000000000C0000060180600000000000000 0030C00000000000000000000C30000000000000000000030C000000000000000 0600003000000000000000018C00000000000000000000000000000000000C000 00301808000000000000000008000100000000000000000240000000000000000 08000100000000000000000200004000000000000000004000100000000000000 000000000000000000C000001C181000000000000000000400020000000000000 00001800000000000000000400020000000000000000010000800000000000000 0002000200000000000000000000000000000000C00000063C100000000000000 00004000400000000000000000100010000000000000040004000000000000000 00100010000000000000000002000400000000000000000000000000000000C00 000033C2000000000000000000200080000000000000080000002000000000000 00200080000000000000000008002000000000000000000100080000000000000 0000000000000000000C000870118200000000000000000010008000000000000 00400000020000000000000010008000000000000000000400200000000000000 08000000800000000000000000000000000000000C00087011840000000000000 00800000100000000000000020000004000000000000000800000100000000000 000020040000000000000008000001000000000000000000000000000000000F8 07877F18800000000000000080000020000000000000002000000800000000000 00008000002000000000000000200800000000000000080000020000000000000 00000000000000000000000000001880000000000000004000002000000000000 00010000008000000000000000400000200000000000000010080000000000000 004000002000000000000000000000000000000000000000003C0001000000000 00020000040000000000000000800001000000000000000020000040000000000 00800000000100000000000020000040000000000000000000000000000000000 00000003C00020000000000002000008000000000000000080000200000000000 00000200000800000000000080000000020000000000002000008000000000000 00000000000000000000000000000180002000000000000100000800000000000 00000400002000000000000000010000080000000000004000000002000000000 00010000080000000000000000000000000000000000000000018000400000000 00001000000001000000000000040000400000000000000001000010000000000 00040000000040000000000001000000001000000000000000000000000000000 00000000180004000000000000080000000100000000000002000040000000000 00080000000100000000000002000000004000000000000080000000100000000 00000000000000000000000000000018000800000000000008000000020000000 00000020000800000000000008000000020000000000000200000000800000000 00000800000002000000000000000000000000000000000000003C00080000000 00000040000000200000000000001000080000000000000400000002000000000 00001000000010000000000000040000000400000000000000000000000000000 0000000003C001000000000000004000000040000000000000100000001000000 00004000000040000000000000100000001000000000000004000000040000000 00000000000000000000000000000001800100000000000000200000004000000 00008000000000010000000000200000008000000000000008000000200000000 00000020000000800000000000000000000000000000000000000180020000000 00000002000000080000000000800000000002000000000020000000800000000 00000080000002000000000000002000000080000000000000000000000000000 00000000001800200000000000000100000008000000000040000000000200000 00000100000008000000000000004000000200000000000000100000008000000 00000000000000000000000000000000180040000000000000010000001000000 00000400000000004000000000010000000000100000000000400000040000000 00000001000000080000000000000000000000000000000000000018004000000 00000800000000010000000000020000000000400000000000800000000010000 00000002000000400000000000800000000008000000000000000000000000000 000000000003C0080000000000080000000002000000000002000000000080000 00000008000000000200000000000200000080000000000080000000001000000 0000000000000000000000000000000003C008000000000004000000000200000 00000010000000000800000000000400000000020000000000010000008000000 00000400000000010000000000000000000000000000000000000001800000100 00000040000000004000000000001000000000100000000000040000000004000 00000000100000000010000000040000000002000000000000000000000000000 00000000000018000001000000002000000000400000000000080000000010000 00000000200000000040000000080000000000001000000002000000000200000 000000000000000000000000000000000C1800000200000000200000000080000 00000000800000000200000000000020000000008000000008000000000000100 0000002000000000400000000000000000000000000000000000000E180000020 00000001000000000800000000000040000000020000000000001000000000800 00000040000000000001000000001000000000400000000000000000000000000 000000000000FFF00000400000000100000000000010000000004000000004000 00000000010000000010000000004000000000000200000000100000000080000 0000000000000000000000000000000800DFF0000040000000008000000000001 00000000020000000040000000008000000000001000000000200000000000020 00000000800000000800000000000000000000000000000000000000C18000004 00000000080000000000010000000002000000004000000000800000000000100 00000002000000000000200000000080000000000010000000000000000000000 0000000000000C180000080000000008000000000002000000000100000000800 00000008000000000002000000000200000000000040000000008000000000001 00000000000000000000000000000000000C18000008000000000800000000000 20000000001000000008000000000400000000000200000000010000000000004 000000000400000000000100000000000000000000000000000000000C1800001 00000000008000000000004000000000100000000000100000040000000000040 00000000100000000000080000000004000000000002000000000000000000000 00000000000000C3C000010000000000400000000000400000080000000000000 01000000200000000000400000000008000000000008000000000200000000000 200000000000000000000000000000000000C3C00002000000000040000000000 08000000800000000000000200000020000000000040000000000800000000001 0000000000200000000000400000000000000000000000000000000000C180000 20000000000200000000000800000040000000000000020000001000000000004 00000000004000000000010000000000100000000000400000000000000000000 000000000000000C1800004000000000020000000000100000004000000000000 00400000010000000000080000000000400000000002000000000010000000000 0800000000000000000000000000000000807F180000400000000001000000000 01000000020000000000000040000000800000000008000000000020000000000 20000000800000000000000800000000000000000000000000000000000018000 04000000000010000000000100000002000000000000008000000080000000000 00010000000200000000004000000080000000000000100000000000000000000 000000000000000003C0000800000008000000000000020000000200000000000 00080000000400000000000001000000010000000000400000008000000000000 0100000000000000000000000000000000000003C000080000000800000000000 00200000002000000000000008000000040000000000000100000001000000000 04000000040000000000000100000000000000000000000000000000000001800 00000100008000000000000040000000200000000000001000000004000000000 00002000000010000000000800000004000000000000020000000000000000000 00000000000000000018000000010000400000000000004000000010000000000 00010000000020000000000000200008000000000000080000000200000000000 00200000000000000000000000000000000000001800000002000040000000000 00080000000100000000000001000000002000000000000040000800000000000 00000100002000000000000040000000000000000000000000000000000000180 00000020000200000000000008000000008000000000000100000000100000000 00000400004000000000000000010000100000000000004000000000000000000 00000000000000000003C00000004000020000000000000000100000800000000 00002000000001000000000000080000400000000000000002000010000000000 000800000000000000000000000000000000000003C0000000400001000000000 00000001000004000000000000200000800000000000000008000020000000000 00000020000080000000000008000000000000000000000000000000000000018 00000008000010000000000000000200000400000000000040000080000000000 00000100000200000000000000004000008000000000000000100000000000000 00000000000000000000180000000800000800000000000000020000020000000 00000400000800000000000000010000010000000000000000400000400000000 00000001000000000000000000000000000000000018000000100000080000000 00000000400000200000000000080000080000000000000002000001000000000 00000008000004000000000000000200000000000000000000000000000000001 80000001000000400000000000000040000010000000000008000004000000000 00000020000008000000000000001000000200000000000000040000000000000 00000000000000000000018000000200000020000000000000004008000000000 00000000010020000000000000004000000400000000000000100000010000000 00000000400000000000000000000000000000000003C00000040000002000000 00000000080080000000000000000002002000000000000000800000040000000 00000002000000100000000000000080040000000000000000000000000000000 3C000000400000010000000000000008004000000000000000000200100000000 00000008000000400000000000000200080000000000000000008002000000000 00000000000000000000001800000080000001000000000000001000400000000 00000000004001000000000000000000100040000000000000040008000000000 00000000100020000000000000000000000000000000180000008000800000000 00000000020002000000000000000000800080000000000000000020002000000 0000000080004000000000000000002000100000000000000000000000C000001 E1800000080004000000000000000002000100000000000000000080004000000 00000000000200010000000000000080002000000000000000002000080000000 000000000000000E0010033180000000001200000000000000000400008000000 00000000001000020000000000000000048000000000000000000001100000000 000000000400004000000000000000000000030038061FF000000000210000000 00000000008000040000000000000000200001000000000000000008400000000 00000000000021000000000000000008000020000000000000000000000300380 61FF0000000004080000000000000000000102000000000000000040800000000 00000000000102000000000000000000004080000000000000000000101000000 00000000000000001806806118000000001806000000000000000000860100000 00000000000806100000000000000000060180000000000000000001806000000 000000000000C6000000000000000000000000180600331800000000E00100000 000000000000078000000000000000000001E0000000000000000008007000000 000000000000E0010000000000000000007800000000000000000000000018060 01E18000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000180600331800000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000180680613C0000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000003003 80613C00000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000030038761180000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000E001073318000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000C00 0071E180000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000C3000018000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C300003C00000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 6600003C000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000006600001800000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000003C0000180000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 03C00001800000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000180000180000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000001800003C000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000003C0000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000018000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000001800000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000018000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000001800000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000180000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000003C00000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000003C0000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000018000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000180000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000C000001E18000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000E00100331800000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000030038021FF000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000030038001FF00000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000018068001180000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000001806801D1800000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000018068033180000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000001806806118000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000180680613C0000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000300380613C000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000300387611800000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000E001073318000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000C000071E1800000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000180000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000003C00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000003C0000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000018000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000180000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000018000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000001800 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000003C000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000003C00000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000180 