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평면상의 3점이 주어졌을 때, 그 3점으로 이루어지는 삼각형 안에 원점이 있는지를 판별하는 과제.
임의로 3점을 1, 2, 3 이라고 했을 때, 원점을 중심으로 1->2 의 뱡향, 2->3 의 방향, 3->1 의 방향이 같다면, 원점은 내부의 점. 방향이 바뀐다면, 외부의 점이다.
좌표가 주어진 두 점의 방향있는 각도의 방향은 두 점으로 만든 정방행렬의 판별식의 부호로 알 수 있다. (3차원으로 확장한 두 좌표의 외적으로 해석할 수도 있음. 동일한 것.)
#!/usr/bin/env python
# http://projecteuler.net/index.php?section=problems&id=102
# Given 3 points, check if the triangle formed by these
# contains the origin (0, 0) inside itself.
# -------------------------------------------------------------
# How I solved this problem.
# -------------------------------------------------------------
##
# .2
# .1
# *O
#
#
# .3
# From the above configuration, we see that
# r12 is counterclockwise, r23 is counterclockwise, r31 is counterclockwise
## If O is outside,
# .2
# .1
# .3
#
#
# *O
# From the above configuration, we see that
# r12 is counterclockwise, r23 is clockwise, r31 is clockwise
# From these two examples, we can assume that
# if O is inside, all r12 and r23 and r31 has the same rotational sense.
# if O is outside, one of them has opposite rotational sense.
# -------------------------------------------------------------
# each ele list defines a triangle in XY plane
# ele = ( x1, y1 ) (x2, y2) (x3, y3)
tri_coods = [
[-340, 495, -153, -910, 835, -947],
[-175, 41, -421, -714, 574, -645],
[-547, 712, -352, 579, 951, -786],
[419, -864, -83, 650, -399, 171],
[-429, -89, -357, -930, 296, -29],
[-734, -702, 823, -745, -684, -62],
[-971, 762, 925, -776, -663, -157],
[162, 570, 628, 485, -807, -896],
[641, 91, -65, 700, 887, 759],
[215, -496, 46, -931, 422, -30],
[-119, 359, 668, -609, -358, -494],
[440, 929, 968, 214, 760, -857],
[-700, 785, 838, 29, -216, 411],
[-770, -458, -325, -53, -505, 633],
[-752, -805, 349, 776, -799, 687],
[323, 5, 561, -36, 919, -560],
[-907, 358, 264, 320, 204, 274],
[-728, -466, 350, 969, 292, -345],
[940, 836, 272, -533, 748, 185],
[411, 998, 813, 520, 316, -949],
[-152, 326, 658, -762, 148, -651],
[330, 507, -9, -628, 101, 174],
[551, -496, 772, -541, -702, -45],
[-164, -489, -90, 322, 631, -59],
[673, 366, -4, -143, -606, -704],
[428, -609, 801, -449, 740, -269],
[453, -924, -785, -346, -853, 111],
[-738, 555, -181, 467, -426, -20],
[958, -692, 784, -343, 505, -569],
[620, 27, 263, 54, -439, -726],
[804, 87, 998, 859, 871, -78],
[-119, -453, -709, -292, -115, -56],
[-626, 138, -940, -476, -177, -274],
[-11, 160, 142, 588, 446, 158],
[538, 727, 550, 787, 330, 810],
[420, -689, 854, -546, 337, 516],
[872, -998, -607, 748, 473, -192],
[653, 440, -516, -985, 808, -857],
[374, -158, 331, -940, -338, -641],
[137, -925, -179, 771, 734, -715],
[-314, 198, -115, 29, -641, -39],
[759, -574, -385, 355, 590, -603],
[-189, -63, -168, 204, 289, 305],
[-182, -524, -715, -621, 911, -255],
[331, -816, -833, 471, 168, 126],
[-514, 581, -855, -220, -731, -507],
[129, 169, 576, 651, -87, -458],
[783, -444, -881, 658, -266, 298],
[603, -430, -598, 585, 368, 899],
[43, -724, 962, -376, 851, 409],
[-610, -646, -883, -261, -482, -881],
