example :: [((Int, Int), (Int, Int))]
example = [
        ((0,9), (5,9)),
        ((8,0), (0,8)),
        ((9,4), (3,4)),
        ((2,2), (2,1)),
        ((7,0), (7,4)),
        ((6,4), (2,0)),
        ((0,9), (2,9)),
        ((3,4), (1,4)),
        ((0,0), (8,8)),
        ((5,5), (8,2))
    ]

isHorizontalOrVertical :: ((Int, Int), (Int, Int)) -> Bool
isHorizontalOrVertical ((x1, y1), (x2, y2)) = x1 == x2  || y1 == y2

atPoint (x,y) p =  minX p <= x && x <= maxX p && minY p <= y && y <= maxY p

minX ((x1, _), (x2, _)) = min x1 x2
minY ((_, y1), (_, y2)) = min y1 y2


maxX ((x1, _), (x2, _)) = max x1 x2
maxY ((_, y1), (_, y2)) = max y1 y2


bounds :: (Ord b, Ord a) => [((a, b), (a, b))] -> ((a, b), (a, b))
bounds input = ((x0, y0), (x1, y1))
    where
        x0 = minimum $ map minX input
        y0 = minimum $ map minY input
        x1 = maximum $ map maxX input
        y1 = maximum $ map maxY input

grid ((x0, y0), (x1, y1)) = [ (x, y) | x <- [x0..x1], y <- [y0..y1] ]

counts input = length $ filter (>= 2) intersectionCounts
    where
        intersectionCounts = map (\pos -> length $ filter (atPoint pos) input) gridIndexes
        gridIndexes = grid $ bounds input