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000001800000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000180000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000018 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000003C0000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000003C000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000001 80000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000018000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000001800000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000C0000020 18000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000E00100301800000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000030030038FF0000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000003003003 CFF00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000018060036180000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000001806003318000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000180680 31180000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000001806803118000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000001806807F3C00000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000030030 0303C000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000300307301800000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000E0010730180000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000C000 07301800000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000180000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000003C000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000003C0000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000018000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000001800000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000018000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000001800000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000003C0000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000003C00000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000180000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000018000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000180000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000018000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000003C00000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000003C000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000001800000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000180000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000001800000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000C000001E180000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000E001003318000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00030038061FF0000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000030038061FF000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000180600601800000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00001806006018000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000180600301800000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000001806001C180000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000180600063C00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000300300033C0000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000003003870118000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000E0018701180000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000C000877F18000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000001800000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000003C000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000003C00000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000180000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000001800000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000180000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000018000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000003C0000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000003C000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000001800 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000018000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000001800000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000180 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000003C00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000003C0000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000018 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000180000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000018000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000001 80000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000018000000000000000000000018000000000000000000 00003000000000000000000000003000000000000000000000006000000000000 0000000000060000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F000000000000000000000000000000 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F00000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000C000600000000000000 000000FF0000000000000000000080010600000000000000000080C13F0000000 0000000000080070C00000000000000000080877F000000000000000000000000 001E000F000000000000000000000300000000000000000000C0010F000000000 000000000C0C100000000000000000000C00C1E000000000000000000C08C0100 00000000000000000000000033801900000000000000000000030000000000000 0000000E08119000000001800000000E0C1000000000000000000006018330000 00000000000000609801000000000000000000000000003380190000000000000 00000000300000000000000000000B08119000000001800000000B0C100000000 00000000000060183300000000000000000060980100000000000000000000000 08061C03000000000000000000000030000000000000000000080C13000000000 180000000080C1000000000000000000000098610000000000000000000098010 000000000000000000000008061C030000000000000000000003B000000000000 0000000080C130000000007E0000000080C10E000000000000000000009861000 00000000000000000981D0000000000000000000000008061C030000000000000 00000000670000000000000000000080C13000000000180000000080C11900000 0000000000000008C61000000000000000000008C330000000000000000000000 008061C03000000000000000000000C00000000000000000000080C1300000000 01800000000800130000000000000000000008761000000000000000000000760 0000000000000000000000008061C03000000000000000000000C000000000000 00000000080C13000000000180000000080013000000000000000000080816100 00000000000000008001600000000000000000000000000033801900000000000 000000000C0000000000000000000008081190000000018000000008001300000 00000000000000C00033000000000000000000C00060000000000000000000000 0000033801900000000000000000000C300000000000000000000808119000000 00180000000080C13000000000000000000060003300000000000000000060806 1000000000000000000000000001E000F00000000000000000000660000000000 000000000080010F00000000980100000080811900000000000000000060001E0 00000000000000000600033000000000000000000000000000C00060000000000 00000000003C00000000000000000000F00F0600000000F000000000F00F0F000 000000000000000E01F0C000000000000000000E01F1E00000000000000}} {INP_R 27 0 "> "{TEXT 0 104 "plot(makelist(MySol,1,3),t=0..25, th eta=-0.5..0.5,\012title=`theta(t) for R=0 starting at v=1.2, thet a=0`);"}}{GRH_R 28 0{RASTER 592 274 1 74 000000000000000000000000 000000000000000030000000300C800300E007000000000000300000000000000 00000000006000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000080310060009819C00000600C000F00300 08031000000C00000000CF8003006000C00000F00000000000000000000000000 0000000000000000000000000000000000000000000000000080190060008C19C 00000600C80190030008001000000C00000800F8C013003000C00801900000000 00000000000000000000000000000000000000000000000000000000000000000 000E0DBE1F93CE633F0796C300CC018F07C1EFB9B1D6EC0F3611800068C017C3B 3C9F07C0180000000000000000000000000000000000000000000000000000000 000000000000000000000C0B8333366C63060CC7C3006C018981933DF98337360 6660180006C001187766C60CC0180000000000000000000000000000000000000 000000000000000000000000000000000000000C0181B3360C33060C60CF0C37F 18181830C398B161006660CC1F06E00018636306CC7F180000000000000000000 000000000000000000000000000000000000000000000000000000000608CF919 3E633030C60618066018700C9F61CC9831E0336006000338008C313FC30760180 00000000000000000000000000000000000000000000000000000000000000000 0000000000608C0D1833633030630618E66F0CC08C9961CCD830303360E60F031 C008CB10163E66F0C000000000000000000000000000000000000000000000000 0000000000000000000000000000308C0D8C3133303063061806600CC6C69831C CD830181B40030003060086B1813106600C000000000000000000000000000000 000000000000000000000000000000000000000000000030C6CC8C19331818330 30C03600666C6CC3066CC1C9819C00180610606C6989931036006000000000000 00000000000000000000000000000000000000000000000000000000000000006 0C67818376318181E030C03C0033C8CDB60668C1B7033C00080617E06CC180FE3 06C00300000000000000000000000000000000000000000000000000000000000 000000000000000000000000000060C0000000000000000000000000018000000 00000000040000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000006060000000000000000 00000000600C00000000000000030000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000C 03000000000000000000000000C00700000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000C000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000C000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000C000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000C000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000001E00000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000001E00000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000C00000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 C0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000C0000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000C0000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000C0000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000C000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000C000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000001E000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000001E00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000C00000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000C00000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000C0000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000C0000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000C0000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000600000100C0000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0F00000180C000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000009801009C3F000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000009801009E3F000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000C03001B0C 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000C0380190C00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000C03C0180C00000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000C03C0180C00000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000C0 3C03F0C0000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000980100180C0000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000988103180C0000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000F08003180C0000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000608003181E000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000001E000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000C000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00C00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000C00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000C00000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000C00000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000C0000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000C0000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000C0000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000001E0 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000001E000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000C000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000C000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000C00000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000C00000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000C00000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000C00000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000C00000F000000000000000000E0010000000000000000001E0000 00000000000000E0010000000000000000003C000000000000000000C00300000 000000000000000000000000000000C0000110000000000000000001002000000 00000000000021000000000000000000100200000000000000000022000000000 000000000200400000000000000000000000000000000001E0080200000000000 00000000080400000000000000008040000000000000000000080400000000000 00000004100000000000000000010080000000000000000000000000000000000 