main.nr

use dep::noir_ml::{layers::fc, activations::relu, utils::arg_max};

global w1: [Field; 15680] = [-267, 19159, -29394, -26284, -13756, 9577, -708, 28317, -3169, 9450, -10793, -7020, -34045, -22046, -13115, 1390, 14119, 21429, -24212, -15552, 12972, 29657, -7350, 26725, -5757, 3779, 32338, -33131, -22483, -9042, -13921, 30857, -23149, -16440, -24951, -33449, -21161, 30578, 11180, 7359, -1788, -18012, 8128, -27621, 4438, -12671, 20070, 18006, -37082, -11025, 22841, 35505, 14174, 4825, 23946, -21029, 6655, -27689, -24753, -18449, 16160, 14810, -17745, 15311, 22137, 333, 14540, -58372, -56753, 20403, 24466, 57751, 131116, 27105, -7368, -44437, -22185, -44567, 1051, -22975, -33418, 31732, 27156, -35626, 6685, -6016, -5758, -16324, 13901, -13883, 29549, 50535, 91305, 122192, 115148, 89178, 61824, 102700, 51130, 62848, 141049, -3185, -19652, -116128, -63182, -37779, -58373, -27748, -2246, 6707, -14994, 21192, -21734, 32474, 25595, -29576, 4666, 36827, 78088, 213245, 270294, 265520, 233464, 236996, 143223, 121937, 105148, 18853, 106604, -13418, 92360, -78963, -124897, -129792, -104383, -107131, -31795, -1339, 7388, 22181, 33830, 22709, 34270, 6525, -31283, 50629, 165775, 207621, 128114, 139355, 144347, 115373, 183001, 265601, 174343, 119485, 128453, 84277, 133582, 153511, 56632, 10715, -86427, -99554, -5045, 43587, 4865, 12818, -32145, -2412, 34762, 30492, 66595, 34150, -11230, -26965, 174, 93075, 223920, 140276, 141154, 69078, 119398, 244272, 131261, 159537, 70974, 5277, -34709, 30589, -171495, -32372, 10794, 82899, -12697, -23386, -20811, 13103, -6142, 75426, 80345, 16798, -57810, -106994, 84488, 8286, -37441, -48000, 50427, 151798, 158345, 188199, 142476, 30537, 25498, -63253, 47187, -111067, -9675, -107407, -64388, -32720, 39404, -1400, -32678, 23328, 5455, 93767, 174643, 38824, 69679, 25937, 3376, -49601, 151950, -10668, 179001, 191258, 237398, 120354, -137351, 33262, 69674, 184647, 103956, 84436, 98669, -167292, -96097, -51136, 5481, 5947, 30750, -21903, 11591, 136980, 174633, 117979, 74206, 15318, 38276, 124310, 88225, 144283, 105579, 94646, 136764, 103974, 6120, 135543, 26610, 13675, 119411, 71891, 31207, -78567, -116330, -22720, 39277, 17190, 2831, -44528, -10554, 183927, 187021, 90018, 161261, 36106, 4735, -99396, -136882, -171651, -280085, -390543, -137323, -57930, 357447, 43090, 227263, 182344, 44582, 178668, 155596, -23343, -241399, -62307, 24238, 19821, 15079, -33832, -34924, 89621, 83326, -42799, 17507, 44641, -102375, -108553, -200805, -118175, -229311, -228847, 54294, 52126, 99363, -1482, 109585, 141243, 334799, 196509, 143038, -83684, -147928, -58570, -54645, 14313, 26979, 4588, 16047, 24921, -76206, -157777, -189334, -124788, -402997, -185975, -216689, -195337, -55511, -108775, 168201, 37214, 85182, 114114, 98532, 155310, 78365, 30426, -206012, -190553, -162735, -119306, -42186, 28737, 19304, 30748, 19529, -94938, -189493, -309629, -362662, -186959, -222605, -76065, -201364, -99360, -88175, -51, 93586, -100098, 126956, 177285, 84618, 2472, -56930, -258110, -358085, -253734, -211481, -70659, 7225, -5709, -20418, -19570, -37866, -64520, -185634, -340562, -301856, -125609, -83289, -184007, -111090, -151711, -59452, 73407, 171460, 32541, 79483, 66633, 55144, -103989, -112683, -193354, -465747, -379092, -201170, -86041, 16335, 35124, 1819, -22117, -9523, 201, -141873, -222837, -118350, -121515, -47944, -50022, -29371, -6158, -17408, 77585, 40122, 67933, 68051, 3248, 1211, -145727, -147007, -240498, -358921, -204963, -116991, -15601, -37470, 10636, 1629, -32237, 27824, 83125, 2190, -11705, 118403, 77824, -61608, -4363, -13547, 28170, 97085, 4757, 60214, 80269, 37738, 14788, -143116, -184393, -179593, -67078, -92724, -39950, 113189, 37920, 14012, -33808, -30504, 16789, -10620, 173412, 149348, 2194, -81916, 64002, 63552, 123665, -47679, 30556, 86010, 20199, 98807, 19920, -122966, -33556, -97871, -36678, -136485, -2295, 23960, 51454, 122915, 153119, 55615, 33594, 31408, -18176, 22289, 176236, 233492, 14620, -11499, -90053, -162981, -8825, -57400, 15918, 29329, 64187, 58372, 9002, 42384, -57411, 160122, 57817, -42798, 29046, 115095, 58019, 249466, 197209, 78160, 51852, -26960, -26616, -23815, 62259, 97059, -96750, -51378, 98340, -85088, 38460, 115332, -58274, -43169, -85940, -33834, -3581, 99455, 63659, -2253, 42084, 24813, 64584, 56343, 92863, 195364, 178677, 58398, 5293, -34772, -19546, -2690, 119993, 92677, 56985, 169546, 101820, 140239, 1364, 23937, -83124, -105897, -232433, -94994, -70482, -41983, -26691, 12211, 127313, 101464, 61419, -14115, 196741, 191041, 42124, 19105, 13510, 28299, 29087, 24487, 88369, 25659, 58977, 100251, 31570, 4864, -33661, -107527, -64787, -17900, 4568, -192859, -167761, -116643, 15261, 17822, 49700, 63734, 11161, 110371, 67396, 108590, -5554, 6901, 31053, 17910, 5108, 47671, 82039, 79675, 136689, 56680, 94958, 79585, -111567, -27201, -46095, -32885, -121246, 77467, -15681, 8638, -89017, -77469, -107844, -34082, 28728, 38727, 37068, 7084, -6603, -898, 2509, -23155, 34183, -14255, 49725, 22179, -11446, -90742, 26224, -5537, -52185, -107399, -22749, 81244, 65949, 4040, -23228, -62387, -122143, -45254, -164615, -99662, -32842, -25589, 29659, 12072, 4804, -41347, -5147, -6273, 11574, 18316, 19224, 42514, 8510, 39302, 15692, 55688, -72507, -73675, 18280, -62487, 32796, -36245, 79636, 110914, 93009, 8751, -24576, 99994, 48067, 93575, 40264, 52422, -24895, 8376, 5190, -16716, 12436, -31820, -10853, -30646, 5784, 87407, 168227, 171067, 240605, 114014, 91098, 140889, 216351, 186687, 125804, 185804, 260307, 254613, 206908, 280373, 124901, 50572, 23250, -14240, 8411, 33523, -28611, 21614, -18517, -6956, 28349, -11007, -3600, 7650, 151305, 293831, 361027, 443741, 446729, 394312, 407423, 431780, 332627, 372952, 317246, 238857, 182747, 136920, 63386, -3602, 2054, 26807, 30090, 3332, 8112, -15461, 26959, -14861, -24809, 5533, 21930, -29623, 43914, 39485, 2038, 38916, 83269, 61603, 89454, 120885, 68495, 96554, 73961, 56648, -6549, 42536, -20179, 32924, -34275, -31820, 21936, 3733, 2060, -19777, -14981, -10442, -34791, 1856, 6316, -30, 11533, 33888, 9496, -13074, -14698, -21086, -20553, -5373, -6301, 15888, -15266, 28472, -25060, 102, 32104, 35514, -20688, 6362, 4219, -16745, -12339, 9673, -24834, 5893, 15454, -14011, 29795, -293, 23381, 43940, 458, 35730, 16528, 24765, 21733, 14683, -1338, 24152, 17757, 31664, 2963, 14336, -7780, -27547, 16513, 4570, -14303, -12075, 9340, -6458, 23338, 2023, 13491, 16847, -6469, 28458, 53300, 52400, 86565, 129211, 177943, 107925, 51383, 81649, 4704, 100055, 171455, 149710, 65817, 115470, 107347, 43825, 7369, 37384, -15248, -2862, -15639, -4930, 7762, 4068, -6801, -33046, 12308, 25866, 35510, 49306, 150995, 127177, 81610, -20637, 53992, -51969, -27825, 47596, 119577, 118749, -20925, 47401, 179226, 108537, 109909, 44421, 26289, -13241, 16465, -31660, -2268, 9809, 6166, 25633, -7914, -18176, -64661, -45240, -94862, -66130, -134702, -101785, 49403, -72825, -111355, -128778, -56756, -103124, -124576, -121487, -19173, -189509, -185410, -78386, -53180, -38413, 24819, 22844, -32311, 13904, -54621, -24442, -138632, -70946, -87415, 1001, -20996, -122856, -19024, -40093, 83719, 87449, 11163, 182676, 201021, 77430, 13645, 7638, -128624, -169824, -247419, -154575, -32277, -29938, -10479, -29199, -28550, 21004, -288, -62036, -225399, -138798, 88225, 32634, 71993, -47094, -7964, 23456, -149218, -144433, 77711, -31058, -24023, -152401, -148313, 3024, -174478, -67065, -109095, -143496, -47888, -77546, 23431, -10369, -36403, 22953, -33041, -37764, -227778, -100093, -44435, -75161, -44614, -5930, 59562, -20861, -116907, -149132, -65087, -76910, -158191, -64093, -105623, -121239, -88134, 26096, -91338, -205236, -172045, -93876, -24352, -4814, -8552, 5851, -44903, -71194, -174037, -13524, -77034, 30221, 37171, -25187, -113261, 171123, -30272, -122326, -107557, 87648, -138609, -154673, -86650, -110829, -7087, -5021, -4285, -282845, -258960, -72927, -3248, -27280, -13366, -25734, -25695, -51776, -8638, -33014, -104239, -50949, 34114, 37152, -84933, 85101, 128575, -160196, -306961, 4786, -75324, -121263, 58512, -25687, 41694, 17906, -72591, -305056, -256447, -80736, -3369, -14918, -23922, 567, -71896, -23011, 20877, 60614, 26143, 54501, 114580, -1742, 74401, -10096, 3672, -220987, -295925, -156668, 93892, -49753, 17262, -48368, 66965, 7970, 28969, -203751, -351730, -117354, 4255, -14321, 24750, -17396, -16438, -73125, -123441, -12386, -9744, -148577, 71, 44723, 109641, -11038, 28027, -138612, -393463, -77314, -73970, -52183, 46140, -15278, 124333, 28565, 111779, 31603, -153469, -96884, -16969, -5750, -32370, -24606, -4859, -176042, -119141, -70069, -50659, -75133, 83343, -93148, 52364, 80194, 22975, -303971, -306365, -95513, 28954, -102734, -94181, 59488, 116373, 42482, 250634, 259066, -67604, -28012, -32941, 17752, -30376, 23797, -25321, -216709, -82862, 11633, 10167, 38059, 104117, 67062, -43277, -151295, -63100, -163370, -65530, -100425, -10679, -93160, -128121, -17370, 116163, 166242, 310209, 215738, -8782, 5066, 5103, 9722, -2499, -11147, -7800, -71656, -297, 70406, 213596, -45014, -72917, 107269, 162677, 31766, -35834, -46379, -24069, -24459, -45179, -83098, -71454, -46770, 53403, 83345, 234744, 187342, 76818, 49203, -31082, -23624, -23091, -28257, 81655, -5214, -34176, 82974, 204577, 168742, 256682, 239946, 71321, 94495, -72129, 900, -77420, -70693, -5600, -55681, -55088, -44534, 155238, -25278, 24827, 68204, 82315, 56050, 46381, -14080, -13946, 8275, -38321, -92211, -1565, 108438, 36510, 111535, 110109, 161281, 246684, 179978, -77426, 27544, 49787, 37568, -5823, -64369, -41868, 12346, 15370, -103360, -73553, -17226, 147786, 59357, 31019, -33227, 2373, 45613, -94643, -93181, 52573, -35265, -34979, 21003, 157425, 135916, 254520, -38167, -104221, 107299, -30719, 93702, 95421, 989, -68576, 72985, -9300, -44546, -100463, 114917, 184001, 10149, 37224, -9585, -23142, 34721, -33166, -34872, 94272, -36110, 68484, 154284, 148982, 167367, 171169, 124145, -124411, 56003, 51045, 23820, 56254, 30625, -23758, 884, -28309, 22528, -1064, 146254, 145301, 15573, 23548, -35211, -21775, 26223, -72601, -41881, -1627, -43905, 118174, 207854, 27067, 279818, 297782, 52891, -90492, -13309, 66023, 34072, 111020, -77107, 22368, 33693, 36008, 112496, 118257, -10965, 59873, 4955, 31051, -12922, -8705, 38762, -66618, 32762, 222729, -3643, 76700, 60813, -54865, 173894, 225818, 288564, -16070, 98436, 118455, 244, -20013, 1645, 13101, -76928, -29328, 42819, 103349, 26366, 13798, -37891, 22833, -34023, -6179, -3862, -49926, -23679, 33102, 32989, -8406, -36880, 185225, 56215, 127312, 65373, -46184, 19696, 77615, 99482, 113217, 98111, 72489, 16598, 142600, 147834, 160183, 103009, 19192, 29692, -3166, 3092, -24700, -42710, 4902, 65381, 60589, 39743, 29432, 83734, 45033, 71736, 132497, 215661, 157551, -134041, -95955, -75738, -140062, -92583, 68583, 50444, 133032, 109670, 11625, -19175, -41783, 22724, 14579, -16969, -32795, -28045, -38555, -24227, -67880, -41209, -8122, 97152, -868, 6419, 104976, 249219, 146640, 70987, 85980, 116357, -3821, -1495, 57264, 111704, 45687, 40193, -38668, -7537, -43876, 16315, -33462, -8835, -7264, -12612, -39920, -114705, -159722, -162208, -269010, -163584, -84178, -73032, 23446, 84344, 161615, 3180, -85830, 11957, -151781, -234919, -265055, -252825, -205982, -112972, -117335, -20139, 28112, 491, -22135, 34875, 28649, 15406, -34516, 13185, -105712, -104586, -197838, -278046, -434610, -500381, -552428, -667719, -626413, -415532, -316432, -241907, -219768, -192872, -269619, -248663, -208626, -115230, -66403, -30188, 27029, 8149, -5518, -20629, -32703, -10419, -33073, -7510, -45326, -56161, -77669, -37470, -77252, -93187, -71006, -29780, -45346, -145228, -104697, -97988, -43143, -298, -23886, -17060, -66716, -17973, -22165, -11873, 11508, 15798, -1271, 34030, -24719, 13693, 32167, -6210, 28304, 262, -28101, -21549, 9921, -18099, 9412, 34206, 7504, -11907, 8301, -22549, -31754, -26831, -30259, 5119, -16648, -31167, -35106, 19347, -20265, -5962, -29946, -20149, 14899, -33276, -20366, 26776, 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-251727, -79438, 19087, 125391, 59971, 76259, 28733, 49806, 85994, 170392, 179165, -23067, -268022, -217069, 75747, -9917, -42420, 53440, 58138, 174311, 76166, -31739, -31628, -6803, 22946, 925, -34521, -15965, -144003, -140569, -54243, -31991, -45487, -16706, 53842, 38039, 109591, -27527, -2272, 6599, -150342, -279039, -90328, -35453, -66446, -115398, 156890, 170768, 15017, -97819, -26532, 19994, 2991, 16088, -11563, -52289, -77688, -16252, -140668, 17402, -45047, 57908, 188110, -65451, -9503, 67115, 61592, 77330, -312340, -214737, -216242, -202273, -44499, 4760, 92316, 140983, 47617, -172372, -55875, -31726, -19268, -7670, 7692, -73926, 71725, 1318, -175361, -85276, -14925, 156147, 65920, -31427, 21640, 149925, 11180, 47560, -259932, -130295, -33234, -102605, -143691, 79094, 78440, 110180, 54189, -171881, -50651, 14065, -27015, -19838, 540, -42002, -20630, 85665, -46350, -25434, 46294, 58581, -31734, -27261, 20090, 32910, -76905, -78888, -289004, -221803, -130967, -30051, -8901, 92262, 17569, 45695, -94713, -221594, -82403, 44, 29780, 13738, 5179, -67888, -92796, 87630, 185180, -16470, -62580, 141425, 156262, 60184, -12584, -3570, -52101, -281712, -75835, -88830, 32103, -44065, 62796, 72357, -55112, -21715, -93733, -162606, -17148, -41864, -35656, 9156, -35892, -72306, -73055, -71233, 116478, 91463, 2341, 149328, 170025, 3880, -32284, -78298, -63232, 35215, -82001, 73335, -40947, -48377, 57632, -182671, -9289, -97891, -109921, -134103, -57703, 15788, 34936, 29953, -21617, -134558, -123151, -100819, -28675, 13525, 110058, 156563, 114043, 292825, 90565, -8736, -13616, -7674, 79406, -81600, -39590, -30995, -9966, -66637, 26726, 11501, -56436, -48208, -44057, -5718, 11569, -1107, -11253, -89930, -149721, -41259, 23100, 48745, 152917, -3993, 229855, 180108, 194256, 9587, 64015, 76168, -43541, 34061, -67458, -102192, -31832, 14007, -13416, -94672, -54971, -52095, -26183, -3498, -6435, 22521, -35905, -68486, -164233, -49999, -32492, 94986, 39981, 94401, 141930, 182914, 190316, 9188, -14205, -15003, -34094, -60360, -127478, -184027, 56680, 78040, -60148, -149544, -96312, 1233, -3279, -32203, 7570, 10877, 27272, -80272, -127007, 17195, 67193, 168466, -33442, -1257, -28950, -7324, 60755, 36008, 100890, -39022, -92075, 42366, 1606, -66349, -33074, -141284, -152534, -55786, -36871, -21117, 2783, -17613, -16509, -21925, -12475, -58696, -133039, -41917, -3008, 1694, 18551, 38845, 101538, 7379, 264581, 170555, 214632, 132792, 310960, 226053, -151399, -132363, -166716, -201889, -121006, -6909, 8307, 5265, -17273, 1766, 2278, 8995, 22368, -38977, -95145, -252088, -252203, -270354, -105318, 21277, -107634, -5985, 42483, -1859, 63937, -20994, 16461, -83242, 3126, -59194, -73450, -113785, -120143, -61262, -12092, 31107, -31988, 9559, 11248, 18391, -28317, 20431, -25479, -202752, -246582, -256207, -304262, -260403, -208239, -22408, -129168, -221609, -215234, -201859, -178849, -130523, -52405, -51382, -99496, -49221, -34847, -28858, -22839, 35102, -18796, -32390, -33501, -23713, -26591, 30591, 12299, -97713, -77179, -150274, -87941, -156167, -125754, -136852, -133445, -162199, -235715, -138690, -71621, -43749, -47724, -25153, -21053, 21884, 24081, 35779, -9577, -16482, -22646, -10464, -1214, -28784, 17586, -20366, 19780, 14173, 14171, -4777, -29664, 21123, -39957, 35167, 1630, 24680, -17231, -42724, 29717, -8250, 11609, -29644, 16431, 4485, 8432, -33136, -18591, -401, -21501, -14370];
global b1: [Field; 20] = [-887127339840, 357286568, -688299417496, 266051530838, 510404169559, -367371439934, -87618887424, -227530956268, 1281285643578, 551842808723, 767115116119, 86816608906, 151371315122, -193017750978, 420045584440, 727648556232, 69962143898, 307075470686, -226460248232, 389632344246];

global w2: [Field; 200] = [-390918, 663741, -1003359, 769490, -237069, -1497802, -235386, -1355245, 974008, -1088395, -746983, 610130, -1087264, -282890, 743219, -950127, 745972, -481135, -764404, 663408, 518524, -1356668, 646930, -162982, -1107148, -726342, 1651281, 871035, -818552, 929081, 520283, -447047, 768281, -308833, -1171800, -922269, -630291, -828320, -739073, 263864, 773456, 547440, -69828, 747748, 493796, -564768, -516525, 955772, 116544, 1060558, 720003, 554999, -238334, 491156, -210995, -75323, 1026112, -150879, -208433, 3750, 679934, -608980, -505457, 722685, -419604, 572334, -659705, 411768, -355090, 425902, -73732, 612415, 1343595, -310627, -267430, -250328, 924483, -594480, -532952, -689212, -1103675, 458775, -11276, -773987, 620964, 621954, 117987, -1098258, -872139, -1049286, 485643, -1538241, -855578, 346325, -722569, 944574, -615289, 985363, 837967, -512629, -224596, 194527, -385929, 659823, -320190, 541506, -283652, -112487, 767481, -87095, -18047, 571218, 1301168, 565477, 147988, 349987, -228959, -687031, 746807, 523865, -1551080, 649871, 776545, 765067, 632006, -1302211, -333039, -657831, 321211, 751823, 674355, -1049057, -484908, 675448, 629116, -1103406, -913456, 557281, 602855, 485092, 639553, -950100, -384770, -1057958, 511678, 450516, 95435, 926982, 835654, 961750, -438433, 580823, -824253, -1414095, 640789, 1037016, 716627, 1013683, -857723, -704034, 657337, 434253, 675776, 72182, -584001, 496438, -298518, 786675, -692999, -346824, -531933, 509333, -649802, 538473, -318882, -405163, -5743, -767440, 733624, 470744, 485155, -163013, 639452, -600027, 620124, 654232, 199801, -698870, -229029, -1186328, -1300698, 389761, 909429, -673444, 537976, 911341, -922283, 868579, 609785, -601244];
global b2: [Field; 10] = [-183820188045501696, 1192338466644287232, -1316067576408386304, 559926211833953856, 418076992034912128, 50735618919134144, -993632256984710656, -819676637649536128, 484559565782547008, 218293786048889152];

fn main(input: [Field; 784]) -> pub Field {
  let output = input;
  let output = relu(fc(output, w1, b1));
  let output = arg_max(fc(output, w2, b2));
  output
}

////////////////////
//     TESTS      //
////////////////////
#[test]
fn test_main_001() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 474510, 474510, 474510, 474510, 745098, 474510, 745098, 745098, 635294, 854902, 474510, 474510, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 419608, 858824, 976471, 988235, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 988235, 988235, 984314, 941176, 941176, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 905882, 988235, 988235, 988235, 909804, 619608, 854902, 988235, 792157, 992157, 988235, 850980, 929412, 988235, 988235, 988235, 752941, 592157, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 913725, 988235, 988235, 988235, 764706, 121569, 0, 98039, 152941, 74510, 152941, 152941, 98039, 396078, 988235, 988235, 415686, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 729412, 976471, 988235, 988235, 933333, 400000, 82353, 0, 0, 0, 0, 0, 98039, 768627, 988235, 988235, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466667, 854902, 988235, 988235, 988235, 729412, 188235, 0, 0, 0, 90196, 501961, 988235, 988235, 831373, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 749020, 870588, 988235, 988235, 952941, 650980, 74510, 78431, 784314, 988235, 988235, 945098, 380392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 474510, 952941, 988235, 988235, 796078, 800000, 988235, 988235, 952941, 376471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 776471, 988235, 988235, 992157, 988235, 968627, 639216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 815686, 988235, 988235, 992157, 988235, 619608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 474510, 827451, 992157, 992157, 992157, 1000000, 992157, 800000, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 568627, 988235, 988235, 988235, 988235, 764706, 772549, 988235, 988235, 780392, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 839216, 988235, 988235, 988235, 949020, 592157, 47059, 50980, 945098, 988235, 988235, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 890196, 988235, 988235, 988235, 772549, 329412, 0, 0, 0, 772549, 988235, 988235, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 831373, 988235, 988235, 917647, 615686, 66667, 0, 0, 0, 0, 556863, 988235, 988235, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 949020, 988235, 988235, 615686, 0, 0, 0, 0, 0, 211765, 949020, 988235, 988235, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474510, 988235, 988235, 988235, 207843, 0, 109804, 160784, 160784, 435294, 992157, 988235, 988235, 690196, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 956863, 988235, 988235, 701961, 627451, 874510, 988235, 988235, 988235, 992157, 988235, 698039, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 941176, 439216, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 658824, 988235, 988235, 988235, 988235, 988235, 682353, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_002() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 501961, 43137, 0, 0, 0, 0, 94118, 992157, 270588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 925490, 619608, 454902, 0, 0, 0, 0, 176471, 988235, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600000, 988235, 988235, 807843, 98039, 0, 0, 125490, 666667, 988235, 917647, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 941176, 988235, 988235, 588235, 66667, 0, 0, 454902, 992157, 988235, 988235, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 988235, 988235, 988235, 0, 0, 0, 0, 454902, 992157, 988235, 988235, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725490, 992157, 992157, 43137, 19608, 27451, 168627, 945098, 1000000, 992157, 968627, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 721569, 988235, 988235, 796078, 698039, 729412, 113725, 615686, 992157, 988235, 431373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 721569, 988235, 988235, 992157, 988235, 988235, 603922, 596078, 992157, 988235, 670588, 439216, 721569, 482353, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 792157, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 537255, 537255, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 905882, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 454902, 898039, 992157, 988235, 901961, 572549, 454902, 454902, 454902, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 811765, 988235, 901961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 862745, 988235, 901961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 988235, 988235, 529412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 988235, 988235, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 870588, 992157, 745098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 819608, 988235, 537255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 843137, 988235, 741176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 988235, 701961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 988235, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 4);