[-117, -237, 978, 641, 101, -747],
[579, 125, -715, -712, 208, 534],
[672, -214, -762, 372, 874, 533],
[-564, 965, 38, 715, 367, 242],
[500, 951, -700, -981, -61, -178],
[-382, -224, -959, 903, -282, -60],
[-355, 295, 426, -331, -591, 655],
[892, 128, 958, -271, -993, 274],
[-454, -619, 302, 138, -790, -874],
[-642, 601, -574, 159, -290, -318],
[266, -109, 257, -686, 54, 975],
[162, 628, -478, 840, 264, -266],
[466, -280, 982, 1, 904, -810],
[721, 839, 730, -807, 777, 981],
[-129, -430, 748, 263, 943, 96],
[434, -94, 410, -990, 249, -704],
[237, 42, 122, -732, 44, -51],
[909, -116, -229, 545, 292, 717],
[824, -768, -807, -370, -262, 30],
[675, 58, 332, -890, -651, 791],
[363, 825, -717, 254, 684, 240],
[405, -715, 900, 166, -589, 422],
[-476, 686, -830, -319, 634, -807],
[633, 837, -971, 917, -764, 207],
[-116, -44, -193, -70, 908, 809],
[-26, -252, 998, 408, 70, -713],
[-601, 645, -462, 842, -644, -591],
[-160, 653, 274, 113, -138, 687],
[369, -273, -181, 925, -167, -693],
[-338, 135, 480, -967, -13, -840],
[-90, -270, -564, 695, 161, 907],
[607, -430, 869, -713, 461, -469],
[919, -165, -776, 522, 606, -708],
[-203, 465, 288, 207, -339, -458],
[-453, -534, -715, 975, 838, -677],
[-973, 310, -350, 934, 546, -805],
[-835, 385, 708, -337, -594, -772],
[-14, 914, 900, -495, -627, 594],
[833, -713, -213, 578, -296, 699],
[-27, -748, 484, 455, 915, 291],
[270, 889, 739, -57, 442, -516],
[119, 811, -679, 905, 184, 130],
[-678, -469, 925, 553, 612, 482],
[101, -571, -732, -842, 644, 588],
[-71, -737, 566, 616, 957, -663],
[-634, -356, 90, -207, 936, 622],
[598, 443, 964, -895, -58, 529],
[847, -467, 929, -742, 91, 10],
[-633, 829, -780, -408, 222, -30],
[-818, 57, 275, -38, -746, 198],
[-722, -825, -549, 597, -391, 99],
[-570, 908, 430, 873, -103, -360],
[342, -681, 512, 434, 542, -528],
[297, 850, 479, 609, 543, -357],
[9, 784, 212, 548, 56, 859],
[-152, 560, -240, -969, -18, 713],
[140, -133, 34, -635, 250, -163],
[-272, -22, -169, -662, 989, -604],
[471, -765, 355, 633, -742, -118],
[-118, 146, 942, 663, 547, -376],
[583, 16, 162, 264, 715, -33],
[-230, -446, 997, -838, 561, 555],
[372, 397, -729, -318, -276, 649],
[92, 982, -970, -390, -922, 922],
[-981, 713, -951, -337, -669, 670],
[-999, 846, -831, -504, 7, -128],
[455, -954, -370, 682, -510, 45],
[822, -960, -892, -385, -662, 314],
[-668, -686, -367, -246, 530, -341],
[-723, -720, -926, -836, -142, 757],
[-509, -134, 384, -221, -873, -639],
[-803, -52, -706, -669, 373, -339],
[933, 578, 631, -616, 770, 555],
[741, -564, -33, -605, -576, 275],
[-715, 445, -233, -730, 734, -704],
[120, -10, -266, -685, -490, -17],
[-232, -326, -457, -946, -457, -116],
[811, 52, 639, 826, -200, 147],
[-329, 279, 293, 612, 943, 955],
[-721, -894, -393, -969, -642, 453],
[-688, -826, -352, -75, 371, 79],
[-809, -979, 407, 497, 858, -248],
[-485, -232, -242, -582, -81, 849],
[141, -106, 123, -152, 806, -596],
[-428, 57, -992, 811, -192, 478],
[864, 393, 122, 858, 255, -876],
[-284, -780, 240, 457, 354, -107],
[956, 605, -477, 44, 26, -678],
[86, 710, -533, -815, 439, 327],