1E004040000000000000000000040400000000000000004080000000000000000 00008080000000000000000808000000000000000000008100000000000000000 0000000000000000000C002040000000000000000000020400000000000000002 08000000000000000000004080000000000000000408000000000000000000004 1000000000000000000000000000000000000C002080000000000000000000020 80000000000000000200001000000000000000004100000000000000000400001 0000000000000000042000000000000000000000000000000000000C001080000 00000000000000001080000000000000000100001000000000000000002100000 00000000000020000100000000000000000220000000000000000000000000000 00000000C00100001000000000000000001100000000000000000100002000000 00000000000220000000000000000020000200000000000000000240000000000 00000000000001800000000000C00080001000000000000008000100000000000 00000008000200000000000000000120000000000000000010000200000000000 00000014000000000000000000000001800000000000C00080001000000000000 00800010000000000000000008000200000000000000000120000000000000000 01000020000000000000000014000000000000000000000181800000600000C00 04000200000000000000400020000000000000000004000400000000000000800 04000000000000000001000040000000000000000018000000000000000000000 181800000600000C0004000200000000000000400020000000000000000004000 40000000000000080004000000000000000000800040000000000000080008000 000000000000000000181800000600001E0004000200000000000000400020000 00000000000000400040000000000000080004000000000000000000800040000 0000000000800080000000000000000000007ED881871FF8001E0002000400000 00000000020004000000000000000000400080000000000000040008000000000 0000000004000800000000000000400080000000000000000000001838C30C068 C010C000200040000000000000020004000000000000000000400080000000000 00004000800000000000000000040008000000000000004000800000000000000 0000000181866180680010C000100040000000000000020004000000000000000 00040008000000000000004000800000000000000000040008000000000000004 00080000000000000000000001818E61F06FC010C000100080000000000000010 00800000000000000000020010000000000000002000000100000000000000020 0100000000000000020000001000000000000000000181866000686010C000100 08000000000000001000800000000000000000020010000000000000002000000 10000000000000002001000000000000000200000010000000000000000001818 66000686010C80000008000000000000001000800000000000000000020010000 00000000000200000010000000000000002001000000000000000200000010000 000000000000009819C6186686010C80000008000000000000000800800000000 00000000001001000000000000000100000010000000000000001001000000000 00000020000001000000000000000000F018866F3C7C0F0C80000010000000000 00000080000010000000000000001001000000000000000100000020000000000 00000100200000000000000020000002000000000000000000000000F00080190 C8000001000000000000000080000010000000000000001001000000000000000 10000002000000000000000100200000000000000020000002000000000000000 0000000009801C0B03F4000001000000000000000040000010000000000008000 00100000000000000008000002000000000000800000200000000000000010000 0020000000000000000000000009801C0B03F4000001000000000000000040000 01000000000000800000100000000000000008000002000000000000800000200 0000000000000100000020000000000000000000000000C0300300C4000002000 00000000000004000002000000000000800000200000000000000008000004000 0000000008000004000000000000000100000040000000000000000000000000C 0300300C200000200000000000000002000002000000000000400000200000000 00000000800000400000000000080000040000000000000001000000400000000 00000000000000000C0300180C200000200000000000000002000002000000000 00040000020000000000000000400000400000000000040000040000000000000 00080000040000000000000000000000000C03000E0C200000200000000000000 00200000200000000000040000020000000000000000400000400000000000040 00004000000000000000080000040000000000000000000000000C0300030C200 00020000000000000000200000200000000000040000020000000000000000400 00040000000000004000008000000000000000080000080000000000000000000 00000980180010C10000040000000000000000100000400000000000020000040 00000000000000020000080000000000002000008000000000000000040000080 000000000000000000000009881C3000C10000040000000000000000100000400 00000000002000004000000000000000020000080000000000002000008000000 00000000004000008000000000000000000000000F080C3000C10000040000000 00000000010000040000000000002000004000000000000000020000080000000 000002000008000000000000000040000080000000000000000000000006080C3 3F1E1000004000000000000000010000040000000000002000004000000000000 00002000008000000000000200000800000000000000004000008000000000000 000000000000000000001E0800004000000000000000010000040000000000001 00000400000000000000001000010000000000000100000000100000000000002 000010000000000000000000000000000000000C0800008000000000000000010 00008000000000000100000800000000000000001000010000000000000100000 000100000000000002000010000000000000000000000000000000000C0800008 00000000000000001000008000000000000100000800000000000000001000010 00000000000010000000010000000000000200001000000000000000000000000 0000000000C080000800000000000000001000008000000000000100000800000 00000000000100001000000000000010000000010000000000000200001000000 0000000000000000000000000000C040000800000000000008000000008000000 00000008000080000000000000800000001000000000000008000000010000000 0000001000010000000000000000000000000000000000C040000800000000000 00800000000800000000000008000080000000000000800000002000000000000 0080000000200000000000001000020000000000000000000000000000000000C 04000000010000000000800000001000000000000008000000010000000000800 00000200000000000000800000002000000000000010000200000000000000000 00000000000000000C04000000010000000000800000001000000000000008000 00001000000000080000000200000000000000800000002000000000000010000 20000000000000000000000000000000000C02000000010000000000400000001 00000000000000400000001000000000040000000200000000000000800000002 00000000008000000020000000000000000000000000000000001E02000000010 00000000040000000100000000000000400000001000000000040000000200000 00000000080000000200000000008000000020000000000000000000000000000 000001E0200000001000000000040000000100000000000000400000001000000 00004000000020000000000000080000000200000000008000000020000000000 000000000000000000000000C0200000002000000000040000000200000000000 00040000000200000000004000000020000000000000080000000400000000008 000000040000000000000000000000000000000000C0100000002000000000020 00000020000000000000020000000200000000002000000020000000000000040 000000400000000004000000040000000000000000000000000000000000C0100 00000200000000002000000020000000000000020000000200000000002000000 02000000000000004000000040000000000400000004000000000000000000000 0000000000000C010000000200000000002000000020000000000000020000000 20000000000200000002000000000000004000000040000000000400000004000 0000000000000000000000000000000C010000000200000000002000000020000 00000000002000000020000000000200000002000000000000004000000040000 0000004000000040000000000000000000000000000000008C000000000400000 00000100000004000000000000001000000040000000000100000004000000000 00000200000008000000000040000000800000000000000000000000000000000 08C00000000040000000000100000004000000000000001000000040000000000 10000000400000000000000200000008000000000020000000800000000000000 00000000000000000008C00000000040000000000100000004000000000000001 00000004000000000010000000400000000000000200000008000000000020000 00080000000000000000000000000000000009E00000000040000000000100000 00400000000000000100000004000000000010000000400000000000000200000 00800000000002000000080000000000000000000000000000000009E00000000 04000000000010000000400000000000000100000004000000000010000000400 00000000000020000000800000000002000000080000000000000000000000000 000000004C0000000004000000000008000000400000000000800000000004000 00000000800000040000000000000010000000800000000001000000080000000 000000000000000000000000004C0000000004000000000008000000800000000 00080000000000800000000000800000080000000000000010000001000000000 001000000000010000000000000000000000000000004C0000000004000000000 00800000080000000000080000000000800000000000800000080000000000000 010000001000000000001000000000010000000000000000000000000000004C0 00000000400000000000800000080000000000080000000000800000000000800 00008000000000000001000000100000000000100000000001000000000000000 0000000000000004C000000000400000000000400000080000000000040000000 00080000000000040000008000000000008000000000100000000000080000000 0010000000000000000000000000000004C000000000400000000000400000080 00000000004000000000080000000000040000008000000000008000000000100 0000000000800000000010000000000000000000000000000004C000000000400 00000000040000008000000000004000000000080000000000040000008000000 00000800000000010000000000008000000000200000000000000000000000000 00004C00000000080000000000040000000001000000004000000000100000000 00004000000000100000000800000000020000000000008000000000200000000 00000000000000000000003E00000000080000000000020000000001000000004 00000000010000000000004000000000100000000800000000020000000000008 00000000020000000000000000000000000000003E00000000080000000000020 00000000100000000200000000010000000000002000000000100000000400000 00002000000000000400000000020000000000000000000000000000002C00000 00008000000000002000000000100000000200000000010000000000002000000 00010000000040000000002000000000000400000000020000000000000000000 000000000002C0000000008000000000002000000000100000000200000000010 00000000000200000000010000000040000000002000000000000400000000020 000000000000000000000000000002C0000000008000000000002000000000100 00000020000000001000000000000200000000010000000040000000002000000 000000400000000040000000000000000000000000000001C0000000010000000 00000100000000020000000010000000002000000000000200000000020000000 02000000000400000000000020000000004000000000000000000000000000000 1C000000001000000000000100000000020000000010000000002000000000000 20000000002000000002000000000400000000000020000000004000000000000 0000000000000000001C000000001000000000000100000000020000000010000 00000200000000000020000000002000000002000000000400000000000020000 0000040000000000000000000000000000001C000000001000000000000100000 00002000000001000000000200000000000020000000002000000002000000000 4000000000000200000000040000000000000000000000000000000C000000001 00000000000010300000002000000001000800100200000000000020000C00002 00000000200000000060000000000002000000000418000000000000000000000 0000080FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF1F000 0000000000000000000000080FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFF1F00000000000000000000000000000C00000000200000000080 000300000004000000000800800100400000000000010000C0000400000000100 0000000E000000000000100000000081800000000000000000000000000060C00 00000020000000008000000000000400000000080000000040000000000001000 00000040000000010000000008000000000000100000000080000000000000000 0000000000000F0C0000000020000000004000000000000400000000040000000 04000000000800000000000040000000008000000008000000000800000000000 080000000000000000000000000080190C03000000200000000040E01F0000000 40000000004000C300040000000008000000006FF04000000000800000080870C 000000800000000000E8E11F000000000000000000000080198C0700000020000 00000406000000000040000000004000E78004000000000800000000703040000 000008000000C08C1E0000008000000000003863000000000000000000000000C 030CC0C0000004000000000406000000000080000000004000FCC008000000000 80000080070308000000000800000060983300000080000000000018660000000 00000000000000000C030CC0C0000004000000000406000000000080000000004 800DCC008000000000800000C0060308000000000800000060983300000080000 00000001866000000000000000000000000C0306C180000004000000000206000 000000080000000002000C8601800000000040000000060308000000000400000 00098610000004000000000001066000000000000000000000000C0307E180000 004000000000206007000000080000000002000C8601800000000040000000063 B0800000000040000000098610000004000000000001066070000000000000000 000000C0307E18000000400000000020E00C000000080000000002000C8601800 0000000400000000667080000000004000000008C6100000040000000000010E3 0C000000000000000000000080196C18000000400000000020001800000008000 0000002000C860180000000004000000006C00800000000040000000087610000 00400000000000D00118000000000000000000000080196C18000000800000000 0100018000000100000000001000C860100010000002000000006C01000000000 020000008081610000002000000000006000180000000000000000000000000FC C0C0000008000000000100018000000100000000001000CCC0000010000002000 000006C0100000000002000000C00033000000200000000000300018000000000 00000000000000006CC0C0000008000000000106018000000100000000001000C CC00000100C0002000000006C3100000000002000000600033000000200000000 000386018000000000000000000000000008C07000000800000000010C00C0000 00100000000001000C7800000100C000200000000666100000000002000000600 01F00000020000000000038C00C000000000000000000000000000C0300000080 00000000108007000000100000000001807F3000000100C000200000C03F3C100 