}

#[test]
fn test_main_003() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 619608, 905882, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 254902, 568627, 568627, 345098, 0, 54902, 831373, 992157, 282353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 145098, 258824, 725490, 992157, 937255, 913725, 992157, 596078, 454902, 992157, 807843, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 870588, 992157, 992157, 937255, 803922, 270588, 145098, 647059, 996078, 992157, 898039, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 901961, 992157, 992157, 482353, 0, 0, 0, 588235, 996078, 811765, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 603922, 992157, 788235, 192157, 0, 466667, 984314, 984314, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 764706, 992157, 929412, 807843, 976471, 992157, 564706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 501961, 921569, 992157, 992157, 992157, 901961, 384314, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 992157, 992157, 992157, 996078, 992157, 937255, 584314, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 992157, 788235, 66667, 294118, 517647, 811765, 992157, 847059, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 901961, 996078, 545098, 0, 0, 0, 70588, 564706, 984314, 862745, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 807843, 992157, 94118, 0, 0, 0, 0, 0, 666667, 992157, 690196, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 509804, 992157, 388235, 0, 0, 0, 0, 0, 90196, 780392, 992157, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270588, 968627, 647059, 643137, 0, 0, 0, 0, 0, 286275, 992157, 458824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 854902, 992157, 992157, 117647, 0, 0, 0, 0, 286275, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 831373, 992157, 874510, 325490, 0, 0, 0, 70588, 850980, 905882, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 980392, 996078, 886275, 309804, 0, 0, 235294, 956863, 866667, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 996078, 992157, 839216, 309804, 0, 286275, 992157, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 992157, 992157, 976471, 788235, 815686, 992157, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 317647, 811765, 992157, 992157, 854902, 360784, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_004() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 203922, 992157, 996078, 835294, 917647, 596078, 596078, 278431, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 988235, 992157, 988235, 992157, 988235, 992157, 988235, 874510, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 717647, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 196078, 278431, 592157, 835294, 988235, 992157, 988235, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 992157, 839216, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 988235, 992157, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 992157, 996078, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 988235, 835294, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 992157, 556863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 992157, 988235, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 913725, 996078, 992157, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 988235, 992157, 831373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 839216, 992157, 996078, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 992157, 988235, 913725, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 992157, 996078, 992157, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 913725, 988235, 992157, 670588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 835294, 1000000, 992157, 878431, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 988235, 992157, 988235, 796078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 992157, 1000000, 992157, 482353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 909804, 992157, 509804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_005() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 905882, 474510, 0, 74510, 643137, 698039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 403922, 196078, 866667, 992157, 635294, 403922, 623529, 992157, 992157, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 231373, 992157, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 992157, 384314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 643137, 992157, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 992157, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 996078, 992157, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 1000000, 996078, 835294, 411765, 384314, 298039, 50980, 878431, 996078, 996078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 996078, 925490, 47059, 0, 0, 0, 435294, 992157, 992157, 666667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 537255, 337255, 0, 0, 0, 278431, 945098, 992157, 941176, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 670588, 992157, 992157, 776471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 996078, 992157, 870588, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 768627, 1000000, 996078, 686275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 956863, 996078, 925490, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 823529, 992157, 996078, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 823529, 992157, 992157, 572549, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 992157, 235294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 231373, 937255, 996078, 996078, 376471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 937255, 992157, 992157, 917647, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 996078, 992157, 992157, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 996078, 980392, 454902, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 996078, 764706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_006() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 772549, 1000000, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 662745, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 552941, 992157, 996078, 992157, 996078, 992157, 996078, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 992157, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 662745, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 662745, 1000000, 992157, 447059, 447059, 776471, 992157, 996078, 992157, 996078, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 992157, 984314, 0, 0, 109804, 768627, 992157, 984314, 992157, 984314, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 992157, 1000000, 329412, 0, 0, 0, 0, 223529, 882353, 996078, 992157, 996078, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 984314, 768627, 109804, 0, 0, 0, 0, 0, 658824, 992157, 984314, 992157, 768627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 662745, 996078, 992157, 662745, 0, 0, 0, 0, 0, 0, 0, 996078, 992157, 996078, 992157, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 992157, 984314, 219608, 0, 0, 0, 0, 0, 0, 0, 545098, 984314, 992157, 984314, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 552941, 992157, 996078, 768627, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 996078, 992157, 662745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 992157, 984314, 992157, 325490, 0, 0, 0, 0, 0, 0, 0, 447059, 772549, 984314, 992157, 984314, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 662745, 996078, 992157, 447059, 0, 0, 0, 0, 0, 0, 223529, 333333, 772549, 996078, 992157, 996078, 992157, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 878431, 992157, 984314, 0, 0, 0, 0, 0, 0, 223529, 878431, 992157, 984314, 992157, 984314, 992157, 541176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 996078, 992157, 223529, 0, 113725, 772549, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 882353, 658824, 772549, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 329412, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 662745, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 768627, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 882353, 996078, 992157, 996078, 992157, 996078, 992157, 662745, 658824, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 545098, 984314, 992157, 541176, 329412, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_007() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 647059, 917647, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 996078, 996078, 905882, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 996078, 996078, 850980, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 839216, 996078, 996078, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 996078, 996078, 894118, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 996078, 996078, 827451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 423529, 996078, 996078, 501961, 0, 39216, 294118, 658824, 513726, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 870588, 996078, 898039, 109804, 39216, 611765, 996078, 996078, 996078, 678431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 996078, 996078, 501961, 39216, 611765, 996078, 996078, 996078, 996078, 905882, 541176, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 996078, 996078, 364706, 172549, 996078, 996078, 819608, 266667, 717647, 996078, 996078, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 886275, 996078, 498039, 305882, 996078, 996078, 619608, 0, 74510, 721569, 996078, 611765, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 584314, 996078, 964706, 925490, 996078, 996078, 266667, 0, 0, 227451, 949020, 996078, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192157, 996078, 996078, 996078, 996078, 996078, 266667, 0, 0, 0, 439216, 996078, 729412, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 996078, 996078, 996078, 996078, 996078, 266667, 0, 0, 0, 58824, 878431, 996078, 262745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 490196, 996078, 996078, 996078, 996078, 447059, 0, 0, 0, 0, 854902, 996078, 580392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 678431, 996078, 996078, 996078, 850980, 290196, 0, 0, 0, 854902, 996078, 949020, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 858824, 1000000, 996078, 996078, 972549, 905882, 509804, 584314, 984314, 996078, 619608, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 858824, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 862745, 996078, 996078, 996078, 996078, 996078, 996078, 623529, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 141176, 509804, 509804, 509804, 509804, 929412, 368627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_008() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 86275, 86275, 86275, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 494118, 662745, 690196, 988235, 988235, 992157, 878431, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 415686, 690196, 964706, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 596078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 650980, 992157, 992157, 992157, 992157, 968627, 827451, 792157, 415686, 415686, 996078, 992157, 909804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 905882, 486275, 207843, 0, 0, 0, 313726, 992157, 988235, 596078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 498039, 494118, 149020, 200000, 0, 0, 0, 0, 23529, 635294, 992157, 988235, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 525490, 988235, 952941, 600000, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 419608, 937255, 988235, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 305882, 960784, 992157, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 988235, 988235, 905882, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 600000, 992157, 988235, 988235, 690196, 152941, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 388235, 662745, 882353, 988235, 992157, 988235, 988235, 988235, 988235, 937255, 662745, 662745, 556863, 250980, 250980, 250980, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 686275, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 839216, 725490, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 992157, 980392, 827451, 486275, 419608, 415686, 415686, 313726, 349020, 419608, 552941, 827451, 827451, 968627, 1000000, 992157, 992157, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 658824, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 207843, 317647, 658824, 658824, 658824, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_009() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 58824, 0, 0, 0, 0, 15686, 529412, 1000000, 709804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 964706, 823529, 396078, 298039, 298039, 454902, 564706, 992157, 992157, 886275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 313726, 984314, 992157, 992157, 992157, 992157, 984314, 972549, 988235, 992157, 878431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 400000, 400000, 788235, 733333, 254902, 0, 658824, 992157, 717647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 764706, 992157, 886275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 992157, 992157, 886275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 992157, 992157, 623529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 835294, 992157, 992157, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 933333, 992157, 992157, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 933333, 992157, 749020, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 956863, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 992157, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 992157, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 992157, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 992157, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 992157, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 992157, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 207843, 968627, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 952941, 992157, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 749020, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_010() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 529412, 603922, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 925490, 996078, 996078, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 698039, 996078, 996078, 996078, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 427451, 945098, 996078, 996078, 996078, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 843137, 701961, 490196, 996078, 996078, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 23529, 231373, 0, 27451, 231373, 15686, 847059, 996078, 933333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 627451, 956863, 247059, 0, 0, 0, 0, 839216, 996078, 952941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 733333, 996078, 501961, 0, 0, 0, 0, 0, 839216, 996078, 952941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 850980, 831373, 427451, 35294, 0, 0, 0, 0, 74510, 874510, 996078, 960784, 125490, 235294, 176471, 188235, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603922, 788235, 282353, 290196, 305882, 305882, 305882, 305882, 415686, 839216, 996078, 996078, 996078, 890196, 996078, 937255, 949020, 800000, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 843137, 937255, 964706, 882353, 925490, 996078, 996078, 996078, 996078, 1000000, 996078, 1000000, 996078, 996078, 996078, 996078, 996078, 996078, 850980, 407843, 0, 0, 0, 0, 0, 0, 0, 0, 525490, 376471, 458824, 90196, 90196, 501961, 552941, 552941, 552941, 447059, 580392, 996078, 996078, 956863, 90196, 90196, 90196, 90196, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 996078, 996078, 952941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 996078, 996078, 898039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 996078, 996078, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 996078, 996078, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 996078, 850980, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 137255, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 4);
}

#[test]
fn test_main_011() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 996078, 831373, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 439216, 996078, 996078, 996078, 811765, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 478431, 380392, 901961, 996078, 960784, 490196, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 960784, 996078, 666667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 882353, 996078, 596078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 996078, 972549, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 898039, 996078, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 686275, 996078, 898039, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 176471, 274510, 376471, 964706, 996078, 898039, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776471, 921569, 960784, 996078, 996078, 827451, 513726, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 831373, 929412, 521569, 180392, 180392, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 996078, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 972549, 772549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 709804, 901961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 545098, 976471, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 674510, 960784, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 996078, 905882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 450980, 807843, 333333, 101961, 215686, 674510, 964706, 960784, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 815686, 996078, 882353, 913725, 996078, 996078, 839216, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 898039, 1000000, 796078, 631373, 368627, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_012() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 729412, 996078, 466667, 0, 19608, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 968627, 992157, 992157, 607843, 0, 725490, 886275, 635294, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 878431, 992157, 992157, 941176, 274510, 0, 839216, 992157, 992157, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 800000, 996078, 505882, 341176, 239216, 0, 0, 62745, 650980, 992157, 992157, 560784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 992157, 670588, 35294, 0, 0, 0, 0, 0, 309804, 992157, 992157, 764706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 537255, 996078, 388235, 0, 0, 0, 0, 0, 0, 541176, 996078, 996078, 1000000, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 505882, 992157, 384314, 0, 0, 0, 0, 0, 274510, 945098, 949020, 972549, 996078, 529412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 992157, 501961, 0, 0, 0, 0, 541176, 945098, 992157, 341176, 764706, 996078, 529412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 866667, 976471, 741176, 533333, 592157, 917647, 996078, 831373, 192157, 7843, 764706, 996078, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 698039, 992157, 992157, 992157, 992157, 756863, 94118, 0, 0, 764706, 996078, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 384314, 384314, 90196, 0, 0, 0, 98039, 905882, 1000000, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 992157, 886275, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 992157, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 992157, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192157, 964706, 996078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 635294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 725490, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_013() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 827451, 996078, 996078, 756863, 564706, 396078, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 545098, 694118, 968627, 992157, 992157, 992157, 996078, 992157, 992157, 968627, 694118, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325490, 894118, 992157, 992157, 992157, 992157, 992157, 992157, 172549, 172549, 172549, 435294, 992157, 858824, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 839216, 992157, 992157, 992157, 988235, 831373, 474510, 98039, 0, 0, 0, 43137, 811765, 992157, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 262745, 992157, 992157, 992157, 823529, 364706, 0, 0, 0, 0, 0, 0, 0, 556863, 992157, 980392, 537255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600000, 992157, 925490, 215686, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 992157, 992157, 882353, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 796078, 709804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 239216, 992157, 992157, 992157, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 619608, 992157, 992157, 509804, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 858824, 992157, 992157, 964706, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 941176, 992157, 662745, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 992157, 992157, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466667, 976471, 870588, 94118, 0, 0, 0, 0, 0, 0, 0, 654902, 992157, 992157, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 231373, 745098, 996078, 980392, 490196, 266667, 188235, 117647, 94118, 658824, 1000000, 996078, 996078, 996078, 823529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 301961, 823529, 992157, 992157, 992157, 956863, 901961, 992157, 972549, 639216, 843137, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 