[-906, -626, -834, 763, 426, -48],
[201, -150, -904, 652, 475, 412],
[-247, 149, 81, -199, -531, -148],
[923, -76, -353, 175, -121, -223],
[427, -674, 453, 472, -410, 585],
[931, 776, -33, 85, -962, -865],
[-655, -908, -902, 208, 869, 792],
[-316, -102, -45, -436, -222, 885],
[-309, 768, -574, 653, 745, -975],
[896, 27, -226, 993, 332, 198],
[323, 655, -89, 260, 240, -902],
[501, -763, -424, 793, 813, 616],
[993, 375, -938, -621, 672, -70],
[-880, -466, -283, 770, -824, 143],
[63, -283, 886, -142, 879, -116],
[-964, -50, -521, -42, -306, -161],
[724, -22, 866, -871, 933, -383],
[-344, 135, 282, 966, -80, 917],
[-281, -189, 420, 810, 362, -582],
[-515, 455, -588, 814, 162, 332],
[555, -436, -123, -210, 869, -943],
[589, 577, 232, 286, -554, 876],
[-773, 127, -58, -171, -452, 125],
[-428, 575, 906, -232, -10, -224],
[437, 276, -335, -348, 605, 878],
[-964, 511, -386, -407, 168, -220],
[307, 513, 912, -463, -423, -416],
[-445, 539, 273, 886, -18, 760],
[-396, -585, -670, 414, 47, 364],
[143, -506, 754, 906, -971, -203],
[-544, 472, -180, -541, 869, -465],
[-779, -15, -396, 890, 972, -220],
[-430, -564, 503, 182, -119, 456],
[89, -10, -739, 399, 506, 499],
[954, 162, -810, -973, 127, 870],
[890, 952, -225, 158, 828, 237],
[-868, 952, 349, 465, 574, 750],
[-915, 369, -975, -596, -395, -134],
[-135, -601, 575, 582, -667, 640],
[413, 890, -560, -276, -555, -562],
[-633, -269, 561, -820, -624, 499],
[371, -92, -784, -593, 864, -717],
[-971, 655, -439, 367, 754, -951],
[172, -347, 36, 279, -247, -402],
[633, -301, 364, -349, -683, -387],
[-780, -211, -713, -948, -648, 543],
[72, 58, 762, -465, -66, 462],
[78, 502, 781, -832, 713, 836],
[-431, -64, -484, -392, 208, -343],
[-64, 101, -29, -860, -329, 844],
[398, 391, 828, -858, 700, 395],
[578, -896, -326, -604, 314, 180],
[97, -321, -695, 185, -357, 852],
[854, 839, 283, -375, 951, -209],
[194, 96, -564, -847, 162, 524],
[-354, 532, 494, 621, 580, 560],
[419, -678, -450, 926, -5, -924],
[-661, 905, 519, 621, -143, 394],
[-573, 268, 296, -562, -291, -319],
[-211, 266, -196, 158, 564, -183],
[18, -585, -398, 777, -581, 864],
[790, -894, -745, -604, -418, 70],
[848, -339, 150, 773, 11, 851],
[-954, -809, -53, -20, -648, -304],
[658, -336, -658, -905, 853, 407],
[-365, -844, 350, -625, 852, -358],
[986, -315, -230, -159, 21, 180],
[-15, 599, 45, -286, -941, 847],
[-613, -68, 184, 639, -987, 550],
[334, 675, -56, -861, 923, 340],
[-848, -596, 960, 231, -28, -34],
[707, -811, -994, -356, -167, -171],
[-470, -764, 72, 576, -600, -204],
[379, 189, -542, -576, 585, 800],
[440, 540, -445, -563, 379, -334],
[-155, 64, 514, -288, 853, 106],
[-304, 751, 481, -520, -708, -694],
[-709, 132, 594, 126, -844, 63],
[723, 471, 421, -138, -962, 892],
[-440, -263, 39, 513, -672, -954],
[775, 809, -581, 330, 752, -107],
[-376, -158, 335, -708, -514, 578],
[-343, -769, 456, -187, 25, 413],
[548, -877, -172, 300, -500, 928],
[938, -102, 423, -488, -378, -969],
[-36, 564, -55, 131, 958, -800],
[-322, 511, -413, 503, 700, -847],
[-966, 547, -88, -17, -359, -67],