000000002000000E01F0D000000200000000000F8870700000000000000000000 0000000C00000000800000000008000000000010000000000100000000000100F 00310000000000010000000000100000000000100000010000000000020000000 0000000000000000000000000C000000000001000000080000000000100000000 00100000000000200C00010000000000020000000000100000000000200000010 0000000000400000000000000000000000000000001E000000000001000000080 00000000010000000000100000000000200C00010000000000020000000000100 0000000002000000100000000000400000000000000000000000000000001E000 00000000100000008000000000010000000000100000000000200C00010000000 00002000000000010000000000020000001000000000004000000000000000000 00000000000000C00000000000100000004000000000010000000800000000000 000200C0000800000000002000000080000000000000020000000800000000004 00000000000000000000000000000000C00000000000100000004000000000010 000000800000000000000200C0000800000000002000000080000000000000020 00000080000000000400000000000000000000000000000000C00000000000100 000004000000000010000000800000000000000200C00C0800000000002000000 08000000000000004000000080000000000800000000000000000000000000000 000C0000000000020000000400000000002000000080000000000000040080070 80000000000400000008000000000000004000000080000000000800000000000 000000000000000000000C0000000000020000000400000000002000000080000 00000000004000000080000000000400000008000000000000004000000080000 000000800000000000000000000000000000000C0000000000020000000200000 00000200000004000000000000004000000040000000000400000004000000000 000004000000080000000000800000000000000000000000000000000C0000000 00002000000020000000000200000004000000000000004000000040000000000 40000000400000000000000400000008000000000080000000000000000000000 0000000000C000000000002000000020000000000200000004000000000000004 00000004000000000040000000400000000000000400000008000000000080000 0000000000000000000000000001E000000000004000000020000000000400000 00400000000000000800000004000000000080000000400000000000000800000 0080000000000000100000000000000000000000000001E000000000004000000 01000000000040000000200000000000000800000002000000000080000000200 0000000000008000000040000000000000100000000000000000000000000000C 00000000000400000001000000000040000000200000000000000800000002000 00000008000000020000000000000080000000400000000000001000000000000 00000000000000000C00000000000400000001000000000040000000200000000 00000080000000200000000008000000020000000000000080000000400000000 00000100000000000000000000000000000C00000000000400000001000000000 04000000020000000000000080000000200000000008000000020000000000000 08000000040000000000000100000000000000000000000000000C00000000000 40000800000000000004000000010000000000000080000000100000000008000 00001000000000000008000000020000000000000100000000000000000000000 000000C0000000000080000800000000000008000000010000000000000100000 00010000000000000100001000000000000010000000020000000000000200000 000000000000000000000000C0000000000080000800000000000008000000010 00000000000010000000010000000000000100001000000000000010000000020 000000000000200000000000000000000000000000C0000000000080000800000 00000000800000001000000000000010000000010000000000000100001000000 000000010000000020000000000000200000000000000000000000000000C0000 00000008000040000000000000800000000800000000000010000080000000000 00000010000080000000000001000000001000000000000020000000000000000 0000000000001E000000000008000040000000000000800000000800000000000 01000008000000000000000010000080000000000001000000001000000000000 0200000000000000000000000000001E000000000010000040000000000000000 10000080000000000002000008000000000000000020000080000000000002000 0000010000000000000200000000000000000000000000000C000000000010000 04000000000000000010000080000000000002000008000000000000000020000 08000000000000200000000100000000000002000000000000000000000000000 00C00000000001000004000000000000000010000040000000000002000004000 00000000000002000004000000000000200000800000000000000002000000000 00000000000000000000C00000000001000004000000000000000010000040000 00000000200000400000000000000002000004000000000000200000800000000 00000000200000000000000000000000000000C00000000001000004000000000 00000001000004000000000000200000400000000000000002000004000000000 00020000080000000000000000400000000000000000000000000000C00000000 00200000400000000000000002000004000000000000400000400000000000000 00400000400000000000040000080000000000000000400000000000000000000 000000000C0000000000200000200000000000000002000002000000000000400 00020000000000000000400000200000000000040000040000000000000000400 0000000000000000006000000F0C0000000000200000200000000000000002000 00200000000000040000020000000000000000400000200000000000040000040 000000000000000400000000000000000000F00080190C0000000000200000200 00000000000000200000200000000000040000020000000000000000400000200 0000000000400000400000000000000004000000000000000000009801C0B03F0 00000000040000010000000000000000400000100000000000040000010000000 00000000080000020000000000008000002000000000000000080000000000000 00000009801C0B03F000000000040000010000000000000000400000100000000 00004000001000000000000000080000020000000000008000002000000000000 00008000000000000000000000C0300300C000000000040000010000000000000 00040000010000000000004000001000000000000000080000020000000000008 00000200000000000000008000000000000000000000C0300300C000000000040 00001000000000000000040000010000000000004000001000000000000000080 00002000000000000800000200000000000000008000000000000000000FF0C03 00180C00000000008000000800000000000000080080000000000000008000000 80000000000000010000001000000000000000100100000000000000010000000 000000000000000C03000E0C00000000008000000800000000000000080080000 00000000000800000080000000000000010000001000000000000000100100000 000000000010000000000000000000000C0300030C00000000008000000800000 00000000008008000000000000000800000080000000000000010000001000000 00000000010010000000000000001000000000000000000000980180010C00000 00000800000040000000000000008004000000000000000800000040000000000 00001000800000000000000000010008000000000000000000000000000000000 0009881C3000C0000000000000100040000000000000010004000000000000000 00010004000000000000002000800000000000000000020008000000000000000 000000000000000000000F080C3000C0000000000000100040000000000000010 00400000000000000000010004000000000000002000800000000000000000020 0080000000000000000000000000000000000006080C33F1E0000000000000100 02000000000000001000200000000000000000010002000000000000002000400 00000000000000002000400000000000000000000000000000000000000000000 1E000000000000010002000000000000001000200000000000000000010002000 00000000000400040000000000000000004000400000000000000000000000000 0000000000000000000C000000000000020002000000000000002000200000000 00000000002000200000000000000400040000000000000000004000400000000 0000000000000000000000000000000000000C000000000000020001000000000 00000200010000000000000000002000100000000000000400020000000000000 0000040002000000000000000000000000000000000000000000000C000000000 00002000100000000000000200010000000000000000002000100000000000000 40002000000000000000000800020000000000000000000000000000000000000 00000000C00000000000004800000000000000000400008000000000000000004 00010000000000000080001000000000000000000800010000000000000000000 00000000000000000000000000C00000000000004800000000000000000400008 00000000000000000400010000000000000080001000000000000000000800010 00000000000000000000000000000000000000000000C00000000000008800000 00000000000080000800000000000000000800010000000000000080001000000 00000000000100001000000000000000000000000000000000000000000000C00 00000000000840000000000000000080000400000000000000000880000000000 00000008000080000000000000000108000000000000000000000000000000000 000000000000000C0000000000001040000000000000000000010400000000000 00000108000000000000000000001080000000000000000208000000000000000 000000000000000000000000000000001E0000000000001020000000000000000 00001020000000000000000104000000000000000000001040000000000000000 204000000000000000000000000000000000000000000000001E0000000000001 01000000000000000000002010000000000000000202000000000000000000002 02000000000000000040200000000000000000000000000000000000000000000 0000C000000000000101000000000000000000002010000000000000000202000 00000000000000000202000000000000000040200000000000000000000000000 0000000000000000000000C000000000000200C000000000000000000C4000000 00000000000040180000000000000000008401000000000000000080100000000 0000000000000000000000000000000000000000C000000000000C00300000000 00000000007800000000000000000080070000000000000000007800000000000 0000000000F00000000000000000000000000000000000000000000000C000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000C00000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000C00000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000C00000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 C0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000001E0000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000001E0000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000C0000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000C000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000C000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000C000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000C00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000C00000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000C00000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 001E0000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000001E0000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000C0000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000C0000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000C000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000C000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000C000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000C 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000600000100C00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000F00000180C00000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000009801009C3F00000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000980 1009E3F0000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000C03001B0C0000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000C0380190C0000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000FF0C03C0180C0000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000C03C0180C000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000C03C03F0C000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000980100180C000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000009881031 80C00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000F08003181E00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000608003181E00000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000C00000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000C0000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000C0000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000C0000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000C0 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000C000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000C000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000C000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00001E00000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000001E00000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000C00000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000C00000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000C0000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000C0000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000}}{COM_R 29 0{TEXT 1 207 "With a little thought, we can see that this initial condition represent s a glider that is flying along a wavy path (because the velocity is always positive, and the angle varies between -.3 and +.3 rad ians)."}}{SEP_R 30 0}{COM_R 31 0{TEXT 1 666 "However, we might wa nt to see the flight of the glider in space coordinates (ie, x vs y). To accomplish this, we need a way to convert a list of poin ts of the form [t,v,theta] to [t,x,y]. Since at each time t,\012 the glider will move from (x,y) to (approximately) \015 \+ (x+(delta t)*v*cos(theta), y+(delta t)*v*sin(theta) )\015we ca n do this readily.