172549, 305882, 772549, 945098, 874510, 839216, 549020, 0, 780392, 992157, 647059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 35294, 27451, 27451, 0, 0, 780392, 992157, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 780392, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 780392, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 992157, 901961, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 945098, 992157, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647059, 992157, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 992157, 690196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_014() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 298039, 682353, 741176, 721569, 682353, 454902, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 784314, 996078, 937255, 866667, 592157, 847059, 996078, 843137, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 737255, 933333, 478431, 105882, 0, 0, 0, 333333, 992157, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 992157, 490196, 0, 0, 0, 0, 0, 7843, 521569, 803922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 913725, 972549, 98039, 0, 0, 0, 0, 0, 125490, 980392, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 972549, 980392, 192157, 0, 0, 0, 0, 86275, 937255, 254902, 474510, 686275, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 956863, 749020, 121569, 0, 0, 86275, 431373, 992157, 992157, 913725, 537255, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 945098, 686275, 23529, 372549, 937255, 992157, 898039, 458824, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 992157, 886275, 984314, 803922, 396078, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 705882, 992157, 992157, 501961, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 803922, 811765, 521569, 929412, 701961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 498039, 537255, 62745, 0, 521569, 992157, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466667, 737255, 0, 0, 0, 125490, 960784, 619608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 937255, 411765, 0, 0, 0, 0, 658824, 796078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 992157, 372549, 0, 0, 0, 0, 619608, 972549, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 996078, 254902, 0, 0, 0, 0, 623529, 1000000, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 976471, 372549, 0, 0, 0, 0, 619608, 988235, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 811765, 992157, 482353, 47059, 0, 47059, 886275, 874510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 227451, 976471, 996078, 764706, 556863, 764706, 992157, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 392157, 815686, 992157, 815686, 392157, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_015() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 764706, 929412, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760784, 996078, 921569, 384314, 384314, 384314, 278431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 996078, 996078, 996078, 996078, 996078, 956863, 839216, 839216, 827451, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 313726, 780392, 780392, 780392, 976471, 996078, 996078, 996078, 996078, 882353, 450980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 321569, 321569, 380392, 941176, 996078, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 996078, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 996078, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 756863, 996078, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592157, 996078, 996078, 403922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 745098, 996078, 866667, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 784314, 996078, 976471, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 643137, 996078, 984314, 568627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 662745, 996078, 996078, 580392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 945098, 996078, 905882, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 956863, 996078, 996078, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 356863, 933333, 996078, 996078, 996078, 901961, 866667, 556863, 329412, 329412, 329412, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 815686, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 886275, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 929412, 996078, 996078, 913725, 835294, 352941, 443137, 835294, 835294, 925490, 835294, 835294, 658824, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 996078, 996078, 949020, 447059, 0, 0, 0, 0, 0, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 866667, 627451, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_016() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 454902, 23529, 0, 0, 125490, 870588, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 556863, 509804, 286275, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 603922, 992157, 847059, 0, 129412, 858824, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 992157, 992157, 847059, 0, 631373, 956863, 921569, 921569, 921569, 921569, 921569, 945098, 992157, 925490, 988235, 694118, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 992157, 992157, 847059, 0, 0, 203922, 0, 0, 0, 0, 0, 152941, 411765, 39216, 384314, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 823529, 992157, 992157, 866667, 125490, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 992157, 992157, 992157, 992157, 992157, 921569, 525490, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 454902, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 909804, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 909804, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 772549, 713726, 290196, 290196, 662745, 992157, 992157, 913725, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 780392, 992157, 992157, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 992157, 921569, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 913725, 992157, 992157, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572549, 992157, 992157, 674510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 603922, 525490, 0, 0, 0, 0, 0, 0, 247059, 992157, 992157, 784314, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 992157, 945098, 368627, 145098, 0, 0, 0, 0, 35294, 788235, 992157, 992157, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 811765, 992157, 992157, 921569, 509804, 0, 0, 0, 0, 752941, 992157, 992157, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 313726, 811765, 992157, 992157, 980392, 576471, 211765, 415686, 772549, 972549, 992157, 992157, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 811765, 992157, 992157, 992157, 960784, 992157, 992157, 992157, 992157, 992157, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 811765, 992157, 992157, 992157, 992157, 992157, 992157, 858824, 137255, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 94118, 505882, 839216, 992157, 874510, 376471, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_017() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 588235, 749020, 996078, 1000000, 729412, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 635294, 992157, 992157, 992157, 992157, 992157, 925490, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 839216, 992157, 823529, 447059, 113725, 278431, 960784, 992157, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 964706, 992157, 843137, 101961, 0, 0, 0, 635294, 992157, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 360784, 992157, 658824, 109804, 0, 0, 0, 219608, 933333, 835294, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 992157, 952941, 105882, 0, 0, 0, 231373, 921569, 992157, 686275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 992157, 572549, 0, 0, 121569, 627451, 945098, 992157, 992157, 498039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 992157, 831373, 388235, 423529, 862745, 992157, 992157, 992157, 811765, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 458824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 725490, 992157, 992157, 988235, 705882, 384314, 984314, 780392, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 396078, 607843, 262745, 0, 313726, 992157, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 901961, 992157, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 207843, 992157, 992157, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 207843, 992157, 788235, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 611765, 992157, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 870588, 890196, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 431373, 992157, 607843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 431373, 992157, 513726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 431373, 992157, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_018() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 996078, 831373, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 992157, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 992157, 992157, 745098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 992157, 992157, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 662745, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 996078, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 996078, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 698039, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 992157, 992157, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 992157, 992157, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 992157, 992157, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 996078, 996078, 541176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 945098, 992157, 537255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600000, 992157, 870588, 250980, 0, 200000, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 929412, 992157, 980392, 815686, 945098, 631373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 239216, 952941, 996078, 992157, 537255, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_019() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 211765, 552941, 749020, 1000000, 992157, 992157, 992157, 1000000, 992157, 847059, 552941, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 662745, 992157, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 811765, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 941176, 988235, 992157, 988235, 729412, 658824, 219608, 219608, 219608, 219608, 219608, 509804, 917647, 988235, 992157, 941176, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 952941, 988235, 988235, 945098, 254902, 23529, 0, 0, 0, 0, 0, 0, 0, 86275, 698039, 992157, 988235, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 992157, 992157, 1000000, 968627, 588235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 752941, 992157, 992157, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 623529, 768627, 768627, 772549, 403922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 988235, 988235, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 458824, 988235, 729412, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 945098, 988235, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 945098, 996078, 819608, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 772549, 988235, 870588, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 333333, 74510, 149020, 384314, 917647, 988235, 988235, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 905882, 929412, 992157, 988235, 988235, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 690196, 956863, 992157, 992157, 996078, 819608, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 733333, 988235, 988235, 721569, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 494118, 992157, 988235, 988235, 498039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 882353, 992157, 988235, 498039, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 996078, 894118, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 988235, 992157, 988235, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 952941, 992157, 988235, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 600000, 890196, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_020() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 349020, 666667, 996078, 996078, 996078, 752941, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 650980, 992157, 992157, 992157, 992157, 992157, 992157, 870588, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152941, 886275, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 980392, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 807843, 992157, 952941, 784314, 466667, 282353, 600000, 980392, 992157, 933333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 952941, 992157, 486275, 0, 0, 0, 0, 266667, 992157, 976471, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 992157, 992157, 333333, 0, 0, 0, 23529, 596078, 992157, 992157, 858824, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 949020, 992157, 654902, 94118, 0, 0, 764706, 992157, 992157, 992157, 992157, 968627, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 858824, 992157, 992157, 823529, 180392, 603922, 992157, 992157, 894118, 898039, 941176, 992157, 976471, 349020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 262745, 847059, 992157, 992157, 992157, 992157, 992157, 686275, 86275, 94118, 156863, 427451, 886275, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 11765, 419608, 941176, 992157, 992157, 992157, 819608, 345098, 31373, 0, 0, 11765, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 941176, 992157, 988235, 984314, 992157, 992157, 807843, 301961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 505882, 992157, 956863, 325490, 219608, 686275, 992157, 992157, 894118, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 847059, 992157, 635294, 0, 0, 3922, 682353, 992157, 992157, 843137, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294118, 992157, 901961, 43137, 0, 0, 0, 454902, 690196, 992157, 992157, 290196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 992157, 658824, 0, 0, 0, 0, 0, 490196, 992157, 996078, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294118, 992157, 658824, 0, 0, 0, 0, 294118, 949020, 992157, 964706, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 980392, 705882, 7843, 0, 0, 121569, 819608, 992157, 992157, 788235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760784, 992157, 541176, 356863, 584314, 945098, 992157, 992157, 650980, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 992157, 992157, 996078, 992157, 992157, 952941, 615686, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 627451, 992157, 992157, 992157, 678431, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_021() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 674510, 1000000, 745098, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 952941, 929412, 815686, 733333, 964706, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 631373, 964706, 27451, 0, 39216, 854902, 792157, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 972549, 513726, 0, 0, 0, 274510, 992157, 380392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 701961, 949020, 54902, 0, 0, 0, 50980, 882353, 831373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 866667, 670588, 0, 0, 0, 0, 0, 705882, 831373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 933333, 345098, 0, 0, 0, 0, 0, 450980, 972549, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 992157, 94118, 0, 0, 0, 0, 0, 450980, 949020, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 815686, 854902, 39216, 0, 0, 0, 0, 0, 450980, 980392, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 886275, 352941, 0, 0, 0, 0, 0, 0, 450980, 835294, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 996078, 129412, 0, 0, 0, 0, 0, 0, 564706, 835294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 941176, 356863, 0, 0, 0, 0, 0, 0, 666667, 933333, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192157, 992157, 447059, 0, 0, 0, 0, 0, 11765, 792157, 694118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 447059, 0, 0, 0, 0, 0, 388235, 976471, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 992157, 447059, 0, 0, 0, 0, 11765, 780392, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 992157, 447059, 0, 0, 0, 0, 231373, 992157, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 956863, 447059, 0, 0, 0, 7843, 729412, 835294, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647059, 866667, 141176, 0, 86275, 800000, 976471, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 262745, 956863, 850980, 627451, 941176, 984314, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 278431, 960784, 992157, 678431, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_022() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192157, 705882, 992157, 1000000, 909804, 419608, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 470588, 894118, 988235, 988235, 992157, 988235, 988235, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 988235, 988235, 988235, 866667, 478431, 603922, 988235, 603922, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 772549, 992157, 988235, 890196, 466667, 98039, 0, 184314, 988235, 988235, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 854902, 988235, 992157, 988235, 843137, 290196, 0, 0, 184314, 988235, 658824, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 870588, 992157, 992157, 207843, 290196, 572549, 737255, 43137, 0, 184314, 992157, 631373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 858824, 988235, 921569, 400000, 0, 0, 0, 0, 0, 0, 184314, 988235, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 541176, 988235, 988235, 501961, 0, 0, 0, 0, 0, 0, 0, 509804, 988235, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 988235, 600000, 35294, 0, 0, 0, 0, 0, 0, 35294, 760784, 988235, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 901961, 992157, 615686, 23529, 0, 0, 0, 0, 0, 0, 0, 94118, 988235, 866667, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 913725, 992157, 866667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 545098, 992157, 478431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 607843, 988235, 905882, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 831373, 874510, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 988235, 988235, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 780392, 992157, 482353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 760784, 988235, 854902, 54902, 0, 0, 0, 0, 0, 0, 0, 101961, 525490, 972549, 752941, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 478431, 988235, 988235, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 545098, 992157, 992157, 180392, 0, 0, 0, 0, 0, 0, 50980, 462745, 992157, 960784, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 541176, 988235, 988235, 176471, 0, 0, 0, 0, 66667, 184314, 831373, 988235, 815686, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 419608, 988235, 988235, 603922, 274510, 274510, 274510, 600000, 819608, 988235, 992157, 815686, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 529412, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 384314, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 419608, 909804, 988235, 992157, 988235, 866667, 537255, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_023() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 188235, 329412, 980392, 709804, 380392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 611765, 996078, 996078, 996078, 996078, 980392, 568627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 247059, 894118, 968627, 941176, 454902, 447059, 62745, 164706, 658824, 878431, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 996078, 996078, 996078, 737255, 7843, 0, 0, 0, 23529, 760784, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 941176, 996078, 996078, 643137, 329412, 3922, 0, 0, 0, 0, 674510, 756863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 494118, 1000000, 996078, 690196, 0, 0, 0, 0, 0, 0, 58824, 898039, 956863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466667, 1000000, 996078, 996078, 211765, 0, 0, 0, 0, 0, 0, 443137, 980392, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 509804, 996078, 996078, 835294, 58824, 0, 0, 0, 0, 0, 0, 494118, 733333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 509804, 1000000, 768627, 121569, 0, 0, 0, 0, 0, 0, 7843, 835294, 733333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 941176, 254902, 0, 0, 0, 0, 0, 0, 0, 556863, 996078, 647059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 921569, 709804, 0, 0, 0, 0, 0, 0, 0, 419608, 941176, 996078, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 964706, 709804, 0, 0, 0, 0, 0, 0, 270588, 972549, 949020, 266667, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 933333, 996078, 403922, 0, 0, 0, 0, 0, 58824, 839216, 996078, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 996078, 682353, 19608, 0, 0, 0, 0, 50980, 768627, 996078, 933333, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 717647, 862745, 164706, 0, 0, 0, 0, 149020, 823529, 996078, 623529, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 996078, 450980, 0, 0, 0, 223529, 921569, 996078, 917647, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 996078, 764706, 0, 0, 176471, 749020, 996078, 627451, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 878431, 898039, 43137, 427451, 949020, 996078, 823529, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 478431, 996078, 996078, 996078, 996078, 807843, 450980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 800000, 1000000, 803922, 321569, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_024() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 27451, 156863, 509804, 509804, 509804, 929412, 1000000, 796078, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 50980, 498039, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 792157, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 419608, 992157, 992157, 968627, 894118, 894118, 741176, 411765, 670588, 992157, 992157, 949020, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 623529, 388235, 294118, 0, 0, 0, 211765, 