[637, -341, -437, -181, 527, -153],
[-74, 449, -28, 3, 485, 189],
[-997, 658, -224, -948, 702, -807],
[-224, 736, -896, 127, -945, -850],
[-395, -106, 439, -553, -128, 124],
[-841, -445, -758, -572, -489, 212],
[633, -327, 13, -512, 952, 771],
[-940, -171, -6, -46, -923, -425],
[-142, -442, -817, -998, 843, -695],
[340, 847, -137, -920, -988, -658],
[-653, 217, -679, -257, 651, -719],
[-294, 365, -41, 342, 74, -892],
[690, -236, -541, 494, 408, -516],
[180, -807, 225, 790, 494, 59],
[707, 605, -246, 656, 284, 271],
[65, 294, 152, 824, 442, -442],
[-321, 781, -540, 341, 316, 415],
[420, 371, -2, 545, 995, 248],
[56, -191, -604, 971, 615, 449],
[-981, -31, 510, 592, -390, -362],
[-317, -968, 913, 365, 97, 508],
[832, 63, -864, -510, 86, 202],
[-483, 456, -636, 340, -310, 676],
[981, -847, 751, -508, -962, -31],
[-157, 99, 73, 797, 63, -172],
[220, 858, 872, 924, 866, -381],
[996, -169, 805, 321, -164, 971],
[896, 11, -625, -973, -782, 76],
[578, -280, 730, -729, 307, -905],
[-580, -749, 719, -698, 967, 603],
[-821, 874, -103, -623, 662, -491],
[-763, 117, 661, -644, 672, -607],
[592, 787, -798, -169, -298, 690],
[296, 644, -526, -762, -447, 665],
[534, -818, 852, -120, 57, -379],
[-986, -549, -329, 294, 954, 258],
[-133, 352, -660, -77, 904, -356],
[748, 343, 215, 500, 317, -277],
[311, 7, 910, -896, -809, 795],
[763, -602, -753, 313, -352, 917],
[668, 619, -474, -597, -650, 650],
[-297, 563, -701, -987, 486, -902],
[-461, -740, -657, 233, -482, -328],
[-446, -250, -986, -458, -629, 520],
[542, -49, -327, -469, 257, -947],
[121, -575, -634, -143, -184, 521],
[30, 504, 455, -645, -229, -945],
[-12, -295, 377, 764, 771, 125],
[-686, -133, 225, -25, -376, -143],
[-6, -46, 338, 270, -405, -872],
[-623, -37, 582, 467, 963, 898],
[-804, 869, -477, 420, -475, -303],
[94, 41, -842, -193, -768, 720],
[-656, -918, 415, 645, -357, 460],
[-47, -486, -911, 468, -608, -686],
[-158, 251, 419, -394, -655, -895],
[272, -695, 979, 508, -358, 959],
[-776, 650, -918, -467, -690, -534],
[-85, -309, -626, 167, -366, -429],
[-880, -732, -186, -924, 970, -875],
[517, 645, -274, 962, -804, 544],
[721, 402, 104, 640, 478, -499],
[198, 684, -134, -723, -452, -905],
[-245, 745, 239, 238, -826, 441],
[-217, 206, -32, 462, -981, -895],
[-51, 989, 526, -173, 560, -676],
[-480, -659, -976, -580, -727, 466],
[-996, -90, -995, 158, -239, 642],
[302, 288, -194, -294, 17, 924],
[-943, 969, -326, 114, -500, 103],
[-619, 163, 339, -880, 230, 421],
[-344, -601, -795, 557, 565, -779],
[590, 345, -129, -202, -125, -58],
[-777, -195, 159, 674, 775, 411],
[-939, 312, -665, 810, 121, 855],
[-971, 254, 712, 815, 452, 581],
[442, -9, 327, -750, 61, 757],
[-342, 869, 869, -160, 390, -772],
[620, 601, 565, -169, -69, -183],
[-25, 924, -817, 964, 321, -970],
[-64, -6, -133, 978, 825, -379],
[601, 436, -24, 98, -115, 940],
[-97, 502, 614, -574, 922, 513],
[-125, 262, -946, 695, 99, -220],
[429, -721, 719, -694, 197, -558],
[326, 689, -70, -908, -673, 338],
[-468, -856, -902, -254, -358, 305],
[-358, 530, 542, 355, -253, -47],
[-438, -74, -362, 963, 988, 788],