\015\015Below is a maple procedure which does t his for us. We assume that the glider starts at (0,0). We ret urn the path in [t,x,y] coordinates rather than in just [x,y] so \+ that if you wanted to make a plot of, say, x(t), it would be poss ible. As before, makelist can be used to extract whatever data i s wanted. "}}{INP_R 32 0 "> "{TEXT 0 524 "VThetaToXY := proc(Sol )\012 local currX, currY, currT, deltaT, low, hi, SolXY, i;\012 \012 currX := 0.0; currY := 0.0; currT := Sol[1][1];\012 \+ low := op(1,op(2,eval(Sol))); \012 hi := op(2,op(2,eval(Sol))) ;\012 SolXY := array(low..hi-1);\012\012 for i from low to (h i-1) do\012 deltaT := Sol[i+1][1] - currT;\012 curr T := Sol[i+1][1];\012 currX := currX + deltaT*Sol[i][2]*co s(Sol[i][3]);\012 currY := currY + deltaT*Sol[i][2]*sin(So l[i][3]);\012 SolXY[i] := [currT,currX,currY];\012 od;\01 2 RETURN(op(SolXY));\012end:"}}{SEP_R 33 0}{COM_R 34 0{TEXT 1 90 "Just to see how that works out, we produce a plot of the path of the glider computed above"}}{INP_R 35 0 "> "{TEXT 0 108 "plot (makelist(VThetaToXY (MySol),2,3),axes=FRAME,\012title=`Path of a glider with R=0, inital v=1.2, theta=0`);"}}{GRH_R 36 0{RASTER 539 157 1 68 0000000000000000000000000000E00F003000001C0000801930 00000060C000F8010000C000180030000000000000C0000000000000000000000 00000000000000000000000000000000000000000000000601880310000060000 80193000000060C6001803C003C000980130000080011F00C600800100E001000 00000000000000000000000000000000000000000000000000000601880190000 060000C000180000000066001803600600008001180000F081310066008001003 003000000000000000000000000000000000000000000000000000000003098E7 DB019E0F3CC0CD8C1B8F0D33B36F070C0330066076ECF3180C03C08031806F87E 7F300180300000000000000000000000000000000000000000000000000000000 30CCCCB80333036660CECC9C990F3333E30E8C01300660CECC98190C03C000380 0E3CECC9801180300000000000000000000000000000000000000000000000000 000000F007CC1883310360306C6CD898013333630CFCF01F0660C6CC800D8CF9C 3001C00636CCC80F90F0300000000000000000000000000000000000000000000 00000000000018C0678C81B1013E306666CCCF00BB99310686011806306366F80 CCC006000078031E667F8000C0300000000000000000000000000000000000000 0000000000000000001860668CC19801331866366CC000AB99310686F91B03306 366CC0CCCFC61800380313660CCFC8D0100000000000000000000000000000000 0000000000000000000000001830368CC19881311866366CC000EED8300686011 803306336C60C680060C000C0303630C6008C0100000000000000000000000000 0000000000000000000000000000000C3033C6C0CC801998333367660066CC180 3C30098199831336606380030CCC0C01833336600CC0000000000000000000000 0000000000000000000000000000000000000CE066C680C700377033E3C663006 68C1903C300F018983163DC06180030CCCF8019E361DC00780000000000000000 00000000000000000000000000300000000000000000000000000000000003000 00000000000000000001000000000000000000080000000000000000000000000 00000000000000000000000000000000300000000000000000000000000000008 C0100000000000000000000000C00000000000000000060000000000000000000 00000000000000000000000000000000000000300000000000000000000000000 00000F80000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000300803000000000001E0000000 000000000780000000000000000E0010000000000000000070000000000000000 1C0000000000000000F00000000000000000000000800700C0300000000000110 00000000000000084000000000000000020020000000000000080080000000000 000000220000000000000000880000000000000000000000C00C00E0FC0100000 00021000000000000000084000000000000000010020000000000000040100000 000000000000410000000000000000080100000000000000000000C00C00F0FC0 10000000041000000000000000004010000000000000010040000000000000040 10000000000000000041000000000000000008020000000000000000000060180 0D830000000008040000000000000000002020000000000000008080000000000 00004020000000000000000081000000000000000004020000000000000000000 0601800CC30000000004040000000000000000001020000000000000008080000 00000000002020000000000000008080000000000000000002020000000000000 0000000601800C630000000004080000000000000000001020000000000000008 08000000000000002040000000000000008000010000000000000002040000000 0000000000000601800C630000000004080000000000000000001020000000000 00000408000000000000001040000000000000004000010000000000000002040 0000000000000000000601800FE31000000004000010000000000000001040000 00000000000410000000000000001040000000000000004000020000000000000 0020800000000000000000000C00C00C070000000002000010000000000008000 04000000000000000210000000000000001040000000000000004000020000000 0000000010800000000000000000000C00C1CC070000000002000010000000000 00800004000000000000000220000000000000001080000000000000004000020 000000000000001080000000000000000000080071CC030000000001000010000 00000000400008000000000000000220000000000000000880000000000000002 000020000000000008000080000000000000000000000031CC030000000001000 01000000000000400008000000000000000220000000000000000880000000000 00000200002000000000000800008000000000000000000000000000030000000 00100002000000000000400008000000000000000240000000000000000800010 00000000000200004000000000000800010000000000000000000000000000030 00000000080002000000000000400008000000000000000140000000000000000 40001000000000000100004000000000000800010000000000000000000000000 00007000000000080002000000000000400008000000000000000140000000000 00000040001000000000000100004000000000000800000000000000000000000 00000000007000000000080004000000000000200010000000000000800040000 00000000000020001000000000000100008000000000000400000000000000000 00000000000000003000000000080004000000000000200010000000000000800 04000000000000000020001000000000000100008000000000000400000000000 00000000000000000000003000000000080004000000000000200010000000000 00080004000000000000000020001000000000000100008000000000000400000 00000000000000000000000000003000000000040008000000000000100020000 00000000040008000000000000000020002000000000000100008000000000000 40000000000000000000000000000000003000000000040008000000000000100 02000000000000040008000000000000000020002000000000000080008000000 00000020000000000000000000000000000000007000000000040008000000000 00010002000000000000040008000000000000000020002000000000000080008 00000000000020000000000000000000000000000000007000000000040008000 00000000010002000000000000040000001000000000000020004000000000000 08001000000000000020000000000000000000000000000000003000000000020 00800000000000010002000000000000040000001000000000000010004000000 00000004001000000000000010000000000000000000000000000000003000000 00002000800000000000010002000000000000040000001000000000000010004 00000000000004001000000000000010000000000000000000000000000000003 00000000002000800000000000010002000000000000040000001000000000000 01000800000000000004002000000000000010000000000000000000000000000 00000300000000002001000000000000008004000000000000020000001000000 00008000000800000000000002002000000000000010000000000000000000000 00000000000700000000002001000000000000008004000000000000020000001 00000000008000000800000000000002002000000000000010000000000000000 00000000000000000700000000002001000000000000008004000000000000020 00000100000000008000000800000000000002002000000000000010000000000 00000000000000000000000300000000002002000000000000008008000000000 00002000000200000000008000000800000000000002004000000000000010000 00000000000000000000000000000300000000001002000000000000004008000 00000000001000000200000000008000000800000000000002004000000000000 00800000000000000000000000000000000300000000001002000000000000004 00800000000000001000000200000000008000000800000000000002004000000 00000000800000000000000000000000000030078300000000001002000000000 00000400800000000000001000000200000000008000000800000000000002004 000000000000008000000000000000000000000800700CC300000000001002000 00000000000400000100000000001000000400000000008000001000000000000 002004000000000000008000000000000000000000000C00C0086FD0100008000 00200000000000000200000100000000001000000400000000004000001000000 000000001004000000000000004000000000000000000000000C00C0086FD0100 00800000200000000000000200000100000000001000000400000000004000001 00000000000000100400000000000000400000000000000000000000060180080 31000000800000200000000000000200000100000000001000000400000000004 00000100000000000000100400000000000000400000000000000000000000060 1800C030000000800000400000000000000200000100000000001000000800000 00000400000200000000000000100800000000000000400000000000000000000 00006018007030000000400000400000000000000200000100000000000800000 80000000000200000200000000000800000800000000000000200000000000000 0000000000601800C030000000400000400000000000000200000100000000000 80000080000000000200000200000000000800000800000000000000200000000 00000000000000006018008071000000400000400000000000000200000100000 00000080000080000000000200000200000000000800000800000000000000200 0000000000000000000000C00C008671000000400000800000000000000200000 20000000000080000080000000000200000400000000000800000000100000000 0002000000000000000000000000C00C1C8631000000400000800000000000000 10000020000000000040000080000000000100000400000000000400000000100 000000000200000000000000000000000080071CCC30000000400000800000000 00000010000020000000000040000080000000000100000400000000000400000 000100000000000200000000000000000000000000031C7830000000400000800 00000000000010000020000000000040000080000000000100000400000000000 40000000010000000000020000000000000000000000000000000030000000400 00000010000000000010000040000000000040000100000000000100000400000 00000040000000020000000000020000000000000000000000000000000070000 00020000000010000000080000000040000000000020000100000000000080000 40000000000040000000020000000000010000000000000000000000000000000 07000000020000000010000000080000000040000000000020000100000000000 08000040000000000040000000020000000000010000000000000000000000000 00000003000000020000000010000000080000000040000000000020000100000 00000008000040000000000040000000020000000000010000000000000000000 00000000000003000000020000000010000000080000000040000000000020000 10000000000008000080000000000040000000020000000000010000000000000 00000000000000000003000000010000000020000000040000000080000000000 01000020000000000008000080000000000040000000020000000000010000000 00000000000000000000000003000000010000000020000000040000000080000 00000001000020000000000008000080000000000020000000020000000080000 00000000000000000000000000000007000000010000000020000000040000000 08000000000001000020000000000008000080000000000020000000020000000 08000000000000000000000000000000000007000000010000000020000000040 00000008000000000001000020000000000008000080000000000020000000020 00000008000000000000000000000000000000000003000000010000000020000 00004000000010000000000001000040000000000008000000010000000020000 00004000000008000000000000000000000000000000000003000000008000000 02000000002000000010000000000001000040000000000004000000010000000 01000000004000000004000000000000000000000000000000000003000000008 00000002000000002000000010000000000001000040000000000004000000010 00000001000000004000000004000000000000000000000000000000000003000 00000800000002000000002000000010000000000001000040000000000004000 00001000000001000000004000000004000000000000000000000000000000000 00300000000800000002000000002000000010000000000001000080000000000 00400000002000000001000000008000000004000000000000000000000000000 00000000700000000400000004000000002000000010000000008000000080000 00000000200000002000000000800000008000000004000000000000000000000 00000000000000700000000400000004000000002000000010000000008000000 08000000000000200000002000000000800000008000000002000000000000000 00000000000000000000300000000400000004000000002000000010000000008 00000008000000000000200000002000000000800000008000000002000000000 00000000000000000000000000300000000400000004000000002000000010000 00000800000008000000000000200000002000000000800000008000000002000 00000000000000000000000000030078300000000400000008000000002000000 02000000000800000008000000000000200000004000000000800000010000000 002000000000000000000000000000800700CC300000000400000008000000001 00000002000000000400000008000000000000100000004000000000400000010 000000002000000000000000000000000000C00C0086FD0100000400000008000 00000100000002000000000400000008000000000000100000004000000000400 000010000000002000000000000000000000000000C00C0086FD0100000400000 00800000000100000002000000000400000008000000000000100000004000000 00040000001000000000200000000000000000000000000060180080310000000 40000000800000000100000002000000000400000008000000000000100000004 00000000040000002000000000200000000000000000000000000060180080310 00000020000001000000000080000004000000000200000000001000000800000 00000400000000040000002000000000200000000000000000000000000060180 0C030000000020000001000000000080000004000000000200000000001000000 80000000000400000000040000002000000000100000000000000000000000000 06018007030000000020000001000000000080000004000000000200000000001 00000080000000000400000000040000002000000000100000000000000000000 00000006018001870000000020000001000000000080000004000000000200000 00000100000080000000000400000000040000002000000000100000000000000 0000000000000C00C000C70000000020000002000000000080000008000000000 20000000000200000080000000000800000000040000002000000000100000000 0000000000000000000C00C1C0630000000010000002000000000040000008000 00000010000000000200000080000000000800000000020000002000000000080 000000000000000000000000080071C0630000000010000002000000000040000 00800000000010000000000200000080000000000800000000020000002000000 