937255, 992157, 992157, 498039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 439216, 992157, 992157, 933333, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 992157, 992157, 992157, 498039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 196078, 196078, 196078, 839216, 992157, 992157, 819608, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 768627, 992157, 992157, 992157, 992157, 992157, 815686, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 317647, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 356863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 992157, 992157, 921569, 345098, 717647, 992157, 992157, 592157, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 560784, 580392, 156863, 0, 70588, 486275, 992157, 992157, 333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345098, 992157, 992157, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 925490, 992157, 780392, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 368627, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345098, 992157, 992157, 580392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 780392, 925490, 768627, 0, 0, 0, 0, 0, 0, 0, 125490, 596078, 992157, 992157, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 992157, 980392, 901961, 901961, 662745, 901961, 541176, 101961, 0, 756863, 992157, 992157, 831373, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 588235, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 572549, 819608, 980392, 992157, 992157, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 333333, 811765, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 607843, 352941, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 19608, 105882, 600000, 992157, 992157, 992157, 850980, 352941, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_025() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 752941, 796078, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592157, 847059, 839216, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 262745, 917647, 992157, 866667, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 870588, 988235, 992157, 866667, 98039, 0, 0, 0, 0, 0, 0, 0, 690196, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 847059, 992157, 992157, 886275, 149020, 0, 0, 0, 0, 0, 0, 360784, 992157, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 988235, 988235, 988235, 345098, 0, 0, 0, 0, 0, 0, 0, 356863, 988235, 556863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 988235, 988235, 643137, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 878431, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592157, 945098, 988235, 988235, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 749020, 1000000, 992157, 807843, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 482353, 988235, 992157, 941176, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 988235, 988235, 992157, 768627, 0, 0, 0, 0, 0, 298039, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 988235, 988235, 945098, 231373, 0, 200000, 447059, 541176, 882353, 976471, 980392, 784314, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 701961, 992157, 992157, 639216, 0, 90196, 898039, 996078, 992157, 992157, 992157, 996078, 992157, 847059, 749020, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 988235, 988235, 988235, 541176, 101961, 870588, 988235, 992157, 988235, 988235, 890196, 992157, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 988235, 988235, 988235, 921569, 627451, 941176, 988235, 992157, 666667, 219608, 121569, 415686, 584314, 988235, 643137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 501961, 988235, 988235, 992157, 988235, 988235, 988235, 698039, 35294, 0, 0, 247059, 564706, 988235, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 898039, 992157, 1000000, 992157, 992157, 992157, 996078, 698039, 552941, 749020, 996078, 992157, 956863, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 478431, 866667, 992157, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 988235, 556863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 494118, 992157, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 807843, 364706, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 647059, 792157, 988235, 992157, 988235, 839216, 545098, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_026() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 286275, 623529, 980392, 996078, 996078, 1000000, 666667, 235294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 396078, 741176, 992157, 992157, 992157, 992157, 992157, 996078, 992157, 945098, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 407843, 992157, 992157, 972549, 694118, 231373, 219608, 219608, 588235, 917647, 992157, 925490, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 407843, 901961, 627451, 184314, 0, 0, 0, 0, 0, 50980, 733333, 992157, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 407843, 992157, 709804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 584314, 992157, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 992157, 780392, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 533333, 588235, 823529, 988235, 992157, 478431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 984314, 992157, 992157, 996078, 992157, 992157, 674510, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 709804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 725490, 423529, 98039, 98039, 372549, 760784, 996078, 996078, 784314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 764706, 992157, 984314, 501961, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 949020, 992157, 992157, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 992157, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 509804, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 890196, 992157, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 976471, 431373, 3922, 0, 0, 0, 0, 0, 0, 180392, 956863, 843137, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 992157, 992157, 494118, 50980, 0, 0, 0, 0, 333333, 862745, 992157, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 992157, 992157, 960784, 682353, 592157, 588235, 878431, 980392, 992157, 835294, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 474510, 956863, 992157, 992157, 992157, 996078, 992157, 992157, 956863, 603922, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 623529, 937255, 992157, 996078, 800000, 623529, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_027() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 584314, 1000000, 1000000, 286275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192157, 729412, 992157, 992157, 992157, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 949020, 992157, 992157, 992157, 992157, 827451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 317647, 960784, 992157, 992157, 992157, 992157, 992157, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 505882, 992157, 992157, 992157, 992157, 992157, 992157, 572549, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 439216, 956863, 992157, 992157, 992157, 992157, 937255, 247059, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 956863, 992157, 992157, 992157, 992157, 925490, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 827451, 992157, 992157, 992157, 992157, 776471, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 407843, 992157, 992157, 992157, 992157, 909804, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 992157, 992157, 992157, 992157, 992157, 82353, 0, 0, 19608, 215686, 215686, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 992157, 992157, 992157, 925490, 490196, 19608, 0, 133333, 776471, 992157, 992157, 882353, 403922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 992157, 992157, 992157, 764706, 0, 43137, 450980, 956863, 992157, 992157, 992157, 992157, 980392, 376471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870588, 992157, 992157, 964706, 129412, 82353, 607843, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 858824, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870588, 992157, 992157, 603922, 74510, 772549, 992157, 992157, 992157, 992157, 992157, 682353, 815686, 992157, 992157, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870588, 992157, 992157, 776471, 619608, 992157, 992157, 992157, 992157, 901961, 364706, 94118, 580392, 992157, 992157, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 580392, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 470588, 678431, 933333, 992157, 992157, 992157, 337255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 717647, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 960784, 694118, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 611765, 964706, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 964706, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 494118, 992157, 992157, 992157, 992157, 992157, 992157, 647059, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_028() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 498039, 980392, 980392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 741176, 980392, 980392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 980392, 980392, 980392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 980392, 980392, 980392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 988235, 988235, 988235, 850980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 988235, 980392, 980392, 760784, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 988235, 980392, 733333, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 988235, 980392, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 988235, 980392, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 858824, 1000000, 988235, 494118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 768627, 980392, 933333, 650980, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 498039, 980392, 980392, 823529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 498039, 980392, 980392, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 278431, 901961, 980392, 980392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 905882, 823529, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 439216, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 988235, 815686, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 988235, 980392, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 988235, 701961, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_029() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 490196, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 847059, 992157, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 843137, 984314, 992157, 992157, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 854902, 992157, 992157, 898039, 482353, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 521569, 976471, 992157, 992157, 694118, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 976471, 992157, 882353, 227451, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 850980, 874510, 227451, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 796078, 980392, 874510, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603922, 992157, 992157, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 149020, 176471, 262745, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 976471, 882353, 262745, 23529, 0, 0, 0, 0, 0, 0, 294118, 768627, 882353, 882353, 905882, 976471, 882353, 752941, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 866667, 992157, 443137, 0, 0, 0, 0, 0, 0, 180392, 611765, 921569, 992157, 992157, 992157, 850980, 780392, 992157, 992157, 600000, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 898039, 39216, 0, 0, 0, 0, 0, 203922, 929412, 992157, 992157, 850980, 709804, 278431, 105882, 23529, 305882, 898039, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 615686, 11765, 0, 0, 0, 0, 58824, 411765, 992157, 952941, 447059, 94118, 0, 0, 0, 0, 0, 447059, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 733333, 992157, 458824, 11765, 0, 0, 133333, 674510, 992157, 741176, 254902, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 870588, 992157, 992157, 662745, 443137, 576471, 941176, 992157, 745098, 82353, 0, 0, 0, 0, 0, 0, 78431, 419608, 831373, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 917647, 992157, 992157, 992157, 992157, 992157, 992157, 545098, 105882, 105882, 105882, 105882, 105882, 105882, 156863, 839216, 992157, 992157, 890196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 917647, 988235, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 988235, 627451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 607843, 960784, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 960784, 901961, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 458824, 890196, 968627, 968627, 968627, 584314, 458824, 811765, 886275, 458824, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_030() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 149020, 149020, 584314, 1000000, 1000000, 588235, 572549, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 231373, 705882, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 882353, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 525490, 964706, 992157, 988235, 819608, 545098, 270588, 125490, 125490, 717647, 992157, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 388235, 992157, 992157, 811765, 317647, 0, 0, 0, 0, 66667, 866667, 992157, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 717647, 992157, 933333, 352941, 23529, 0, 0, 0, 0, 0, 109804, 992157, 862745, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 568627, 992157, 972549, 427451, 0, 0, 0, 0, 0, 0, 0, 101961, 658824, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 992157, 933333, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 615686, 447059, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 772549, 992157, 674510, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 592157, 992157, 992157, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870588, 992157, 286275, 0, 0, 0, 0, 0, 0, 0, 43137, 603922, 992157, 992157, 968627, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870588, 992157, 345098, 0, 0, 0, 0, 0, 0, 109804, 729412, 992157, 992157, 992157, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 992157, 925490, 407843, 141176, 0, 156863, 78431, 364706, 866667, 992157, 992157, 992157, 992157, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 568627, 972549, 992157, 956863, 933333, 960784, 945098, 992157, 949020, 627451, 898039, 992157, 972549, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 760784, 905882, 992157, 980392, 670588, 337255, 164706, 156863, 929412, 992157, 639216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 188235, 176471, 0, 0, 0, 576471, 992157, 905882, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 992157, 886275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 745098, 992157, 886275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 992157, 992157, 713726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 992157, 992157, 756863, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 509804, 992157, 992157, 964706, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 850980, 992157, 705882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_031() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 482353, 839216, 200000, 200000, 200000, 200000, 200000, 200000, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 952941, 992157, 988235, 992157, 988235, 992157, 988235, 992157, 909804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 678431, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 988235, 992157, 988235, 992157, 988235, 992157, 670588, 592157, 752941, 992157, 988235, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 992157, 996078, 992157, 717647, 400000, 0, 0, 0, 482353, 996078, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 992157, 988235, 913725, 435294, 0, 0, 0, 0, 82353, 874510, 992157, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 674510, 160784, 0, 0, 0, 0, 0, 596078, 992157, 996078, 513726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 39216, 0, 0, 0, 0, 0, 0, 756863, 988235, 835294, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 996078, 992157, 717647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 796078, 992157, 988235, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 992157, 996078, 752941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 913725, 988235, 992157, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 996078, 992157, 796078, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 796078, 992157, 988235, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 992157, 996078, 913725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 988235, 992157, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 1000000, 992157, 956863, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 992157, 988235, 635294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 403922, 1000000, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 992157, 509804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_032() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 454902, 941176, 698039, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 392157, 992157, 992157, 996078, 301961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 992157, 992157, 823529, 360784, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 937255, 992157, 992157, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 780392, 992157, 992157, 831373, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325490, 949020, 992157, 858824, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 666667, 992157, 952941, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 992157, 992157, 513726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 992157, 992157, 513726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 992157, 992157, 513726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 996078, 996078, 517647, 0, 0, 0, 188235, 678431, 996078, 996078, 901961, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 992157, 992157, 513726, 47059, 262745, 639216, 996078, 992157, 992157, 992157, 992157, 647059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 992157, 992157, 913725, 854902, 992157, 992157, 996078, 890196, 603922, 976471, 992157, 933333, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 662745, 992157, 992157, 992157, 992157, 917647, 231373, 31373, 0, 305882, 964706, 992157, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 992157, 992157, 992157, 509804, 47059, 0, 0, 0, 19608, 725490, 917647, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 827451, 992157, 992157, 701961, 47059, 0, 0, 0, 392157, 992157, 647059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 988235, 992157, 992157, 733333, 482353, 478431, 647059, 992157, 992157, 627451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647059, 992157, 992157, 992157, 1000000, 992157, 992157, 992157, 596078, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 333333, 784314, 992157, 996078, 992157, 874510, 274510, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 694118, 752941, 560784, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_033() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 203922, 945098, 831373, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 921569, 992157, 992157, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 619608, 988235, 992157, 992157, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 674510, 996078, 992157, 992157, 992157, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 576471, 992157, 996078, 992157, 992157, 992157, 800000, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 498039, 992157, 992157, 996078, 901961, 858824, 992157, 992157, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192157, 878431, 992157, 992157, 996078, 211765, 368627, 992157, 992157, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 992157, 992157, 992157, 949020, 43137, 368627, 992157, 992157, 780392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 698039, 992157, 992157, 992157, 223529, 0, 156863, 905882, 992157, 780392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 490196, 992157, 992157, 992157, 713726, 0, 0, 0, 839216, 992157, 780392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 266667, 996078, 996078, 949020, 501961, 0, 0, 0, 176471, 917647, 996078, 788235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 266667, 992157, 992157, 886275, 0, 0, 0, 0, 368627, 992157, 992157, 780392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 733333, 992157, 933333, 282353, 0, 0, 0, 0, 839216, 992157, 992157, 588235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270588, 960784, 992157, 666667, 0, 0, 0, 0, 800000, 976471, 992157, 768627, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 317647, 992157, 992157, 313726, 0, 0, 141176, 792157, 984314, 992157, 992157, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 317647, 992157, 992157, 313726, 23529, 239216, 870588, 996078, 992157, 992157, 647059, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 317647, 992157, 992157, 780392, 713726, 992157, 992157, 1000000, 992157, 741176, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 972549, 992157, 992157, 992157, 992157, 992157, 1000000, 396078, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 980392, 992157, 992157, 992157, 964706, 694118, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 827451, 937255, 470588, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_034() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 443137, 443137, 447059, 47059, 101961, 443137, 443137, 447059, 443137, 443137, 443137, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 713726, 988235, 988235, 992157, 894118, 905882, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 941176, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 862745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 894118, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 741176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 615686, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 690196, 992157, 992157, 635294, 0, 690196, 992157, 992157, 