inputs :: [((Int, Int), (Int, Int))]
inputs = [
    ((911, 808), (324, 221)),
    ((161, 890), (808, 243)),
    ((174, 59), (174, 760)),
    ((983, 983), (10, 10)),
    ((321, 12), (870, 12)),
    ((66, 936), (941, 61)),
    ((670, 141), (670, 550)),
    ((783, 935), (496, 648)),
    ((973, 651), (635, 989)),
    ((535, 47), (535, 154)),
    ((355, 183), (754, 582)),
    ((172, 111), (892, 111)),
    ((353, 66), (907, 620)),
    ((741, 960), (741, 805)),
    ((113, 895), (946, 895)),
    ((777, 280), (563, 280)),
    ((679, 815), (626, 815)),
    ((651, 848), (651, 673)),
    ((205, 834), (205, 599)),
    ((895, 118), (82, 931)),
    ((685, 303), (93, 895)),
    ((973, 38), (62, 949)),
    ((867, 23), (867, 300)),
    ((784, 947), (784, 47)),
    ((96, 168), (755, 827)),
    ((909, 321), (909, 716)),
    ((59, 881), (692, 881)),
    ((964, 19), (69, 914)),
    ((752, 869), (67, 184)),
    ((974, 877), (138, 41)),
    ((432, 389), (137, 684)),
    ((458, 822), (458, 402)),
    ((818, 852), (308, 342)),
    ((882, 484), (441, 925)),
    ((82, 959), (976, 65)),
    ((117, 487), (117, 429)),
    ((214, 673), (429, 673)),
    ((72, 955), (72, 829)),
    ((587, 109), (587, 368)),
    ((576, 17), (576, 872)),
    ((685, 102), (685, 905)),
    ((563, 394), (716, 394)),
    ((966, 145), (150, 961)),
    ((555, 582), (555, 385)),
    ((453, 31), (453, 207)),
    ((639, 815), (547, 723)),
    ((431, 869), (431, 811)),
    ((646, 938), (599, 938)),
    ((215, 513), (900, 513)),
    ((809, 82), (798, 82)),
    ((768, 344), (244, 868)),
    ((39, 962), (39, 601)),
    ((675, 186), (61, 186)),
    ((861, 967), (28, 967)),
    ((860, 550), (538, 550)),
    ((283, 740), (571, 740)),
    ((72, 297), (72, 645)),
    ((727, 801), (727, 526)),
    ((799, 519), (799, 497)),
    ((915, 24), (174, 765)),
    ((795, 943), (136, 943)),
    ((518, 971), (599, 971)),
    ((594, 676), (594, 461)),
    ((850, 799), (363, 799)),
    ((958, 575), (958, 231)),
    ((752, 576), (398, 576)),
    ((891, 433), (398, 433)),
    ((524, 126), (397, 126)),
    ((10, 890), (796, 104)),
    ((57, 228), (168, 228)),
    ((168, 521), (338, 691)),
    ((230, 83), (777, 83)),
    ((865, 677), (640, 452)),
    ((866, 821), (825, 821)),
    ((17, 143), (17, 596)),
    ((113, 916), (113, 601)),
    ((268, 187), (551, 470)),
    ((794, 167), (220, 167)),
    ((459, 17), (459, 931)),
    ((211, 31), (526, 31)),
    ((680, 57), (756, 57)),
    ((926, 190), (926, 800)),
    ((85, 284), (63, 284)),
    ((44, 988), (44, 701)),
    ((110, 941), (176, 941)),
    ((480, 163), (480, 112)),
    ((574, 538), (574, 371)),
    ((584, 473), (69, 473)),
    ((303, 621), (303, 380)),
    ((762, 652), (762, 89)),
    ((286, 195), (276, 185)),
    ((957, 87), (217, 827)),
    ((561, 858), (561, 437)),
    ((384, 55), (81, 55)),
    ((19, 977), (981, 15)),
    ((454, 747), (938, 263)),
    ((425, 836), (425, 617)),
    ((860, 135), (775, 50)),
    ((633, 131), (633, 651)),
    ((904, 912), (242, 250)),
    ((880, 177), (480, 577)),
    ((470, 162), (964, 656)),
    ((585, 376), (585, 470)),
    ((696, 760), (594, 862)),
    ((534, 225), (534, 717)),
    ((258, 816), (258, 847)),
    ((990, 244), (990, 93)),
    ((463, 462), (463, 533)),
    ((434, 928), (537, 825)),
    ((813, 734), (533, 734)),
    ((498, 673), (395, 673)),
    ((564, 312), (55, 312)),
    ((280, 550), (939, 550)),
    ((591, 247), (396, 52)),
    ((127, 516), (127, 235)),
    ((850, 425), (552, 127)),
    ((894, 428), (894, 598)),
    ((366, 960), (592, 960)),
    ((579, 488), (170, 488)),
    ((775, 92), (775, 586)),
    ((49, 909), (930, 28)),
    ((856, 113), (284, 685)),
    ((263, 175), (120, 175)),
    ((332, 592), (276, 592)),