000080000000000000000000000000000031CFE31000000010000002000000000 04000000800000000010000000000200000080000000000800000000020000002 00000000008000000000000000000000000000000000030000000010000002000 00000004000000800000000010000000000200000080000000001000000000020 00000400000000008000000000000000000000000000000000070000080000000 00400000000002000000000100000008000000000400000040000000001000000 00002000000400000000008000000000000000000000000000000000070000080 00000000400000000002000000000100000008000000000400000040000000001 00000000001000000400000000004000000000000000000000000000000000030 00008000000000400000000002000000000100000008000000000400000040000 00000100000000001000000400000000004000000000000000000000000000000 00003000008000000000400000000002000000000100000008000000000400000 04000000000100000000001000000400000000004000000000000000000000000 00000000003000008000000000400000000002000000000200000008000000000 80000004000000000200000000001000000800000000004000000000000000000 00000000000000003000004000000000400000000001000000000200000008000 00000080000002000000000200000008000000000800000000002000000000000 00000000000000000000003000004000000000400000000001000000000200000 00800000000080000002000000000200000008000000000800000000002000000 00000000000000000000000000007000004000000000400000000001000000000 20000000800000000080000002000000000200000008000000000800000000002 00000000000000000000000000000000007000004000000000800000000001000 00000020000000800000000100000002000000000400000008000000000000100 00000200000000000000000000000000000000003000002000000000800000000 00100000000020000000400000000100000001000000000400000004000000000 00010000000100000000000000000000000000000000003000002000000000800 00000000100000000020000000400000000100000001000000000400000004000 00000000010000000100000000000000000000000000000000003000002000000 00080000000000100000000020000000400000000100000001000000000400000 00400000000000010000000100000000000000000000000000000000003000002 00000000080000000000100000000020000000400000000100000001000000000 80000000400000000000020000000100000000000000000000000000000000007 00000100000000000010000000100000000040000000400000000200000001000 00000080000000400000000000020000000100000000000000000000000000000 00000700000100000000000010000800000000000040000000200000000200000 00080000000080000000200000000000020000800000000000000000000000000 00000000000300000100000000000010000800000000000040000000200000000 20000000080000000080000000200000000000020000800000000000000000000 00000000000000000300000100000000000010000800000000000040000000200 00000020000000080000000080000000200000000000040000800000000000000 00000000000000000030030300000100000000000020000800000000000080000 00020000000040000000080000000000010000200000000000040000800000000 00000000000000000000080070038300000080000000000020000400000000000 08000000010000000040000000040000000000010000100000000000040000800 000000000000000000000000000C00C003CFC0100080000000000020000400000 00000008000000010000000040000000040000000000010000100000000000040 000800000000000000000000000000000C00C0036FC0100080000000000020000 40000000000008000000010000000040000000040000000000010000100000000 00008000080000000000000000000000000000060180030300000080000000000 04000040000000000010000000010000000040000000040000000000020000100 00000000008000080000000000000000000000000000060180030300000080000 00000004000020000000000010000080000000000040000000020000000000020 00008000000000008000040000000000000000000000000000060180030300000 08000000000004000020000000000010000080000000000040000000020000000 00002000008000000000008000040000000000000000000000000000060180030 30000008000000000004000020000000000010000080000000000040000000020 00000000004000008000000000010000040000000000000000000000000000060 18003070000004000000000008000020000000000020000080000000000080000 00002000000000004000008000000000010000040000000000000000000000000 0000C00C003070000004000000000008000010000000000020000040000000000 08000000001000000000004000004000000000010000020000000000000000000 0000000000C00C1C3030000004000000000008000010000000000020000040000 00000008000000001000000000004000004000000000010000020000000000000 000000000000000080071C3030000004000000000010000010000000000040000 04000000000000001000001000000000008000004000000000020000020000000 000000000000000000000000031CFE31000002000000000010000008000000000 04000002000000000000001008000000000000008000002000000000020000010 00000000000000000000000000000000000030000002000000000010000008000 00000004000002000000000000001008000000000000008000002000000000020 00001000000000000000000000000000000000000070000002000000000010000 00800000000004000002000000000000001008000000000000008000002000000 00002000001000000000000000000000000000000000000070000001000000000 02000000400000000008000001000000000000002008000000000000008000002 00000000004000001000000000000000000000000000000000000030000001000 00000002000000400000000008000001000000000000002004000000000000008 00000200000000004000000800000000000000000000000000000000000030000 00100000000002000000400000000008000001000000000000002004000000000 00000800000200000000004000000800000000000000000000000000000000000 03000800000000000004000000400000000000001001000000000000004004000 00000000001000000200000000008000000800000000000000000000000000000 00000003000800000000000004000000200000000000001000800000000000004 00200000000000001000000100000000008000000400000000000000000000000 00000000000003000800000000000004000000200000000000001000800000000 00000400200000000000001000000100000000008000000400000000000000000 00000000000000000007000400000000000008000000200000000000002000800 00000000000800200000000000002000000100000000000001000400000000000 00000000000000000000000007000400000000000008000000100000000000002 00040000000000000800100000000000002000800000000000000001000200000 00000000000000000000000000000003000400000000000008000000100000000 00000200040000000000000800100000000000002000800000000000000001000 20000000000000000000000000000000000003000200000000000000001800000 00000000000400020000000000001000080000000000004000400000000000000 00200020000000000000000000000000000000000003000200000000000000001 80000000000000000400020000000000001000080000000000004000400000000 00000000200010000000000000000000000000000000000003000200000000000 00000280000000000000000800020000000000002000080000000000008000400 00000000000000400010000000000000000000000000000000000007000100000 00000000000240000000000000000800010000000000002000040000000000008 00020000000000000000480000000000000000000000000000000000000007000 10000000000000000440000000000000001000010000000000004000040000000 00000000120000000000000000880000000000000000000000000000000000000 00300008000000000000000420000000000000001080000000000000004000020 00000000000000110000000000000000840000000000000000000000000000000 00000000300008000000000000000820000000000000002080000000000000008 00002000000000000000210000000000000001040000000000000000000000000 00000000000000300004000000000000000810000000000000002040000000000 00000800001000000000000000208000000000000001020000000000000000000 00000000000000000000300002000000000000001008000000000000004020000 00000000000008100000000000000000404000000000000002010000000000000 00000000000000000000000000FC0101000000000000002004000000000000008 01000000000000000004200000000000000000802000000000000004008000000 00000000000000000000000000000000FCC10000000000000000C003000000000 00000000F00000000000000003C0000000000000000F001000000000000008007 00000000000000000000000000000000000000300000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000030F0FFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFF1F00000000000000000000000078E0FFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFF1F000000000000000000000000CC009801000 000000000000080010000000000000000000FCC0000000000000000E0C1000000 0000000000000C6306000000000000000000000000000000000000000000CC009 801000000000000000080010000000000000000800DCC0000000000000000B0C1 0000000000000000000C630600000000000000000000000000000000000000000 086010C03000000000000000080010000000000000000000C8601000000000000 0080C100000000000000000000330C00000000000000000000000000000000000 000000086010C030000000000000000801D0000000000000000000C8601000000 0000000080C10E000000000000000000330C00000000000000000000000000000 000000000000086010C03000000000000000080330000000000000000000C8601 0000000000000080C119000000000000000080310C00000000000000000000000 000000000000000000086010C0300000000000000000060000000000000000000 0C8601000000000000008001300000000000000000E0300C00000000000000000 000000000000000000000000086010C0300000000000000000060000000000000 0000000C860100000000000000800130000000000000000030300C00000000000 0000000000000000000000000000000CC00980100000000000000000060000000 0000000000000CCC0000000000000000800130000000000000000018600600000 0000000000000000000000000000000000000CC00980100000000000000008061 0000000000000000000CCC000000000000000080C13000000000000000000C600 60000000000000000000000000000000000000000007800F00000000000000000 0000330000000000000000000C780000000000000000808119000000000000000 00CC0030000000000000000000000000000000000000000003000600000000000 00000000001E0000000000000000807F300000000000000000F00F0F000000000 0000000FC830100000000000000000000000000000000}}{COM_R 37 0{TEXT 1 188 "\015For comparison purposes, lets compute the path of a gli der with an initial velocity of 2, and plot that on the same axes . We'll do it all in one command, just to be complicated about i t."}}{COM_R 38 0{TEXT 1 0 ""}}{INP_R 39 0 "> "{TEXT 0 165 "plot(\ {makelist(VThetaToXY (MySol),2,3),\012 makelist(VThetaTo XY(rungekuttahf([vdot,thdot],[0,2,0],.05,500)),2,3)\},\012axes=FR AME,\012title=`Flights of two gliders`);"}}{GRH_R 40 0{RASTER 777 200 1 98 0000000000000000000000000000000000000000000000000000000 00000000000000000000000007F33000600000070000000000066C00000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000033300060C000018300000000066C0000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000830100030C0000183000000000036000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000808119373B9F07783EFC99F10037336E3C360F0 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000008081993977C60CCC0C9899998139337366BE19 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000080DFD83063C600C60C98998DC1B0B16163860 10000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000C0C0CC98318303C6068CDD8CC19899313F03 07000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000C0C06C9831030663068CD5C66098D9B0010 30C00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000C0C06C98B1310663060677C66098D9B001 630C0000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000606066CE983103330306336660CECC9C9 96106000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000006060C6CD18E3011E030C333CC0CD8C1B 8FC10300000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000C0000000000000000000C000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000030060000000000000000300600 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000E0030000000000000000E0030 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000F80000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000F8000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000C000001E3000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000E000003330000000F000000000 00070000000070000000008007000000003C00000000C00100000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000F0008061FF030000100100000 08008000000008C00000000400400000000640000000020020000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000D8008061FF03000008020000 00801000000000840000000020080000000082000000002004000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000C0008061300000000402000 00040100000000004010000002010000000008100000000100400000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000C0000033F8000000020200 00002020000000000201000000201000000000810000000008080000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000C000001EF800000002040 00000202000000000010200000010100000000081000000000808000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000C0000033300000000204 00000010400000000001020000000810000000800001000000081000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000C000806130000000020 80000001040000000800002000000082000000080000100000004100000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000C0008061F800000001 08000000104000000080000400000008200000004000020000000410000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000C0008761F80000000 10800000010400000008000040000000840000000400002000000041000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000C000073330000000 01080000000880000000800004000000084000000040000200000002200000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000F807071EF800008 00008000000088000000080000800000004400000004000020000000220000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000F80000 