[137, 717, 467, 622, 319, -380],
[-86, 310, -336, 851, 918, -288],
[721, 395, 646, -53, 255, -425],
[255, 175, 912, 84, -209, 878],
[-632, -485, -400, -357, 991, -608],
[235, -559, 992, -297, 857, -591],
[87, -71, 148, 130, 647, 578],
[-290, -584, -639, -788, -21, 592],
[386, 984, 625, -731, -993, -336],
[-538, 634, -209, -828, -150, -774],
[-754, -387, 607, -781, 976, -199],
[412, -798, -664, 295, 709, -537],
[-412, 932, -880, -232, 561, 852],
[-656, -358, -198, -964, -433, -848],
[-762, -668, -632, 186, -673, -11],
[-876, 237, -282, -312, -83, 682],
[403, 73, -57, -436, -622, 781],
[-587, 873, 798, 976, -39, 329],
[-369, -622, 553, -341, 817, 794],
[-108, -616, 920, -849, -679, 96],
[290, -974, 234, 239, -284, -321],
[-22, 394, -417, -419, 264, 58],
[-473, -551, 69, 923, 591, -228],
[-956, 662, -113, 851, -581, -794],
[-258, -681, 413, -471, -637, -817],
[-866, 926, 992, -653, -7, 794],
[556, -350, 602, 917, 831, -610],
[188, 245, -906, 361, 492, 174],
[-720, 384, -818, 329, 638, -666],
[-246, 846, 890, -325, -59, -850],
[-118, -509, 620, -762, -256, 15],
[-787, -536, -452, -338, -399, 813],
[458, 560, 525, -311, -608, -419],
[494, -811, -825, -127, -812, 894],
[-801, 890, -629, -860, 574, 925],
[-709, -193, -213, 138, -410, -403],
[861, 91, 708, -187, 5, -222],
[789, 646, 777, 154, 90, -49],
[-267, -830, -114, 531, 591, -698],
[-126, -82, 881, -418, 82, 652],
[-894, 130, -726, -935, 393, -815],
[-142, 563, 654, 638, -712, -597],
[-759, 60, -23, 977, 100, -765],
[-305, 595, -570, -809, 482, 762],
[-161, -267, 53, 963, 998, -529],
[-300, -57, 798, 353, 703, 486],
[-990, 696, -764, 699, -565, 719],
[-232, -205, 566, 571, 977, 369],
[740, 865, 151, -817, -204, -293],
[94, 445, -768, 229, 537, -406],
[861, 620, 37, -424, -36, 656],
[390, -369, 952, 733, -464, 569],
[-482, -604, 959, 554, -705, -626],
[-396, -615, -991, 108, 272, -723],
[143, 780, 535, 142, -917, -147],
[138, -629, -217, -908, 905, 115],
[915, 103, -852, 64, -468, -642],
[570, 734, -785, -268, -326, -759],
[738, 531, -332, 586, -779, 24],
[870, 440, -217, 473, -383, 415],
[-296, -333, -330, -142, -924, 950],
[118, 120, -35, -245, -211, -652],
[61, 634, 153, -243, 838, 789],
[726, -582, 210, 105, 983, 537],
[-313, -323, 758, 234, 29, 848],
[-847, -172, -593, 733, -56, 617],
[54, 255, -512, 156, -575, 675],
[-873, -956, -148, 623, 95, 200],
[700, -370, 926, 649, -978, 157],
[-639, -202, 719, 130, 747, 222],
[194, -33, 955, 943, 505, 114],
[-226, -790, 28, -930, 827, 783],
[-392, -74, -28, 714, 218, -612],
[209, 626, -888, -683, -912, 495],
[487, 751, 614, 933, 631, 445],
[-348, -34, -411, -106, 835, 321],
[-689, 872, -29, -800, 312, -542],
[-52, 566, 827, 570, -862, -77],
[471, 992, 309, -402, 389, 912],
[24, 520, -83, -51, 555, 503],
[-265, -317, 283, -970, -472, 690],
[606, 526, 137, 71, -651, 150],
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[253, -756, 262, -888, -778, -214],
[793, -451, 323, -251, -401, -458],
[-396, 619, -651, -287, -668, -781],
[698, 720, -349, 742, -807, 546],
[738, 280, 680, 279, -540, 858],