    ((920, 157), (141, 157)),
    ((349, 776), (316, 776)),
    ((187, 863), (279, 863)),
    ((218, 872), (83, 872)),
    ((465, 430), (410, 430)),
    ((710, 218), (857, 218)),
    ((797, 314), (184, 314)),
    ((387, 327), (49, 665)),
    ((950, 812), (205, 67)),
    ((803, 133), (803, 682)),
    ((125, 972), (545, 552)),
    ((353, 901), (840, 414)),
    ((936, 843), (202, 109)),
    ((11, 904), (856, 59)),
    ((725, 757), (954, 986)),
    ((227, 697), (345, 697)),
    ((187, 520), (187, 441)),
    ((860, 262), (135, 987)),
    ((700, 95), (976, 371)),
    ((86, 946), (869, 163)),
    ((898, 806), (461, 806)),
    ((717, 796), (717, 195)),
    ((882, 127), (835, 127)),
    ((133, 48), (133, 191)),
    ((521, 51), (521, 927)),
    ((384, 806), (957, 233)),
    ((570, 139), (570, 842)),
    ((949, 819), (949, 350)),
    ((592, 230), (283, 230)),
    ((315, 856), (741, 856)),
    ((870, 674), (549, 353)),
    ((857, 306), (857, 889)),
    ((428, 217), (267, 217)),
    ((47, 93), (898, 944)),
    ((636, 238), (665, 238)),
    ((202, 910), (202, 737)),
    ((246, 432), (617, 803)),
    ((985, 24), (48, 961)),
    ((965, 876), (956, 867)),
    ((618, 650), (810, 458)),
    ((292, 356), (575, 356)),
    ((394, 585), (910, 585)),
    ((137, 453), (137, 178)),
    ((509, 737), (509, 665)),
    ((193, 350), (531, 688)),
    ((805, 219), (107, 219)),
    ((975, 506), (907, 506)),
    ((435, 303), (435, 380)),
    ((344, 83), (344, 224)),
    ((47, 66), (47, 115)),
    ((570, 516), (857, 516)),
    ((162, 91), (926, 91)),
    ((759, 417), (759, 460)),
    ((445, 942), (445, 699)),
    ((421, 340), (421, 743)),
    ((590, 590), (434, 434)),
    ((453, 38), (453, 327)),
    ((865, 134), (865, 773)),
    ((842, 609), (18, 609)),
    ((662, 282), (62, 882)),
    ((489, 32), (344, 32)),
    ((135, 496), (93, 454)),
    ((552, 211), (421, 211)),
    ((620, 678), (642, 678)),
    ((782, 158), (585, 355)),
    ((733, 509), (733, 574)),
    ((932, 383), (369, 946)),
    ((843, 705), (843, 725)),
    ((747, 414), (676, 343)),
    ((294, 218), (962, 886)),
    ((844, 175), (844, 420)),
    ((255, 489), (531, 213)),
    ((555, 532), (821, 532)),
    ((533, 15), (533, 161)),
    ((631, 778), (631, 401)),
    ((75, 282), (468, 282)),
    ((903, 838), (903, 957)),
    ((46, 293), (543, 790)),
    ((30, 834), (30, 948)),
    ((591, 720), (591, 965)),
    ((624, 36), (339, 36)),
    ((425, 323), (425, 442)),
    ((234, 939), (234, 963)),
    ((482, 912), (968, 912)),
    ((228, 614), (189, 614)),
    ((969, 472), (969, 692)),
    ((871, 494), (871, 172)),
    ((101, 624), (848, 624)),
    ((424, 918), (69, 563)),
    ((929, 671), (93, 671)),
    ((81, 187), (707, 813)),
    ((348, 923), (348, 924)),
    ((921, 524), (921, 828)),
    ((678, 454), (678, 364)),
    ((904, 227), (904, 596)),
    ((163, 344), (609, 790)),
    ((206, 180), (206, 59)),
    ((145, 519), (145, 717)),
    ((317, 679), (317, 417)),
    ((503, 724), (221, 724)),
    ((353, 448), (413, 448)),
    ((363, 643), (837, 643)),
    ((594, 54), (359, 54)),
    ((866, 117), (45, 938)),
    ((939, 210), (284, 865)),
    ((410, 556), (410, 801)),
    ((905, 111), (673, 111)),
    ((983, 167), (574, 167)),
    ((595, 758), (97, 758)),
    ((785, 10), (437, 10)),
    ((517, 414), (517, 734)),
    ((691, 567), (186, 62)),
    ((842, 51), (31, 862)),
    ((36, 199), (282, 199)),
    ((864, 758), (864, 610)),
    ((639, 918), (951, 918)),
    ((245, 516), (245, 474)),
    ((951, 203), (557, 203)),
    ((176, 728), (176, 171)),
    ((322, 217), (387, 217)),
    ((149, 208), (836, 895)),
    ((661, 298), (609, 298)),
    ((46, 47), (981, 982)),
    ((769, 45), (769, 610)),
    ((988, 932), (988, 459)),
    ((901, 97), (901, 908)),