80001000000008000100004000080000000440000000400004000000022000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000030000 08000100000000800010000400008000000044000000020000400000002400000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000003000 00800020000000080001000040000800000002800000002000040000000240000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000F80 00080002000000008000100004000080000000280000000200008000000024000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000C000001EF8 00008000200000000400010000400010000000028000000010000800000001400 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000E00000333 00000400020000000040001000040001000000002000100001000080000000140 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000F0008021 FF030040002000000004000100002000100000000200010000100008000000014 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000D800800 1FF03004000200000000200020000200010000000020001000010000800008000 80000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000C00080 01300000400020000000020002000020001000000001000100001000080000800 08000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000C0008 01D30000040004000000002000200002000100000000100010000100010000080 00800000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000C000 8033F800004000400000000200020000200010000000010001000010001000008 00080000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000C00 08061F80000200040000000020002000020002000000001000100000800100000 80008000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000C0 00806130000020004000000002000200002000200000000100020000080010000 08000800000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000C 00080613000002000400000000200020000100020000000010002000008001000 00800080000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 C0008761F80000200040000000020004000010002000000001000200000800100 00080000001000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0C0000733F8000020004000000002000400001000200000000100020000080010 00008000000100000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00F807071E3000002000400000000200040000100020000080000002000008001 00000800000010000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000F80000200080000000020004000010002000008000000200000800 20000080000001000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000F8000020008000000001000400001000200000800000020000080 02000004000000100000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000003000002000800000000100040000100040000080000002000008 00200000400000010000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000300000200080000000010004000010004000008000000200000 80020000040000001000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000F8000020008000000001000400001000400000800000020000 08002000004000000100000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000C0000020F800002000800000000100040000080040000080000002000 00800200000400000010000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000E0000030300000200080000000010004000008004000008000000200 00080020000040000002000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000F0000038FF030010008000000001000400000800400000800000020 00004002000004000000200000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000D800003CFF03001000800000000100040000080040000080000004 00000400200000400000020000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000C0000036300000100080000000010004000008004000008000000 40000040020000040000002000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000C000003330000010008000000001000800000800400000800000 04000004002000004000000200000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000C0008031F800001000800000000100080000080040000080000 00400000400200000400000020000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000C0008031F80000100080000000010008000008004000008000 00040000040020000040000002000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000C000807F30000010008000000001000800000800400000400 00004000004002000004000000200000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000C0000030F800001000800000000100080000080040000040 00000400000400200000400000020000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000C0000730F80000100080000000010008000008004000004 00000040000040020000020000002000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000C000073030000010008000008000000800000800400000 40000004000004002000002000000200000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000F80707303000001000800000800000080000080040000 04000000400000400200000200000020000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000F80000100080000080000008000008004000 00400000040000040020000020000002000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000F8000010000001008000000800000800400 00040000004000004004000002000000200000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000003000001000000100800000080000080040 00004000000400000400400000200000020000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000F80000100000010080000008000008008 00000400000040000040040000020000002000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000F8000010000001008000000800000800 80000040000004000004004000002000000200000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000C000001E3000001000000100800000080000080 08000004000000400000400400000200000020000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000E0000033300000100000010080000008000008 00800000400000040000040040000020000002000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000F0008061FF030010000001008000000800000 80080000040000004000004004000002000000200000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000D8008061FF03001000000100800000080000 08008000004000000400000400400000200000020000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000C0000060300000100000010080000008000 00800800000400000040000040040000020000002000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000C0000060F8000010000001008000000800 00080080000040000004000004004000002000000200000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000C0000030F800001000000100800000080 00008008000004000000400000400400000200000020000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000C000001C300000100000010080000008 00000800800000400000040000040040000020000002000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000C000000630000010000001008000000 80000080080000040000004000004004000002000000200000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000C0000003F800001000000100800000 08000008008000004000000400000400400000200000020000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000C0008701F80000100000010080000 00800000800400000400000040000040040000020000002000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000C000870130000010000001008000 00080000080040000040000004000004004000002000000200000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000F807877F3000001000000100800 00008000008004000008000000400000400400000200000020000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000F80000100080000080 00000800000800400000800000040000040020000020000002000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000F8000010008000008 00000080000080040000080000004000004002000004000000200000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000003000001000800000 00010008000008004000008000000400000400200000400000020000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000F80000100080000 00001000800000800400000800000040000040020000040000002000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000F8000010008000 00000100080000080040000080000004000004002000004000000200000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000C3000001000800 00000010008000008004000008000000400000400200000400000020000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000E300000100080 00000001000800000800400000800000040000040020000040000002000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000FFF030010008 00000000100040000080040000080000004000004002000004000000200000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000800DFF03001000 80000000010004000008004000008000000400000400200000400000010000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000C300000200 08000000001000400000800400000800000040000080020000040000001000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000CF8000020 00800000000100040000080040000080000002000008002000004000000100000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000CF800002 00080000000010004000008004000008000000200000800200000400000010000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000C300000 20008000000001000400001000400000800000020000080020000040000001000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000C30000 02000800000000100040000100040000080000002000008002000004000000100 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000CF800 00200080000000010004000010004000008000000200000800200000400000010 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000CF80 00020008000000001000400001000200000800000020000080020000040000001 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000C30 00002000800000000100040000100020000080000002000008002000004000000 10000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000807FF 80000200080000000010004000010002000000001000200000800200000400000 01000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 F8000020004000000001000400001000200000000100020000080010000040000 00100000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 03000002000400000000100040000100020000000010002000008001000004000 00010000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00300000200040000000020002000010002000000001000200000800100000800 08000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000F8000020004000000002000200001000200000000100020000080010000080 00800000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000C000 001EF800004000400000000200020000100020000000010002000010001000008 00080000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000E00 10033300000400040000000020002000010002000000001000100001000100000 80008000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000030 038061FF030040002000000002000200001000200000000100010000100010000 08000800000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000003 0038061FF03004000200000000200020000200020000000010001000010000800 00800080000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 18068061300000400020000000020002000020002000000001000100001000080 00000018000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 01806003330000040002000000004000200002000200000000100010000100008 00000001800000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 001806001EF800004000200000000400020000200010000000010001000010000 80000000180000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00018060033F80000400020000000040002000020001000000001800000001000 08000000018000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00001806806130000040002000000004000200002000100000000280000000100 00800000001800000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000030038061F800004000200000000400020000400010000000028000000010 00080000000180000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000030038761F80000400020000000040001000040001000000002800000001 00008000000018000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000E001073330000040002000000008000100004000100000000280000000 10000800000002400000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000C000071E3000004000200000000800010000400008000000028000000 02000080000000240000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000F80000800020000000080001000040000800000002800000 00200008000000024000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000F8000080002000000008000100004000080000000440000 00020000800000002400000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000003000008000100000000800010000400008000000044000 00002000040000000240000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000F80000800010000000080001000080000800000004400 00000200004000000024000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000F8000080001000000010800000008000080000000440 00000020000400000004200000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000C000001E3000008000100000001080000000800004000000044 00000002000040000000420000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000E0010033300000000110000000108000000080000400000004 40000000400004000000042000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000030038021FF030000011000000010800000008000040000000 82000000040000400000004200000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000030038001FF03000001080000001080000000800004000000 