[-789, 387, 530, -36, -551, -491],
[162, 579, -427, -272, 228, 710],
[689, 356, 917, -580, 729, 217],
[-115, -638, 866, 424, -82, -194],
[411, -338, -917, 172, 227, -29],
[-612, 63, 630, -976, -64, -204],
[-200, 911, 583, -571, 682, -579],
[91, 298, 396, -183, 788, -955],
[141, -873, -277, 149, -396, 916],
[321, 958, -136, 573, 541, -777],
[797, -909, -469, -877, 988, -653],
[784, -198, 129, 883, -203, 399],
[-68, -810, 223, -423, -467, -512],
[531, -445, -603, -997, -841, 641],
[-274, -242, 174, 261, -636, -158],
[-574, 494, -796, -798, -798, 99],
[95, -82, -613, -954, -753, 986],
[-883, -448, -864, -401, 938, -392],
[913, 930, -542, -988, 310, 410],
[506, -99, 43, 512, 790, -222],
[724, 31, 49, -950, 260, -134],
[-287, -947, -234, -700, 56, 588],
[-33, 782, -144, 948, 105, -791],
[548, -546, -652, -293, 881, -520],
[691, -91, 76, 991, -631, 742],
[-520, -429, -244, -296, 724, -48],
[778, 646, 377, 50, -188, 56],
[-895, -507, -898, -165, -674, 652],
[654, 584, -634, 177, -349, -620],
[114, -980, 355, 62, 182, 975],
[516, 9, -442, -298, 274, -579],
[-238, 262, -431, -896, 506, -850],
[47, 748, 846, 821, -537, -293],
[839, 726, 593, 285, -297, 840],
[634, -486, 468, -304, -887, -567],
[-864, 914, 296, -124, 335, 233],
[88, -253, -523, -956, -554, 803],
[-587, 417, 281, -62, -409, -363],
[-136, -39, -292, -768, -264, 876],
[-127, 506, -891, -331, -744, -430],
[778, 584, -750, -129, -479, -94],
[-876, -771, -987, -757, 180, -641],
[-777, -694, 411, -87, 329, 190],
[-347, -999, -882, 158, -754, 232],
[-105, 918, 188, 237, -110, -591],
[-209, 703, -838, 77, 838, 909],
[-995, -339, -762, 750, 860, 472],
[185, 271, -289, 173, 811, -300],
[2, 65, -656, -22, 36, -139],
[765, -210, 883, 974, 961, -905],
[-212, 295, -615, -840, 77, 474],
[211, -910, -440, 703, -11, 859],
[-559, -4, -196, 841, -277, 969],
[-73, -159, -887, 126, 978, -371],
[-569, 633, -423, -33, 512, -393],
[503, 143, -383, -109, -649, -998],
[-663, 339, -317, -523, -2, 596],
[690, -380, 570, 378, -652, 132],
[72, -744, -930, 399, -525, 935],
[865, -983, 115, 37, 995, 826],
[594, -621, -872, 443, 188, -241],
[-1000, 291, 754, 234, -435, -869],
[-868, 901, 654, -907, 59, 181],
[-868, -793, -431, 596, -446, -564],
[900, -944, -680, -796, 902, -366],
[331, 430, 943, 853, -851, -942],
[315, -538, -354, -909, 139, 721],
[170, -884, -225, -818, -808, -657],
[-279, -34, -533, -871, -972, 552],
[691, -986, -800, -950, 654, -747],
[603, 988, 899, 841, -630, 591],
[876, -949, 809, 562, 602, -536],
[-693, 363, -189, 495, 738, -1000],
[-383, 431, -633, 297, 665, 959],
[-740, 686, -207, -803, 188, -520],
[-820, 226, 31, -339, 10, 121],
[-312, -844, 624, -516, 483, 621],
[-822, -529, 69, -278, 800, 328],
[834, -82, -759, 420, 811, -264],
[-960, -240, -921, 561, 173, 46],
[-324, 909, -790, -814, -2, -785],
[976, 334, -290, -891, 704, -581],
[150, -798, 689, -823, 237, -639],
[-551, -320, 876, -502, -622, -628],
[-136, 845, 904, 595, -702, -261],
[-857, -377, -522, -101, -943, -805],
[-682, -787, -888, -459, -752, -985],
[-571, -81, 623, -133, 447, 643],