    ((195, 395), (121, 395)),
    ((197, 403), (327, 533)),
    ((159, 456), (857, 456)),
    ((480, 981), (881, 580)),
    ((86, 958), (962, 82)),
    ((375, 198), (763, 198)),
    ((950, 381), (341, 381)),
    ((504, 679), (504, 598)),
    ((756, 659), (680, 583)),
    ((146, 328), (886, 328)),
    ((930, 412), (492, 850)),
    ((954, 54), (954, 940)),
    ((790, 498), (790, 305)),
    ((83, 270), (83, 242)),
    ((939, 268), (939, 563)),
    ((423, 756), (916, 263)),
    ((583, 756), (583, 34)),
    ((957, 639), (614, 639)),
    ((484, 523), (521, 560)),
    ((497, 809), (497, 419)),
    ((76, 17), (979, 920)),
    ((49, 39), (943, 933)),
    ((110, 289), (110, 247)),
    ((874, 868), (874, 172)),
    ((576, 127), (53, 650)),
    ((871, 879), (12, 20)),
    ((436, 711), (592, 711)),
    ((132, 285), (225, 285)),
    ((245, 147), (514, 147)),
    ((158, 882), (956, 84)),
    ((21, 984), (937, 68)),
    ((42, 275), (219, 275)),
    ((877, 143), (889, 143)),
    ((593, 841), (508, 756)),
    ((414, 289), (132, 289)),
    ((687, 655), (767, 655)),
    ((453, 981), (459, 987)),
    ((635, 433), (635, 324)),
    ((671, 347), (170, 848)),
    ((412, 579), (915, 579)),
    ((269, 677), (269, 596)),
    ((587, 121), (367, 341)),
    ((153, 883), (153, 709)),
    ((524, 580), (508, 580)),
    ((541, 232), (651, 232)),
    ((93, 948), (284, 757)),
    ((168, 745), (872, 41)),
    ((831, 657), (925, 563)),
    ((908, 389), (442, 389)),
    ((462, 445), (234, 445)),
    ((735, 493), (895, 493)),
    ((274, 624), (296, 646)),
    ((153, 130), (153, 160)),
    ((466, 214), (466, 769)),
    ((474, 499), (686, 711)),
    ((540, 428), (788, 676)),
    ((858, 215), (959, 215)),
    ((788, 91), (788, 410)),
    ((552, 505), (988, 505)),
    ((978, 312), (978, 202)),
    ((108, 321), (616, 829)),
    ((903, 359), (903, 770)),
    ((480, 331), (480, 769)),
    ((503, 842), (34, 842)),
    ((613, 732), (323, 442)),
    ((767, 949), (654, 949)),
    ((514, 589), (386, 589)),
    ((38, 554), (284, 308)),
    ((689, 268), (689, 711)),
    ((860, 66), (190, 736)),
    ((253, 865), (622, 865)),
    ((87, 658), (698, 47)),
    ((506, 892), (829, 569)),
    ((680, 910), (594, 824)),
    ((824, 603), (958, 603)),
    ((576, 802), (562, 802)),
    ((67, 27), (67, 489)),
    ((969, 461), (517, 913)),
    ((674, 763), (674, 226)),
    ((223, 955), (218, 955)),
    ((147, 540), (569, 962)),
    ((455, 703), (596, 703)),
    ((746, 899), (746, 403)),
    ((516, 476), (756, 476)),
    ((897, 674), (373, 150)),
    ((120, 395), (120, 49)),
    ((722, 443), (722, 244)),
    ((724, 924), (724, 39)),
    ((809, 930), (109, 930)),
    ((822, 816), (874, 816)),
    ((796, 539), (895, 539)),
    ((340, 88), (560, 88)),
    ((223, 158), (593, 158)),
    ((779, 977), (856, 900)),
    ((617, 461), (973, 817)),
    ((515, 62), (515, 140)),
    ((12, 586), (724, 586)),
    ((870, 50), (391, 50)),
    ((308, 123), (308, 696)),
    ((119, 164), (863, 908)),
    ((755, 599), (448, 599)),
    ((129, 526), (633, 526)),
    ((478, 668), (102, 668)),
    ((237, 637), (237, 743)),
    ((270, 102), (72, 300)),
    ((115, 470), (115, 427)),
    ((948, 233), (948, 731)),
    ((983, 135), (468, 650)),
    ((748, 439), (748, 642)),
    ((62, 862), (352, 572)),
    ((765, 901), (660, 901)),
    ((917, 807), (917, 587)),
    ((55, 81), (116, 81)),
    ((954, 972), (102, 120)),
    ((340, 503), (294, 549)),
    ((970, 661), (522, 213)),
    ((618, 92), (618, 247)),
    ((688, 965), (965, 965)),
    ((94, 241), (94, 292)),
    ((15, 132), (15, 492)),
    ((979, 927), (488, 927)),
    ((509, 26), (984, 26)),
    ((840, 530), (840, 95)),
    ((55, 956), (849, 162)),
    ((297, 297), (297, 472)),