08200000004000040000000420000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000018068001300000000108000000108000000000010400000 00820000000400002000000042000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000001806801D30000000010800000010400000000001040000 00082000000040000200000008100000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000018068033F800000002080000002040000000000104000 00008200000008000020000000810000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000018068061F80000000208000000204000000000010200 00000820000000800002000000081000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000001806806130000000020400000020400000000001020 00000081000000080000100000008100000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000030038061F800000004040000002040000000000102 00000010100000000001010000000810000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000030038761F80000000404000000204000000000020 20000001010000000000101000000080800000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000E001073330000000040200000020200000000002 02000000101000000000810000000010080000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000C000071E3000000004020000004020000000000 20200000010100000000081000000001008000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000F80000000802000000402000000000 02010000001010000000008200000000100400000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000F8000000080200000040200000000 00201000000201000000000820000000010040000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000003000000008020000004010000000 00040100000020080000000082000000001004000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000F80000000801000000401000000 00004010000004008000000004200000000100400000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000F8000000080100000080100000 00008400000000400800000000420000000020040000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000C00000203000000008010000008008000 00000880000000040080000000042000000002002000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000E0010030300000001001000000800800 00000088000000004004000000004400000000200200000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000030030038FF03000090000000FC07090 0000000480000000080E43F000000240000000020020000FF0100000000000000 00000000F80F0000000000000000000000C07F000000000000000000000000FE0 300000000000000000000000000000000003003003CFF03000090000000031809 000000004800000000801AC00000002400000000200200C000060000000000000 00000000006300000000000000000000000308001000000000000000000008001 0C00000000000000000000000000000000001806003630000000500000C000600 90000000050000000008006000300002400000000400100300018000000000000 000000008001C000000000000000000000000C000600000000000000000000600 030000000000000000000000000000000000018060033F8000000500000200080 05000000005000000000800300040000140000000040010008002000000000000 00000000040000001000000000000000000000200080000000000000000000010 0040000000000000000000000000000000000018068031F800000060000010000 0070000000030000000008002000800001800000000C000000400400000000000 00000000002000000200000000000000000000010010000000000000000000000 80080000000000000000000000000000000000018068031300000006000000800 00060000000030000000004003001000001800000000800000020080000000000 00000000000100000040000000000000000008000006000000000000000000000 04000000000000000000000000000000000000001806807F30000000600000040 00006000000003000000000200100600000100000000080000001000003000000 00000000000008000018000000000000000000400000800000000000000000000 0020000000000000000000000000000000000000030030030F800000060000002 00000A00000000200000000010010080000018000000008000800000000400000 00000000000000400002000000000000000000020000000010000000000000000 00010000000000000000000000000000000000000030030730F80000006000000 10000160000000030000000000803000001001800000000800140000000080000 00000000000000020000400000000000000000001000000002000000000000000 0800000000000000000000000000000000000000000E001073030000000600080 00000025000000005000000000040300000100280000000040012000000008000 00000000000000001000040000000000000000000080000000400000000000000 00400000000000000000000000000000000000000000C0000730F8000000A0004 00000004900000000500000000082020000020028000000004002100000001000 00000000000000800000008000000000000000000004000000040000000000000 00020000000000000000000000000000000000000000000000000F80000009000 20000000890000000048000000008104000004004400000000400208000000200 00000000000000040000000000100000000000000000200000008000000000000 00001000000000000000000000000000000000000000000000000030000000100 110000080080100000088000000C0400400000800440000000040020600000040 00000000000000003000000000020000000000000080010000001000000000000 000000C0000000000000000000000000000000000000000000000003000000008 010C0000801002000000880000002040080000100042000000002004010000008 00000000000000000080000000004000000000000004000000000200000000000 00000002000000000000000000000000000000000000000000000000F80000000 80202000040100400000004010000204008000020008200000000200401000000 00010000000000000008000000000800000000000000400000000040000000000 0000000020000000000000000000000000000000000000000C000001EF8000000 08020200004020080000000401000010201000004000820000000010880000000 00002000000000000000400000000100000000000000020000000008000000000 00000000010000000000000000000000000000000000000000E00100333000000 00404010000402010000000020100000820100000800001010000001048000000 00000400000000000000020000000020000000000000001000000000800000000 00000008000000000000000000000000000000000000000000030038061FF0300 00048400000020202000000002020000041020000000010101000000083000000 00000080000000000000001000000004000000000000000080000000000030000 000000004000000000000000000000000000000000000000000030038061FF030 00002440000002040400000000102000002102000000082000100000008100000 00000010000000000000800000000000800000000000000004000000000004000 00000000020000000000000000000000000000000000000000000180600603000 00000248000000104080000000010400000210200000008400020000000430000 00000002000000000000080000000000000010000000000000400000000000800 00000000002000000000000000000000000000000000000000000018060060300 00000023800000010808000008000040080010840000000840002000000042C00 00000000200000000000006000000000000001000000000000030000000000100 000000000001800000000000000000000000000000000000000000018060030F8 00000001180000001080000100800008004000084000000048000400000004420 00000000040000000000000100000000000000200000000008000000000000010 000000000000040000000000000000000000000000000000000000001806001CF 80000000114000000080001060080000800200004800000007000040000000241 000000000080010000000000080000000000000C0000000000400000000000006 00000000000000200000000000000000000000000000000000000000018060006 30000080002200000008000108004000100010000480000000600008000000828 00000000000000200000000000400000000000010000000000020000000000000 80000000000000010000000000000000000000000000000000000000003003000 330000080002200000004000210004000100010000200010000A0000800000081 80000000000000040000000000040000000000002000000000002000000000000 00001000000000001000000000000000000000000000000000000000000300387 01F800004080410000000200021000200020000C0002000100009000100000006 10001000000000004000000000003000000000000200000000000180000000000 00000100000000C000000000000000000000000000000000000000000000E0018 701F8000040404000000002000420001000200002000100020000100120000080 10000100000000000800000000800000000000000040000000000004000000000 0000002000000002000000000000000000000000000000000000000000000C000 877F300000202080000000010004C000100040000180000004000008062000008 00800020000000000300000000040000000000000008001000000000200000000 0000000C000000001000000000000000000000000000000000000000000000000 00000F800001018800000800000080001080080C0008000000400000408400000 40060002000000000040000000003000000000000000000200000080010000000 000000010000000000C0000000000000000000000000000000000000000000000 000000F8000010040001008000001000020400802000400000080000041040000 02001000400000000008000000000080000000000000000040000004000000000 00000000200000000002000000000000000000000000000000000000000000000 0000000300000080200020040000010000C040000110020000008000002608000 00900000040000000000000300000004000000000000000018000000300000000 000000000C0000000800100000000000000000000000000000000000000000000 0000000030000086010002002000002000100200000E001000001000800180800 00068000008000000000000040000000300000000000000002000000008000000 00000000000001000040000000000000000000000000000000000000000000000 000000000F800004100000400100000C000E00100000200080000200040000003 01001400001000000000000018000080000000000000000000C00000000400000 00000000000000600002000000000000000000000000000000000000000000000 0000000000F8008030000018000800000001C00000800500040000C0002000000 406000E0000200000000000002000006000000000000000000000030000030000 00000000000000180000180000000000000000000000000000000000000000000 000000000003000400E0000200004000000022007007018000300000001100000 380880030000C0000000000000C001001C000000000000000000000C00E000000 00000000000000060000007000000000000000000000000000000000000000000 000000000000FF03A0010000C00103000000041838000C20C0000000000E0C000 0C031E000000000010000000000000E80030000000000000000000070001C0000 00000000000000008003E00000000000000000000000000000000000000000000 0000000000000FF037E00000000FE00000000F807C0FF03C03F00000000F00300 0000FE3F000000003E000000000000F07F000000000000000000000080FF03000 0000000000000000000FC1F000000000000000000000000000000000000000000 00000000000000300000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000030000300000000000000000000000000001800000000000000 00000000000000C00000000000000000000000000000000600000000000000000 00000000000180000000000000000000000000000000000000000000000000000 0000000000000000F0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF07000000000000000000000 00000000000000000E0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0700000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 0000000000000000000C0000030000000000000000000000000000FF000000000 000000000000000000006180000000000000000000000000030F8070000000000 00000000000000E00103000000000000000000000000000000000000000000000 00000000000000000001E00800700000000000000000000000000000300000000 00000000000000000000073C00000000000000000000000000381800000000000 00000000000000030830700000000000000000000000000000000000000000000 000000000000000000003300C00C0000000000000000000000000000030000000 0000000000000000000800766000000000000000000000000003C180000000000 000000000000000018C60C0000000000000000000000000000000000000000000 0000000000000000000003300C00C000000000000000000000000000003000000 00000000000000000000C00666000000000000000000000000003618000000000 0000000000000000018C60C000000000000000000000000000000000000000000 00000000000000000000806100601800000000000000000000000000000300000 0000000000000000000000006C300000000000000000000000000301800000000 00000000000000000000661800000000000000000000000000000000000000000 000000000000000000000806100601800000000000000000000000000003B0000 00000000000000000000000006C30000000000000000000000000030D80100000 00000000000000000000066180000000000000000000000000000000000000000 00000000000000000000008061006018000000000000000000000000000067000 000000000000000000000000006C3000000000000000000000000003038030000 00000000000000000000006318000000000000000000000000000000000000000 0000000000000000000000080610060180000000000000000000000000000C000 0000000000000000000000000006C300000000000000000000000000300006000 000000000000000000000C0611800000000000000000000000000000000000000 00000000000000000000000080610060180000000000000000000000000000C00 00000000000000000000000000006C30000000000000000000000000030000600 00000000000000000000006060180000000000000000000000000000000000000 0000000000000000000000000003300C00C0000000000000000000000000000C0 00000000000000000000000000000666000000000000000000000000003000060 0000000000000000000000030C00C000000000000000000000000000000000000 00000000000000000000000000003300C00C0000000000000000000000000000C 30000000000000000000000000000066600000000000000000000000000301806 00000000000000000000000018C00C00000000000000000000000000000000000 000000000000000000000000000001E0080070000000000000000000000000000 660000000000000000000000000000063C0000000000000000000000000030300 30000000000000000000000001880070000000000000000000000000000000000 0000000000000000000000000000000C000003000000000000000000000000000 03C00000000000000000000000000C03F1800000000000000000000000000FEE1 01000000000000000000000000F80703000000000000000000000000000000000 000000000000000}}{COM_R 41 0{TEXT 1 203 "The second glider does l oops, and doesnt go as far. We could tell the looping from the p hase portrait (because the theta constantly increases), but deter mining the distance would have been much harder.\015"}}{SEP_R 42 0}{COM_R 43 0{TEXT 1 0 ""}}}{END}