992157, 992157, 1000000, 843137, 549020, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 988235, 988235, 854902, 333333, 992157, 988235, 988235, 988235, 988235, 658824, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 470588, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 988235, 988235, 988235, 988235, 992157, 701961, 329412, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 796078, 992157, 988235, 988235, 988235, 988235, 745098, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 992157, 992157, 1000000, 992157, 992157, 882353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 843137, 988235, 988235, 992157, 988235, 988235, 388235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 784314, 988235, 988235, 988235, 992157, 988235, 937255, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 623529, 988235, 988235, 988235, 988235, 992157, 988235, 764706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 988235, 988235, 678431, 988235, 992157, 988235, 764706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 992157, 992157, 682353, 992157, 1000000, 992157, 768627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 988235, 988235, 988235, 988235, 992157, 988235, 705882, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870588, 988235, 988235, 988235, 988235, 992157, 788235, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 396078, 913725, 988235, 988235, 988235, 635294, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 439216, 439216, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_035() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 474510, 835294, 1000000, 1000000, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 862745, 984314, 992157, 992157, 992157, 992157, 745098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 588235, 984314, 992157, 992157, 992157, 992157, 796078, 972549, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 592157, 917647, 992157, 992157, 992157, 741176, 564706, 152941, 74510, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 992157, 996078, 992157, 701961, 207843, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 211765, 541176, 749020, 992157, 996078, 407843, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 705882, 992157, 992157, 992157, 992157, 996078, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 521569, 898039, 992157, 980392, 858824, 364706, 368627, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 619608, 992157, 992157, 992157, 894118, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 839216, 992157, 992157, 992157, 992157, 968627, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 901961, 996078, 996078, 996078, 996078, 996078, 752941, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 439216, 572549, 615686, 992157, 992157, 996078, 972549, 945098, 368627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 101961, 101961, 996078, 992157, 992157, 960784, 380392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 431373, 909804, 992157, 560784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 894118, 992157, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 435294, 968627, 992157, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 160784, 19608, 0, 0, 0, 109804, 160784, 188235, 682353, 1000000, 992157, 992157, 827451, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 941176, 992157, 666667, 631373, 631373, 631373, 878431, 992157, 992157, 992157, 1000000, 992157, 796078, 380392, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725490, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 1000000, 749020, 419608, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 470588, 913725, 992157, 992157, 992157, 992157, 992157, 713726, 474510, 270588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_036() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 835294, 1000000, 996078, 996078, 996078, 996078, 937255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 643137, 784314, 854902, 992157, 992157, 992157, 992157, 901961, 811765, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 980392, 992157, 992157, 992157, 992157, 694118, 419608, 419608, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 980392, 992157, 992157, 992157, 992157, 874510, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 992157, 937255, 956863, 992157, 992157, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 450980, 486275, 886275, 992157, 992157, 266667, 0, 168627, 545098, 545098, 545098, 545098, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 564706, 992157, 992157, 992157, 952941, 937255, 952941, 992157, 992157, 992157, 992157, 968627, 937255, 549020, 192157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 423529, 984314, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 878431, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572549, 992157, 992157, 992157, 992157, 992157, 725490, 482353, 482353, 482353, 482353, 509804, 992157, 992157, 992157, 992157, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 403922, 984314, 992157, 827451, 690196, 615686, 43137, 0, 0, 0, 0, 7843, 86275, 674510, 992157, 992157, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 298039, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 741176, 992157, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 807843, 992157, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 815686, 992157, 992157, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 490196, 992157, 992157, 964706, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 341176, 992157, 992157, 976471, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 243137, 776471, 945098, 992157, 933333, 360784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 603922, 635294, 176471, 31373, 3922, 98039, 635294, 635294, 666667, 992157, 992157, 992157, 976471, 360784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 968627, 992157, 992157, 458824, 839216, 992157, 992157, 992157, 992157, 992157, 705882, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474510, 992157, 992157, 992157, 992157, 992157, 925490, 780392, 780392, 247059, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 388235, 717647, 992157, 917647, 388235, 270588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_037() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 705882, 1000000, 898039, 756863, 588235, 435294, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 827451, 992157, 992157, 992157, 992157, 992157, 992157, 866667, 631373, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270588, 980392, 552941, 39216, 39216, 47059, 447059, 768627, 933333, 992157, 741176, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 709804, 0, 0, 0, 0, 0, 219608, 780392, 992157, 913725, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 58824, 0, 0, 0, 0, 0, 0, 27451, 898039, 992157, 721569, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 913725, 992157, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 686275, 992157, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466667, 992157, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 713726, 992157, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 552941, 752941, 752941, 650980, 349020, 137255, 0, 0, 0, 0, 713726, 992157, 588235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 847059, 992157, 992157, 992157, 992157, 992157, 960784, 454902, 3922, 0, 168627, 976471, 984314, 286275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 968627, 992157, 835294, 572549, 282353, 282353, 752941, 992157, 992157, 650980, 74510, 819608, 992157, 788235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 403922, 992157, 835294, 82353, 0, 0, 0, 43137, 349020, 862745, 992157, 921569, 988235, 992157, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 772549, 992157, 501961, 0, 0, 0, 0, 0, 54902, 713726, 992157, 992157, 992157, 992157, 317647, 0, 121569, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 992157, 949020, 482353, 450980, 450980, 450980, 458824, 882353, 992157, 988235, 952941, 992157, 992157, 984314, 745098, 862745, 713726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 752941, 843137, 992157, 992157, 992157, 992157, 992157, 992157, 654902, 305882, 0, 396078, 839216, 992157, 992157, 992157, 768627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 552941, 584314, 584314, 584314, 576471, 180392, 39216, 0, 0, 0, 58824, 380392, 862745, 992157, 603922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_038() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 521569, 1000000, 996078, 996078, 764706, 898039, 611765, 466667, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 968627, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 850980, 270588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 725490, 984314, 992157, 901961, 168627, 39216, 39216, 105882, 447059, 847059, 992157, 992157, 874510, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 329412, 992157, 992157, 682353, 90196, 0, 0, 0, 0, 0, 35294, 262745, 921569, 992157, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 835294, 992157, 521569, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 486275, 270588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 992157, 921569, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 992157, 533333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 956863, 992157, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 450980, 898039, 603922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 992157, 486275, 0, 0, 0, 0, 7843, 23529, 490196, 835294, 984314, 992157, 980392, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 992157, 588235, 149020, 0, 0, 172549, 533333, 992157, 992157, 992157, 992157, 992157, 976471, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 886275, 992157, 937255, 792157, 792157, 960784, 992157, 992157, 992157, 992157, 992157, 992157, 752941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 952941, 992157, 992157, 992157, 992157, 992157, 992157, 929412, 596078, 282353, 937255, 992157, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 615686, 647059, 647059, 647059, 647059, 564706, 149020, 0, 0, 937255, 992157, 364706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 945098, 956863, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474510, 992157, 686275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 968627, 992157, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 992157, 992157, 556863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 992157, 992157, 952941, 419608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 992157, 992157, 800000, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 992157, 992157, 356863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_039() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 992157, 992157, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 450980, 988235, 988235, 564706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 850980, 988235, 988235, 564706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 929412, 988235, 988235, 564706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 1000000, 992157, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 929412, 992157, 988235, 988235, 823529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 988235, 992157, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 988235, 992157, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 811765, 1000000, 992157, 992157, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 564706, 992157, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 866667, 992157, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 745098, 992157, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 1000000, 992157, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 564706, 992157, 988235, 988235, 823529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 564706, 992157, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 992157, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_040() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 250980, 749020, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 250980, 749020, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 0, 0, 0, 250980, 749020, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 1000000, 1000000, 1000000, 0, 0, 250980, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 749020, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 749020, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 749020, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_041() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725490, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 772549, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 992157, 364706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 992157, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 894118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 650980, 501961, 0, 0, 0, 0, 749020, 270588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 764706, 450980, 0, 0, 0, 266667, 878431, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466667, 823529, 35294, 0, 0, 0, 776471, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 968627, 462745, 0, 0, 0, 149020, 952941, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 501961, 694118, 0, 0, 0, 0, 733333, 909804, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 741176, 992157, 760784, 364706, 98039, 364706, 498039, 996078, 874510, 658824, 721569, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 866667, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 1000000, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 917647, 996078, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 996078, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 541176, 670588, 537255, 670588, 541176, 752941, 992157, 992157, 541176, 537255, 537255, 537255, 443137, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 992157, 858824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 509804, 968627, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 901961, 701961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 862745, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 807843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 4);
}

#[test]
fn test_main_042() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 772549, 992157, 529412, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 439216, 980392, 956863, 611765, 607843, 156863, 0, 572549, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 972549, 709804, 101961, 0, 0, 0, 98039, 949020, 482353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 968627, 650980, 15686, 0, 0, 0, 0, 133333, 996078, 482353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 803922, 729412, 113725, 0, 0, 0, 0, 0, 545098, 996078, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 996078, 282353, 0, 0, 0, 0, 0, 250980, 960784, 913725, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 827451, 19608, 0, 0, 0, 0, 15686, 760784, 996078, 764706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 670588, 803922, 0, 0, 0, 0, 11765, 619608, 996078, 996078, 431373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 984314, 317647, 0, 0, 192157, 733333, 980392, 321569, 996078, 192157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 792157, 980392, 968627, 968627, 988235, 886275, 215686, 411765, 996078, 192157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 501961, 647059, 647059, 439216, 0, 0, 639216, 913725, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 866667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 768627, 835294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 996078, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 996078, 286275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 996078, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 709804, 1000000, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 996078, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 392157, 996078, 741176, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 913725, 600000, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_043() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 749020, 501961, 0, 501961, 501961, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 749020, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 501961, 501961, 749020, 501961, 1000000, 1000000, 749020, 250980, 0, 0, 0, 501961, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 501961, 0, 0, 250980, 749020, 501961, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 749020, 501961, 1000000, 1000000, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 749020, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 749020, 501961, 501961, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_044() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 788235, 952941, 454902, 27451, 27451, 27451, 19608, 19608, 27451, 27451, 27451, 27451, 27451, 219608, 513726, 301961, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 996078, 996078, 996078, 996078, 996078, 996078, 898039, 874510, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 976471, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 960784, 933333, 952941, 960784, 972549, 996078, 996078, 996078, 941176, 925490, 925490, 949020, 996078, 996078, 1000000, 286275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 203922, 43137, 160784, 203922, 274510, 411765, 411765, 411765, 101961, 0, 31373, 647059, 996078, 960784, 694118, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 996078, 996078, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 807843, 996078, 690196, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 839216, 996078, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 996078, 929412, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 780392, 996078, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 941176, 996078, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 996078, 756863, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 945098, 996078, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 996078, 996078, 192157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 650980, 996078, 584314, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 831373, 996078, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 415686, 996078, 996078, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 709804, 996078, 996078, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 709804, 996078, 996078, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 984314, 996078, 870588, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 713726, 996078, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_045() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 831373, 913725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 784314, 847059, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 992157, 717647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 458824, 984314, 964706, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 19608, 0, 0, 0, 0, 0, 0, 184314, 901961, 996078, 525490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 933333, 54902, 0, 0, 0, 0, 0, 35294, 854902, 992157, 823529, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 968627, 752941, 15686, 0, 0, 0, 0, 23529, 666667, 996078, 992157, 337255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 678431, 976471, 929412, 145098, 0, 0, 0, 0, 0, 337255, 992157, 996078, 486275, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 686275, 996078, 992157, 721569, 0, 0, 0, 0, 0, 184314, 956863, 992157, 917647, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 439216, 917647, 992157, 992157, 992157, 945098, 584314, 584314, 584314, 435294, 584314, 835294, 992157, 992157, 588235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 611765, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 607843, 952941, 843137, 760784, 494118, 368627, 368627, 368627, 372549, 584314, 992157, 996078, 862745, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 54902, 0, 0, 0, 0, 0, 0, 607843, 992157, 886275, 301961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 509804, 988235, 992157, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 968627, 996078, 592157, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 823529, 992157, 733333, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 552941, 988235, 941176, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 992157, 992157, 333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345098, 996078, 549020, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 474510, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 4);
}

#[test]