[-375, -158, 72, -387, -324, -696],
[-660, -650, 340, 188, 569, 526],
[727, -218, 16, -7, -595, -988],
[-966, -684, 802, -783, -272, -194],
[115, -566, -888, 47, 712, 180],
[-237, -69, 45, -272, 981, -812],
[48, 897, 439, 417, 50, 325],
[348, 616, 180, 254, 104, -784],
[-730, 811, -548, 612, -736, 790],
[138, -810, 123, 930, 65, 865],
[-768, -299, -49, -895, -692, -418],
[487, -531, 802, -159, -12, 634],
[808, -179, 552, -73, 470, 717],
[720, -644, 886, -141, 625, 144],
[-485, -505, -347, -244, -916, 66],
[600, -565, 995, -5, 324, 227],
[-771, -35, 904, -482, 753, -303],
[-701, 65, 426, -763, -504, -479],
[409, 733, -823, 475, 64, 718],
[865, 975, 368, 893, -413, -433],
[812, -597, -970, 819, 813, 624],
[193, -642, -381, -560, 545, 398],
[711, 28, -316, 771, 717, -865],
[-509, 462, 809, -136, 786, 635],
[618, -49, 484, 169, 635, 547],
[-747, 685, -882, -496, -332, 82],
[-501, -851, 870, 563, 290, 570],
[-279, -829, -509, 397, 457, 816],
[-508, 80, 850, -188, 483, -326],
[860, -100, 360, 119, -205, 787],
[-870, 21, -39, -827, -185, 932],
[826, 284, -136, -866, -330, -97],
[-944, -82, 745, 899, -97, 365],
[929, 262, 564, 632, -115, 632],
[244, -276, 713, 330, -897, -214],
[-890, -109, 664, 876, -974, -907],
[716, 249, 816, 489, 723, 141],
[-96, -560, -272, 45, -70, 645],
[762, -503, 414, -828, -254, -646],
[909, -13, 903, -422, -344, -10],
[658, -486, 743, 545, 50, 674],
[-241, 507, -367, 18, -48, -241],
[886, -268, 884, -762, 120, -486],
[-412, -528, 879, -647, 223, -393],
[851, 810, 234, 937, -726, 797],
[-999, 942, 839, -134, -996, -189],
[100, 979, -527, -521, 378, 800],
[544, -844, -832, -530, -77, -641],
[43, 889, 31, 442, -934, -503],
[-330, -370, -309, -439, 173, 547],
[169, 945, 62, -753, -542, -597],
[208, 751, -372, -647, -520, 70],
[765, -840, 907, -257, 379, 918],
[334, -135, -689, 730, -427, 618],
[137, -508, 66, -695, 78, 169],
[-962, -123, 400, -417, 151, 969],
[328, 689, 666, 427, -555, -642],
[-907, 343, 605, -341, -647, 582],
[-667, -363, -571, 818, -265, -399],
[525, -938, 904, 898, 725, 692],
[-176, -802, -858, -9, 780, 275],
[580, 170, -740, 287, 691, -97],
[365, 557, -375, 361, -288, 859],
[193, 737, 842, -808, 520, 282],
[-871, 65, -799, 836, 179, -720],
[958, -144, 744, -789, 797, -48],
[122, 582, 662, 912, 68, 757],
[595, 241, -801, 513, 388, 186],
[-103, -677, -259, -731, -281, -857],
[921, 319, -696, 683, -88, -997],
[775, 200, 78, 858, 648, 768],
[316, 821, -763, 68, -290, -741],
[564, 664, 691, 504, 760, 787],
[694, -119, 973, -385, 309, -760],
[777, -947, -57, 990, 74, 19],
[971, 626, -496, -781, -602, -239],
[-651, 433, 11, -339, 939, 294],
[-965, -728, 560, 569, -708, -247],
]
cnt = 0
for x1, y1, x2, y2, x3, y3 in tri_coods:
r12 = x1 * y2 - x2 * y1 # rotatianl sense is defined by the sign (+ or -) of this.
# actually r12/|X1||X2| is the sin value of `signed' angle theta12.
r23 = x2 * y3 - x3 * y2
r31 = x3 * y1 - x1 * y3
if (r12 > 0 and r23 > 0 and r31 > 0) or (r12 < 0 and r23 < 0 and r31 < 0):
cnt += 1
print(cnt)
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