    ((338, 780), (369, 780)),
    ((487, 292), (37, 292)),
    ((122, 117), (206, 201)),
    ((66, 807), (564, 309)),
    ((643, 242), (906, 242)),
    ((909, 833), (909, 441)),
    ((129, 128), (818, 817)),
    ((406, 42), (406, 297)),
    ((53, 20), (967, 934)),
    ((235, 285), (601, 285)),
    ((275, 625), (275, 539)),
    ((199, 732), (430, 963)),
    ((639, 187), (639, 265)),
    ((549, 740), (549, 824)),
    ((603, 140), (603, 748)),
    ((35, 455), (176, 455)),
    ((888, 611), (888, 271)),
    ((134, 154), (484, 154)),
    ((694, 820), (694, 814)),
    ((535, 584), (187, 932)),
    ((642, 510), (642, 249)),
    ((191, 886), (268, 886)),
    ((918, 353), (881, 390)),
    ((977, 13), (343, 13)),
    ((380, 243), (271, 134)),
    ((410, 758), (410, 670)),
    ((613, 551), (519, 645)),
    ((963, 84), (124, 923)),
    ((702, 252), (821, 252)),
    ((405, 237), (405, 22)),
    ((21, 139), (21, 510)),
    ((548, 499), (132, 499)),
    ((196, 104), (196, 680)),
    ((739, 145), (476, 145)),
    ((751, 746), (91, 746)),
    ((975, 628), (975, 847)),
    ((935, 520), (935, 450)),
    ((803, 372), (803, 393)),
    ((872, 77), (872, 373)),
    ((339, 130), (339, 103)),
    ((226, 886), (226, 45)),
    ((794, 647), (794, 257)),
    ((90, 922), (889, 123)),
    ((615, 971), (615, 574)),
    ((26, 278), (26, 719)),
    ((838, 88), (806, 88)),
    ((263, 691), (804, 150)),
    ((309, 721), (910, 721)),
    ((510, 496), (960, 946)),
    ((195, 236), (46, 236)),
    ((610, 143), (610, 610)),
    ((891, 412), (891, 268)),
    ((714, 21), (156, 579)),
    ((320, 935), (320, 96)),
    ((240, 782), (449, 782)),
    ((754, 472), (48, 472)),
    ((105, 481), (529, 57)),
    ((451, 301), (451, 965)),
    ((796, 638), (796, 185)),
    ((908, 553), (771, 553)),
    ((98, 543), (490, 935)),
    ((481, 159), (762, 159)),
    ((593, 527), (419, 353)),
    ((86, 391), (216, 521)),
    ((260, 716), (42, 716)),
    ((734, 538), (375, 179)),
    ((24, 974), (975, 23)),
    ((402, 466), (787, 851)),
    ((344, 409), (262, 327)),
    ((803, 443), (685, 443)),
    ((986, 152), (249, 152)),
    ((125, 738), (90, 773)),
    ((184, 772), (184, 746)),
    ((729, 829), (729, 340)),
    ((226, 527), (226, 375)),
    ((936, 231), (222, 945)),
    ((254, 333), (254, 167)),
    ((451, 234), (451, 273)),
    ((915, 790), (568, 443)),
    ((869, 794), (504, 429)),
    ((11, 878), (836, 53)),
    ((821, 231), (522, 530)),
    ((285, 419), (732, 866)),
    ((191, 272), (191, 679)),
    ((41, 651), (225, 651)),
    ((30, 13), (879, 862)),
    ((980, 488), (20, 488)),
    ((27, 187), (27, 348)),
    ((53, 238), (53, 514)),
    ((778, 306), (379, 705)),
    ((425, 399), (425, 60)),
    ((162, 859), (57, 859)),
    ((652, 926), (652, 589)),
    ((962, 489), (555, 896)),
    ((197, 378), (436, 617)),
    ((310, 190), (310, 760)),
    ((678, 20), (678, 713)),
    ((390, 653), (985, 58)),
    ((938, 351), (656, 69)),
    ((881, 39), (18, 902)),
    ((313, 681), (323, 681)),
    ((910, 907), (288, 907)),
    ((739, 977), (739, 132)),
    ((856, 479), (154, 479)),
    ((893, 785), (761, 785)),
    ((405, 247), (405, 901)),
    ((58, 933), (808, 183)),
    ((643, 156), (676, 189)),
    ((149, 773), (357, 773)),
    ((479, 518), (434, 518)),
    ((389, 518), (556, 685)),
    ((858, 449), (533, 774)),
    ((503, 133), (409, 133)),
    ((340, 315), (219, 194)),
    ((183, 701), (183, 242)),
    ((810, 151), (195, 151)),
    ((446, 686), (446, 912)),
    ((968, 482), (49, 482)),
    ((203, 20), (203, 667)),
    ((493, 516), (647, 516)),
    ((900, 91), (634, 91)),
    ((660, 554), (119, 13)),
    ((964, 864), (964, 919)),
    ((871, 293), (344, 293)),
    ((895, 258), (972, 258))
    ]

{-
5167


-}