fn test_main_046() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 286275, 184314, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 517647, 921569, 925490, 921569, 615686, 878431, 992157, 968627, 976471, 745098, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 972549, 992157, 992157, 996078, 992157, 992157, 980392, 847059, 850980, 847059, 847059, 839216, 580392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 992157, 984314, 921569, 694118, 564706, 388235, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 823529, 992157, 662745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 996078, 996078, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 992157, 654902, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 992157, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 992157, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 992157, 949020, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 949020, 996078, 560784, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 909804, 992157, 815686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 960784, 992157, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603922, 992157, 756863, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 788235, 996078, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 1000000, 996078, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 545098, 921569, 921569, 921569, 921569, 925490, 921569, 921569, 921569, 972549, 996078, 992157, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 890196, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 992157, 996078, 960784, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 62745, 211765, 494118, 564706, 921569, 921569, 921569, 921569, 921569, 921569, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_047() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 396078, 596078, 996078, 1000000, 996078, 996078, 996078, 996078, 592157, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 815686, 992157, 992157, 992157, 898039, 811765, 811765, 811765, 858824, 992157, 898039, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 968627, 992157, 992157, 992157, 572549, 203922, 0, 0, 0, 274510, 992157, 992157, 890196, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 976471, 992157, 792157, 58824, 7843, 0, 0, 0, 0, 274510, 992157, 992157, 992157, 360784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 972549, 992157, 450980, 0, 0, 0, 0, 0, 0, 733333, 992157, 992157, 713726, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 992157, 450980, 0, 0, 0, 0, 0, 266667, 941176, 992157, 741176, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 513726, 301961, 0, 0, 0, 0, 86275, 964706, 992157, 992157, 537255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 992157, 992157, 949020, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 992157, 615686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 831373, 964706, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 913725, 992157, 992157, 745098, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 513726, 992157, 992157, 756863, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 937255, 992157, 968627, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 525490, 992157, 992157, 901961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725490, 992157, 992157, 623529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 952941, 992157, 733333, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352941, 972549, 992157, 992157, 333333, 31373, 31373, 31373, 31373, 31373, 15686, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 545098, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 643137, 976471, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 949020, 992157, 992157, 992157, 992157, 890196, 611765, 592157, 992157, 992157, 984314, 450980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 827451, 992157, 992157, 568627, 200000, 0, 27451, 388235, 533333, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_048() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 313726, 462745, 462745, 462745, 647059, 1000000, 894118, 462745, 462745, 462745, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 831373, 917647, 968627, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 921569, 917647, 494118, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 992157, 992157, 992157, 992157, 992157, 862745, 694118, 694118, 694118, 694118, 866667, 992157, 992157, 992157, 992157, 882353, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 690196, 776471, 776471, 776471, 776471, 149020, 0, 0, 0, 0, 137255, 239216, 458824, 847059, 992157, 992157, 376471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 705882, 992157, 992157, 376471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725490, 992157, 992157, 866667, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 968627, 992157, 992157, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 980392, 992157, 992157, 521569, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 949020, 992157, 992157, 509804, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 929412, 992157, 992157, 223529, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 584314, 992157, 992157, 635294, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 525490, 901961, 992157, 917647, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 913725, 992157, 988235, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 941176, 992157, 901961, 454902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 992157, 992157, 803922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 992157, 992157, 337255, 0, 188235, 588235, 862745, 290196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 862745, 992157, 647059, 235294, 592157, 901961, 992157, 760784, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 850980, 992157, 992157, 752941, 913725, 992157, 886275, 294118, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 952941, 992157, 992157, 992157, 976471, 909804, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 686275, 992157, 847059, 368627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_049() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 533333, 533333, 925490, 1000000, 760784, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 403922, 850980, 992157, 992157, 992157, 992157, 992157, 933333, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 619608, 980392, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 780392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 745098, 992157, 988235, 458824, 254902, 552941, 992157, 992157, 737255, 262745, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 929412, 847059, 200000, 0, 58824, 800000, 992157, 525490, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 66667, 0, 0, 360784, 992157, 866667, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 992157, 839216, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 992157, 992157, 654902, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 729412, 992157, 992157, 831373, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 725490, 992157, 992157, 839216, 427451, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 403922, 964706, 992157, 992157, 756863, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 803922, 992157, 992157, 878431, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 615686, 992157, 992157, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 600000, 992157, 992157, 431373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 588235, 992157, 992157, 964706, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 360784, 650980, 988235, 992157, 956863, 384314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 258824, 364706, 803922, 992157, 992157, 992157, 788235, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 329412, 329412, 329412, 329412, 337255, 807843, 992157, 992157, 992157, 992157, 847059, 215686, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 490196, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 529412, 874510, 992157, 796078, 529412, 529412, 239216, 66667, 66667, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_050() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 745098, 984314, 937255, 917647, 623529, 878431, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 933333, 678431, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 894118, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294118, 941176, 15686, 0, 0, 0, 0, 0, 0, 78431, 701961, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 313726, 937255, 0, 0, 0, 0, 0, 0, 11765, 686275, 996078, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 313726, 937255, 0, 0, 0, 0, 0, 0, 462745, 925490, 988235, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 937255, 0, 0, 0, 0, 0, 258824, 866667, 121569, 937255, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 913725, 474510, 0, 0, 0, 211765, 850980, 458824, 0, 937255, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 949020, 470588, 313726, 603922, 941176, 313726, 11765, 78431, 952941, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 564706, 623529, 525490, 98039, 0, 0, 270588, 996078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 760784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 682353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 603922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 874510, 376471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 890196, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 933333, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 874510, 525490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 682353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_051() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 501961, 992157, 1000000, 992157, 992157, 623529, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 333333, 188235, 113725, 843137, 988235, 988235, 992157, 988235, 988235, 988235, 929412, 494118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 419608, 988235, 898039, 843137, 988235, 988235, 988235, 992157, 729412, 647059, 913725, 988235, 898039, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 874510, 929412, 988235, 988235, 988235, 988235, 941176, 278431, 0, 294118, 988235, 992157, 478431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 619608, 988235, 988235, 988235, 247059, 0, 0, 113725, 988235, 992157, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 992157, 1000000, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 988235, 992157, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 988235, 992157, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 698039, 988235, 941176, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 988235, 988235, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776471, 992157, 992157, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 482353, 964706, 988235, 800000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 223529, 223529, 74510, 0, 349020, 964706, 988235, 901961, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 172549, 662745, 811765, 988235, 988235, 768627, 662745, 811765, 988235, 960784, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 462745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776471, 992157, 992157, 552941, 549020, 898039, 992157, 992157, 1000000, 992157, 870588, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 772549, 988235, 988235, 333333, 823529, 964706, 988235, 988235, 992157, 988235, 988235, 976471, 882353, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 772549, 988235, 988235, 992157, 988235, 988235, 776471, 215686, 219608, 215686, 694118, 988235, 988235, 898039, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 709804, 988235, 988235, 992157, 886275, 447059, 109804, 0, 0, 0, 74510, 388235, 937255, 992157, 878431, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 501961, 678431, 439216, 47059, 0, 0, 0, 0, 0, 0, 0, 247059, 682353, 988235, 764706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_052() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 431373, 913725, 992157, 992157, 1000000, 992157, 521569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 690196, 929412, 992157, 988235, 988235, 988235, 992157, 988235, 968627, 850980, 286275, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 584314, 549020, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 988235, 905882, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 525490, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 862745, 803922, 803922, 992157, 988235, 278431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 525490, 968627, 988235, 988235, 992157, 905882, 619608, 137255, 137255, 98039, 78431, 78431, 992157, 988235, 278431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 988235, 988235, 988235, 988235, 992157, 619608, 0, 0, 0, 0, 0, 0, 992157, 988235, 278431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 329412, 988235, 988235, 988235, 988235, 992157, 137255, 0, 0, 0, 0, 0, 0, 992157, 988235, 603922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 713726, 992157, 992157, 992157, 992157, 423529, 0, 0, 0, 0, 0, 0, 0, 568627, 1000000, 992157, 282353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 949020, 988235, 988235, 988235, 988235, 423529, 0, 0, 0, 0, 0, 0, 611765, 929412, 992157, 905882, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 709804, 988235, 988235, 988235, 988235, 803922, 121569, 0, 0, 0, 0, 62745, 431373, 709804, 988235, 929412, 600000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 988235, 988235, 988235, 988235, 823529, 121569, 0, 0, 0, 0, 0, 427451, 866667, 866667, 988235, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 431373, 992157, 992157, 992157, 992157, 137255, 0, 0, 0, 0, 388235, 992157, 1000000, 992157, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 913725, 988235, 988235, 988235, 988235, 466667, 0, 164706, 286275, 772549, 949020, 988235, 992157, 988235, 945098, 380392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 988235, 741176, 101961, 145098, 627451, 992157, 988235, 988235, 988235, 992157, 945098, 721569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 988235, 988235, 745098, 988235, 988235, 992157, 988235, 988235, 988235, 992157, 701961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 1000000, 992157, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 827451, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 992157, 905882, 619608, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 886275, 988235, 988235, 988235, 988235, 988235, 580392, 282353, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 501961, 988235, 988235, 823529, 423529, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_053() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 996078, 537255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 972549, 996078, 972549, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 972549, 800000, 219608, 427451, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 874510, 894118, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 596078, 854902, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 996078, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 898039, 733333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576471, 968627, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 909804, 564706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 607843, 996078, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 890196, 541176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 580392, 996078, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 458824, 858824, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 866667, 662745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 996078, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 980392, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 811765, 419608, 0, 0, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 854902, 984314, 960784, 960784, 972549, 866667, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 945098, 960784, 996078, 996078, 996078, 1000000, 862745, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352941, 211765, 305882, 705882, 996078, 996078, 1000000, 607843, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_054() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 509804, 992157, 1000000, 854902, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 545098, 976471, 988235, 988235, 992157, 988235, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 513726, 988235, 988235, 988235, 988235, 992157, 988235, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294118, 988235, 988235, 988235, 988235, 988235, 992157, 988235, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 843137, 988235, 988235, 988235, 658824, 113725, 113725, 113725, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 988235, 988235, 988235, 945098, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 988235, 988235, 988235, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 945098, 988235, 988235, 54902, 0, 0, 0, 86275, 145098, 352941, 352941, 215686, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 874510, 988235, 988235, 768627, 756863, 756863, 760784, 811765, 850980, 988235, 811765, 145098, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 988235, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 290196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 925490, 992157, 992157, 992157, 992157, 992157, 1000000, 992157, 349020, 278431, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 988235, 988235, 988235, 988235, 988235, 988235, 992157, 792157, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 988235, 988235, 988235, 929412, 972549, 988235, 992157, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 713726, 988235, 988235, 988235, 54902, 486275, 988235, 992157, 752941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 988235, 988235, 988235, 988235, 54902, 23529, 627451, 992157, 478431, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 988235, 988235, 988235, 988235, 505882, 98039, 584314, 992157, 988235, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 709804, 988235, 988235, 988235, 988235, 905882, 796078, 992157, 988235, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 945098, 988235, 988235, 988235, 988235, 988235, 992157, 988235, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 203922, 643137, 905882, 988235, 988235, 988235, 992157, 807843, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 956863, 882353, 403922, 992157, 411765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_055() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 133333, 545098, 847059, 462745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 231373, 321569, 772549, 992157, 992157, 992157, 647059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 207843, 823529, 823529, 972549, 996078, 992157, 992157, 992157, 737255, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 894118, 992157, 992157, 956863, 909804, 792157, 474510, 247059, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325490, 964706, 956863, 458824, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 780392, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 780392, 992157, 407843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 819608, 949020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 992157, 949020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 992157, 988235, 866667, 866667, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 968627, 996078, 976471, 964706, 996078, 756863, 454902, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 337255, 250980, 223529, 792157, 1000000, 992157, 745098, 278431, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 227451, 874510, 992157, 992157, 513726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 39216, 956863, 984314, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 952941, 992157, 647059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 984314, 992157, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 870588, 992157, 890196, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 607843, 419608, 176471, 576471, 992157, 992157, 509804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 992157, 992157, 996078, 992157, 992157, 796078, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 450980, 749020, 996078, 992157, 466667, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_056() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 823529, 996078, 996078, 996078, 996078, 905882, 490196, 490196, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 819608, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 980392, 631373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 556863, 556863, 556863, 556863, 858824, 992157, 992157, 992157, 988235, 635294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 74510, 192157, 992157, 992157, 941176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 992157, 992157, 941176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576471, 992157, 992157, 941176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 266667, 337255, 333333, 333333, 337255, 674510, 941176, 992157, 992157, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 854902, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 505882, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 835294, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 635294, 933333, 992157, 992157, 815686, 776471, 992157, 992157, 992157, 823529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 254902, 254902, 78431, 39216, 349020, 992157, 992157, 941176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 913725, 992157, 980392, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 992157, 992157, 968627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 156863, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 721569, 992157, 968627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 666667, 992157, 839216, 639216, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 639216, 992157, 984314, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 878431, 933333, 992157, 847059, 611765, 180392, 74510, 0, 0, 0, 0, 0, 0, 0, 156863, 992157, 992157, 976471, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 909804, 992157, 992157, 992157, 866667, 588235, 588235, 207843, 78431, 66667, 0, 117647, 839216, 992157, 992157, 929412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 890196, 960784, 992157, 992157, 992157, 992157, 992157, 992157, 913725, 560784, 839216, 992157, 992157, 964706, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 627451, 968627, 968627, 968627, 988235, 992157, 992157, 992157, 992157, 992157, 976471, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 584314, 992157, 992157, 992157, 941176, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_057() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 839216, 729412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352941, 980392, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 870588, 988235, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 419608, 988235, 988235, 286275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 988235, 737255, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 949020, 988235, 560784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 827451, 988235, 988235, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 949020, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 992157, 988235, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 768627, 992157, 988235, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576471, 992157, 1000000, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572549, 988235, 992157, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 945098, 988235, 380392, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 658824, 988235, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 988235, 945098, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 678431, 988235, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 678431, 988235, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 874510, 988235, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 513726, 988235, 980392, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 458824, 988235, 882353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_058() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 537255, 235294, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576471, 996078, 996078, 713726, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 211765, 152941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 980392, 996078, 996078, 996078, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 780392, 996078, 796078, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 980392, 996078, 996078, 996078, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 996078, 996078, 996078, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 980392, 996078, 996078, 996078, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 996078, 996078, 996078, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 980392, 996078, 996078, 996078, 670588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 537255, 996078, 996078, 286275, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 980392, 996078, 996078, 996078, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 752941, 996078, 996078, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 980392, 996078, 996078, 996078, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 537255, 996078, 996078, 592157, 164706, 164706, 86275, 94118, 62745, 0, 0, 0, 0, 686275, 996078, 996078, 996078, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 996078, 996078, 996078, 996078, 996078, 850980, 866667, 807843, 698039, 341176, 235294, 658824, 635294, 1000000, 996078, 996078, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 670588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 278431, 996078, 996078, 996078, 839216, 807843, 996078, 996078, 1000000, 996078, 1000000, 996078, 996078, 996078, 996078, 996078, 282353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 90196, 90196, 254902, 105882, 54902, 294118, 168627, 443137, 792157, 996078, 996078, 996078, 996078, 996078, 996078, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 11765, 19608, 19608, 286275, 996078, 996078, 996078, 678431, 27451, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 1000000, 996078, 996078, 996078, 803922, 607843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 490196, 996078, 996078, 996078, 996078, 996078, 909804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 19608, 698039, 996078, 996078, 996078, 996078, 870588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 396078, 733333, 996078, 996078, 996078, 996078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 701961, 996078, 996078, 996078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 66667, 66667, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 4);
}

#[test]
fn test_main_059() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 654902, 717647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 741176, 956863, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 996078, 996078, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 984314, 996078, 996078, 431373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 423529, 996078, 588235, 850980, 898039, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 886275, 721569, 19608, 580392, 996078, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 996078, 701961, 0, 180392, 996078, 380392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 796078, 980392, 305882, 0, 39216, 972549, 678431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 549020, 996078, 701961, 0, 0, 0, 760784, 925490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 811765, 996078, 219608, 0, 0, 0, 760784, 937255, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 1000000, 996078, 290196, 0, 0, 356863, 964706, 1000000, 650980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 988235, 800000, 3922, 0, 0, 11765, 411765, 996078, 333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 494118, 1000000, 639216, 0, 0, 0, 0, 290196, 1000000, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576471, 996078, 396078, 0, 0, 0, 0, 694118, 945098, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 980392, 956863, 109804, 0, 0, 0, 160784, 980392, 807843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 984314, 996078, 376471, 0, 0, 0, 0, 670588, 996078, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 584314, 996078, 478431, 3922, 0, 0, 0, 458824, 992157, 513726, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 956863, 996078, 196078, 0, 0, 39216, 580392, 949020, 741176, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 968627, 996078, 976471, 894118, 972549, 976471, 960784, 615686, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 819608, 996078, 996078, 921569, 674510, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_060() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 678431, 992157, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 874510, 674510, 513726, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 996078, 674510, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 952941, 674510, 39216, 0, 0, 0, 0, 0, 321569, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600000, 992157, 0, 0, 0, 0, 0, 0, 839216, 992157, 878431, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 988235, 160784, 0, 0, 0, 82353, 717647, 992157, 988235, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 796078, 996078, 674510, 839216, 674510, 517647, 992157, 796078, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 674510, 831373, 592157, 274510, 513726, 988235, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 678431, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 992157, 670588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 482353, 878431, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 874510, 796078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 992157, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 839216, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 835294, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 988235, 556863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 874510, 1000000, 674510, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 835294, 988235, 713726, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_061() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 913725, 1000000, 631373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 952941, 992157, 764706, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 952941, 992157, 992157, 560784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 952941, 992157, 992157, 560784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 952941, 992157, 952941, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 631373, 992157, 992157, 682353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 992157, 992157, 992157, 627451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 992157, 992157, 705882, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 909804, 992157, 992157, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 905882, 992157, 992157, 470588, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 631373, 992157, 992157, 992157, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 992157, 992157, 992157, 682353, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 952941, 992157, 992157, 992157, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 717647, 992157, 992157, 992157, 674510, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 956863, 992157, 992157, 913725, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 333333, 972549, 992157, 964706, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 941176, 992157, 968627, 615686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 992157, 992157, 945098, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 415686, 992157, 992157, 760784, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 941176, 764706, 235294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_062() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 631373, 843137, 0, 0, 0, 0, 0, 0, 23529, 219608, 427451, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 996078, 847059, 43137, 427451, 435294, 678431, 823529, 823529, 843137, 996078, 996078, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294118, 964706, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 956863, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 611765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294118, 956863, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 862745, 701961, 964706, 996078, 996078, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647059, 996078, 996078, 996078, 996078, 980392, 878431, 498039, 482353, 98039, 54902, 35294, 898039, 996078, 929412, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 901961, 996078, 996078, 827451, 533333, 231373, 0, 0, 0, 0, 0, 407843, 996078, 996078, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 549020, 529412, 568627, 66667, 0, 0, 0, 0, 0, 0, 274510, 980392, 996078, 996078, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 811765, 996078, 996078, 756863, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 623529, 996078, 996078, 941176, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 925490, 996078, 992157, 419608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 850980, 996078, 996078, 721569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 207843, 988235, 996078, 996078, 792157, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 266667, 996078, 996078, 996078, 996078, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 925490, 996078, 996078, 996078, 686275, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 698039, 996078, 996078, 996078, 580392, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 733333, 996078, 996078, 996078, 552941, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 996078, 996078, 996078, 580392, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 686275, 996078, 937255, 392157, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 952941, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_063() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 149020, 376471, 682353, 1000000, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603922, 756863, 470588, 298039, 298039, 298039, 298039, 298039, 298039, 631373, 721569, 784314, 992157, 992157, 992157, 992157, 960784, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 898039, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 976471, 823529, 650980, 400000, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 741176, 674510, 576471, 254902, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 976471, 992157, 992157, 886275, 203922, 105882, 105882, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 513726, 992157, 992157, 462745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 800000, 992157, 866667, 341176, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 917647, 992157, 992157, 952941, 913725, 427451, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 913725, 992157, 992157, 992157, 992157, 772549, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 756863, 992157, 992157, 992157, 992157, 756863, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 90196, 486275, 639216, 988235, 992157, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 972549, 992157, 862745, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 705882, 992157, 992157, 992157, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 470588, 984314, 992157, 992157, 403922, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 580392, 968627, 992157, 992157, 992157, 992157, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 603922, 929412, 992157, 992157, 992157, 992157, 992157, 627451, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 403922, 988235, 992157, 992157, 992157, 992157, 992157, 894118, 435294, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 478431, 992157, 992157, 992157, 992157, 741176, 447059, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 886275, 792157, 490196, 145098, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_064() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 117647, 517647, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 768627, 988235, 988235, 772549, 98039, 98039, 98039, 98039, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 827451, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 662745, 992157, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 670588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 694118, 988235, 992157, 988235, 988235, 945098, 921569, 988235, 988235, 988235, 886275, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 917647, 988235, 980392, 658824, 235294, 243137, 560784, 988235, 988235, 988235, 631373, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 654902, 180392, 0, 117647, 839216, 988235, 988235, 988235, 298039, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 490196, 870588, 988235, 988235, 850980, 211765, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 411765, 674510, 949020, 988235, 988235, 988235, 866667, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 411765, 474510, 964706, 992157, 988235, 988235, 988235, 988235, 976471, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 992157, 992157, 992157, 1000000, 964706, 878431, 560784, 980392, 992157, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 988235, 988235, 898039, 647059, 180392, 0, 109804, 870588, 988235, 654902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 600000, 376471, 19608, 0, 0, 90196, 686275, 988235, 811765, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 192157, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 239216, 831373, 988235, 749020, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 988235, 815686, 235294, 0, 0, 0, 0, 0, 0, 0, 98039, 988235, 988235, 988235, 462745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 745098, 988235, 988235, 741176, 82353, 0, 0, 0, 0, 0, 400000, 780392, 988235, 988235, 447059, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 988235, 988235, 988235, 517647, 333333, 333333, 333333, 533333, 803922, 905882, 988235, 941176, 564706, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 403922, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 992157, 772549, 521569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 219608, 988235, 988235, 988235, 988235, 988235, 988235, 784314, 564706, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 43137, 384314, 513726, 513726, 513726, 313726, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_065() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 643137, 1000000, 823529, 749020, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 850980, 992157, 992157, 992157, 992157, 772549, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 647059, 992157, 992157, 788235, 321569, 933333, 992157, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 690196, 176471, 0, 905882, 992157, 878431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 882353, 992157, 858824, 54902, 0, 0, 905882, 992157, 878431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 611765, 992157, 952941, 266667, 0, 270588, 494118, 941176, 992157, 682353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345098, 988235, 992157, 890196, 0, 0, 305882, 992157, 992157, 992157, 913725, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 827451, 992157, 937255, 192157, 0, 66667, 584314, 992157, 992157, 992157, 992157, 764706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 992157, 992157, 584314, 164706, 458824, 882353, 992157, 992157, 992157, 992157, 921569, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 756863, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 768627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 639216, 839216, 992157, 803922, 690196, 925490, 992157, 992157, 815686, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 160784, 58824, 90196, 850980, 992157, 992157, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 654902, 992157, 992157, 592157, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 847059, 992157, 992157, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 839216, 992157, 992157, 894118, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 992157, 992157, 796078, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 874510, 992157, 992157, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 490196, 992157, 992157, 654902, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 490196, 992157, 992157, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 262745, 745098, 529412, 160784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_066() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 396078, 945098, 1000000, 701961, 396078, 133333, 180392, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 992157, 992157, 992157, 992157, 992157, 854902, 878431, 815686, 784314, 784314, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725490, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 972549, 419608, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325490, 984314, 992157, 992157, 737255, 627451, 627451, 627451, 627451, 262745, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 792157, 992157, 992157, 945098, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 968627, 992157, 992157, 690196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 968627, 992157, 952941, 658824, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 992157, 992157, 886275, 121569, 121569, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 992157, 992157, 992157, 992157, 992157, 654902, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 992157, 992157, 992157, 992157, 992157, 992157, 949020, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 227451, 298039, 866667, 462745, 298039, 933333, 992157, 992157, 537255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 905882, 992157, 992157, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 929412, 992157, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 835294, 992157, 992157, 666667, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 992157, 992157, 992157, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 7843, 0, 0, 435294, 862745, 992157, 992157, 823529, 388235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 588235, 54902, 31373, 364706, 972549, 992157, 992157, 780392, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 992157, 992157, 992157, 992157, 992157, 682353, 568627, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 647059, 992157, 992157, 992157, 588235, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 227451, 607843, 529412, 388235, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_067() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 27451, 7843, 7843, 27451, 203922, 509804, 952941, 1000000, 772549, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 50980, 50980, 396078, 647059, 992157, 635294, 682353, 992157, 992157, 992157, 992157, 992157, 968627, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 623529, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 388235, 835294, 992157, 992157, 972549, 894118, 894118, 894118, 894118, 925490, 992157, 992157, 992157, 992157, 686275, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 992157, 992157, 992157, 972549, 466667, 0, 0, 0, 0, 223529, 913725, 992157, 992157, 882353, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 647059, 788235, 364706, 537255, 0, 0, 0, 0, 188235, 925490, 992157, 992157, 800000, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 611765, 992157, 992157, 929412, 396078, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 682353, 925490, 992157, 831373, 270588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 411765, 992157, 992157, 921569, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 847059, 992157, 992157, 921569, 274510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 670588, 925490, 992157, 992157, 333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 611765, 925490, 992157, 874510, 286275, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 992157, 992157, 921569, 321569, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 505882, 933333, 992157, 992157, 372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 266667, 937255, 992157, 992157, 411765, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 784314, 992157, 992157, 843137, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 686275, 956863, 992157, 858824, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 992157, 992157, 941176, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 972549, 992157, 992157, 407843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 992157, 992157, 658824, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_068() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 415686, 780392, 1000000, 996078, 682353, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270588, 792157, 992157, 952941, 556863, 611765, 992157, 600000, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 870588, 992157, 807843, 145098, 0, 101961, 956863, 992157, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 239216, 992157, 886275, 94118, 0, 0, 70588, 909804, 992157, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 992157, 607843, 0, 0, 0, 125490, 992157, 992157, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 686275, 996078, 380392, 0, 0, 23529, 741176, 996078, 996078, 470588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 992157, 184314, 0, 0, 568627, 992157, 992157, 960784, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 992157, 184314, 0, 564706, 996078, 992157, 992157, 741176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603922, 992157, 388235, 501961, 984314, 996078, 992157, 992157, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 839216, 992157, 992157, 992157, 800000, 992157, 992157, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 313726, 313726, 82353, 996078, 866667, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 992157, 803922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 992157, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 956863, 992157, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 874510, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 1000000, 870588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756863, 996078, 631373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 933333, 996078, 403922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 933333, 960784, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 988235, 933333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 9);
}

#[test]
fn test_main_069() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 807843, 968627, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 588235, 917647, 996078, 956863, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 454902, 996078, 996078, 988235, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 956863, 996078, 905882, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 415686, 972549, 996078, 988235, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 850980, 996078, 984314, 478431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 631373, 996078, 996078, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 988235, 996078, 760784, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 498039, 988235, 996078, 772549, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 996078, 996078, 772549, 66667, 0, 0, 152941, 372549, 505882, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 725490, 996078, 941176, 109804, 0, 262745, 956863, 996078, 996078, 949020, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 996078, 996078, 392157, 0, 0, 682353, 996078, 996078, 949020, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 870588, 996078, 996078, 35294, 19608, 584314, 996078, 996078, 992157, 533333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 996078, 996078, 996078, 321569, 768627, 996078, 996078, 996078, 847059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 996078, 996078, 996078, 996078, 996078, 996078, 1000000, 996078, 384314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 745098, 996078, 996078, 996078, 996078, 996078, 996078, 682353, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 486275, 996078, 996078, 996078, 745098, 294118, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 996078, 996078, 176471, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 996078, 996078, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 639216, 996078, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_070() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 482353, 882353, 882353, 882353, 886275, 882353, 882353, 478431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 964706, 988235, 988235, 988235, 992157, 988235, 988235, 964706, 772549, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 419608, 811765, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 847059, 478431, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 988235, 992157, 988235, 988235, 925490, 439216, 439216, 619608, 988235, 988235, 988235, 992157, 988235, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 811765, 992157, 1000000, 992157, 894118, 494118, 0, 0, 0, 529412, 992157, 992157, 1000000, 992157, 870588, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 713726, 988235, 988235, 992157, 988235, 274510, 0, 0, 0, 0, 23529, 509804, 988235, 992157, 988235, 988235, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 941176, 988235, 988235, 894118, 580392, 47059, 0, 0, 0, 0, 0, 27451, 521569, 992157, 988235, 988235, 964706, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 952941, 988235, 988235, 988235, 549020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 623529, 988235, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 988235, 988235, 988235, 988235, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 988235, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 690196, 992157, 992157, 992157, 745098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 992157, 992157, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 949020, 290196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 623529, 988235, 988235, 988235, 800000, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 874510, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 286275, 772549, 992157, 988235, 988235, 901961, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 890196, 50980, 0, 0, 0, 15686, 113725, 113725, 113725, 611765, 988235, 988235, 992157, 988235, 901961, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 988235, 741176, 309804, 494118, 549020, 600000, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 992157, 992157, 992157, 992157, 1000000, 992157, 992157, 992157, 992157, 1000000, 992157, 992157, 992157, 992157, 800000, 368627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 658824, 952941, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 949020, 654902, 368627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 815686, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 913725, 643137, 192157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 329412, 329412, 329412, 329412, 329412, 329412, 329412, 329412, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_071() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 894118, 1000000, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 886275, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 890196, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 925490, 992157, 654902, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 901961, 992157, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 992157, 992157, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 992157, 992157, 898039, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 992157, 992157, 733333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 850980, 992157, 992157, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 850980, 992157, 992157, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 874510, 992157, 992157, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592157, 992157, 992157, 992157, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 239216, 874510, 992157, 992157, 992157, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 992157, 992157, 384314, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 992157, 992157, 364706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 690196, 992157, 713726, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_072() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 556863, 623529, 870588, 996078, 996078, 870588, 623529, 623529, 623529, 627451, 623529, 623529, 380392, 258824, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 752941, 952941, 596078, 678431, 843137, 949020, 992157, 992157, 992157, 996078, 992157, 992157, 992157, 992157, 941176, 882353, 447059, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164706, 0, 0, 0, 156863, 219608, 396078, 313726, 219608, 219608, 501961, 584314, 584314, 752941, 992157, 992157, 647059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 431373, 992157, 992157, 403922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 976471, 992157, 509804, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 686275, 976471, 984314, 670588, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 847059, 992157, 992157, 533333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 992157, 925490, 360784, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 882353, 972549, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 898039, 992157, 407843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 666667, 1000000, 803922, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 992157, 996078, 286275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 992157, 780392, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 941176, 992157, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 992157, 784314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 894118, 984314, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 878431, 0, 431373, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 905882, 498039, 996078, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 992157, 992157, 552941, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211765, 705882, 949020, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_073() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 262745, 576471, 576471, 576471, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 407843, 988235, 996078, 996078, 996078, 996078, 635294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 450980, 894118, 996078, 992157, 996078, 996078, 996078, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 803922, 996078, 996078, 905882, 435294, 576471, 996078, 996078, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364706, 996078, 996078, 996078, 149020, 0, 407843, 996078, 996078, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 996078, 988235, 447059, 47059, 447059, 937255, 992157, 533333, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 698039, 682353, 156863, 784314, 996078, 996078, 925490, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 678431, 886275, 847059, 952941, 996078, 996078, 996078, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 698039, 933333, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 968627, 996078, 996078, 929412, 211765, 211765, 478431, 996078, 996078, 643137, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 450980, 490196, 333333, 54902, 0, 0, 329412, 996078, 996078, 658824, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 996078, 996078, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 729412, 909804, 996078, 843137, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 960784, 949020, 262745, 0, 0, 0, 0, 0, 0, 0, 47059, 541176, 917647, 996078, 890196, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 866667, 996078, 996078, 643137, 0, 0, 0, 0, 239216, 258824, 258824, 682353, 1000000, 996078, 862745, 454902, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647059, 996078, 996078, 968627, 831373, 831373, 831373, 831373, 984314, 996078, 996078, 996078, 996078, 996078, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 847059, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 952941, 650980, 447059, 98039, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 996078, 996078, 996078, 996078, 996078, 901961, 721569, 627451, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 149020, 149020, 149020, 149020, 149020, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_074() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 1000000, 992157, 1000000, 992157, 337255, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 878431, 992157, 984314, 992157, 984314, 992157, 768627, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 337255, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 545098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 662745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 984314, 992157, 984314, 768627, 325490, 545098, 984314, 992157, 984314, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 772549, 1000000, 992157, 996078, 768627, 0, 0, 223529, 882353, 996078, 992157, 776471, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 768627, 109804, 0, 0, 0, 658824, 992157, 984314, 992157, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 992157, 996078, 992157, 662745, 0, 0, 0, 0, 662745, 996078, 992157, 662745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 984314, 992157, 984314, 658824, 0, 0, 0, 0, 658824, 992157, 984314, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 992157, 996078, 992157, 0, 0, 0, 0, 333333, 992157, 996078, 992157, 662745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 992157, 984314, 992157, 541176, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 772549, 996078, 992157, 886275, 219608, 0, 0, 0, 223529, 996078, 992157, 996078, 992157, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 658824, 0, 0, 0, 223529, 878431, 992157, 984314, 992157, 984314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 996078, 992157, 662745, 0, 0, 0, 552941, 992157, 996078, 992157, 886275, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 658824, 0, 223529, 658824, 992157, 984314, 992157, 984314, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 886275, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 992157, 984314, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 996078, 992157, 996078, 992157, 996078, 992157, 886275, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 325490, 992157, 984314, 992157, 984314, 768627, 325490, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_075() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 396078, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 811765, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 619608, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776471, 803922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 635294, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 976471, 713726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 945098, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 623529, 996078, 490196, 0, 11765, 19608, 39216, 333333, 333333, 333333, 152941, 7843, 0, 90196, 996078, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 996078, 996078, 843137, 698039, 878431, 996078, 996078, 996078, 996078, 996078, 996078, 807843, 274510, 82353, 996078, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 403922, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 988235, 639216, 921569, 741176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 729412, 996078, 996078, 996078, 996078, 996078, 996078, 882353, 835294, 733333, 835294, 925490, 996078, 996078, 996078, 996078, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 996078, 996078, 996078, 878431, 505882, 156863, 47059, 0, 0, 0, 90196, 254902, 690196, 996078, 996078, 913725, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 835294, 996078, 996078, 560784, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 133333, 466667, 949020, 556863, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 996078, 568627, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 611765, 996078, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 15686, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 996078, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 941176, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 854902, 670588, 643137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 800000, 996078, 996078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 996078, 721569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 694118, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 4);
}

#[test]
fn test_main_076() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 168627, 152941, 0, 141176, 239216, 580392, 611765, 992157, 992157, 1000000, 541176, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223529, 501961, 890196, 988235, 968627, 745098, 949020, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 203922, 705882, 964706, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 960784, 905882, 960784, 988235, 992157, 960784, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 909804, 988235, 988235, 988235, 992157, 988235, 988235, 823529, 741176, 329412, 219608, 160784, 882353, 988235, 992157, 384314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 886275, 988235, 988235, 988235, 925490, 576471, 196078, 54902, 0, 0, 141176, 874510, 988235, 988235, 682353, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 796078, 549020, 243137, 0, 0, 0, 0, 70588, 482353, 992157, 992157, 992157, 682353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 607843, 847059, 992157, 988235, 988235, 662745, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 329412, 635294, 917647, 988235, 988235, 992157, 988235, 988235, 937255, 909804, 847059, 498039, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274510, 937255, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 654902, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 662745, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 850980, 576471, 576471, 749020, 992157, 988235, 988235, 776471, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 968627, 968627, 827451, 827451, 549020, 243137, 176471, 0, 0, 0, 0, 70588, 607843, 992157, 992157, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 207843, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 988235, 988235, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 937255, 988235, 968627, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 250980, 854902, 988235, 988235, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 419608, 866667, 988235, 992157, 988235, 745098, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 168627, 411765, 717647, 992157, 992157, 992157, 968627, 690196, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 333333, 713726, 909804, 988235, 992157, 988235, 988235, 988235, 850980, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 929412, 988235, 988235, 988235, 988235, 992157, 960784, 698039, 219608, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 415686, 992157, 988235, 988235, 988235, 886275, 501961, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 819608, 988235, 745098, 164706, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_077() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 992157, 364706, 0, 0, 0, 0, 894118, 992157, 854902, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 976471, 988235, 858824, 0, 0, 0, 0, 886275, 988235, 988235, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 729412, 988235, 988235, 882353, 0, 0, 0, 380392, 976471, 988235, 988235, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345098, 988235, 988235, 972549, 352941, 0, 0, 200000, 933333, 988235, 988235, 698039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 674510, 988235, 988235, 905882, 86275, 0, 0, 556863, 988235, 988235, 988235, 639216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 933333, 988235, 988235, 882353, 0, 0, 0, 941176, 988235, 988235, 933333, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 776471, 988235, 988235, 988235, 603922, 0, 0, 407843, 972549, 988235, 988235, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 988235, 988235, 988235, 988235, 949020, 627451, 627451, 992157, 988235, 988235, 988235, 752941, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 682353, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 988235, 988235, 988235, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 988235, 831373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 647059, 643137, 521569, 521569, 545098, 992157, 1000000, 992157, 992157, 992157, 992157, 992157, 835294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 15686, 0, 0, 31373, 792157, 992157, 988235, 988235, 192157, 50980, 50980, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 694118, 992157, 988235, 850980, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 988235, 992157, 988235, 619608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 576471, 988235, 992157, 878431, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 494118, 988235, 988235, 992157, 568627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 988235, 988235, 992157, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 988235, 988235, 941176, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 988235, 988235, 521569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 988235, 988235, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 4);
}

#[test]
fn test_main_078() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725490, 35294, 0, 0, 0, 0, 0, 0, 0, 721569, 1000000, 996078, 996078, 682353, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 266667, 19608, 3922, 0, 0, 0, 0, 0, 0, 725490, 988235, 992157, 992157, 992157, 992157, 941176, 200000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 901961, 556863, 623529, 768627, 992157, 992157, 917647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 58824, 0, 11765, 156863, 992157, 992157, 964706, 188235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 650980, 992157, 992157, 917647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 611765, 992157, 992157, 968627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 937255, 992157, 992157, 796078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 819608, 929412, 992157, 992157, 976471, 317647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 827451, 992157, 992157, 992157, 972549, 674510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62745, 788235, 992157, 992157, 992157, 964706, 419608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 611765, 992157, 992157, 839216, 694118, 227451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 262745, 901961, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 7843, 0, 0, 0, 0, 337255, 992157, 992157, 992157, 882353, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 737255, 615686, 588235, 588235, 588235, 588235, 909804, 992157, 992157, 976471, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 921569, 972549, 988235, 992157, 992157, 992157, 992157, 992157, 992157, 788235, 0, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 439216, 796078, 486275, 929412, 992157, 992157, 992157, 992157, 972549, 501961, 0, 235294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 439216, 321569, 435294, 929412, 556863, 901961, 847059, 745098, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_079() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 749020, 501961, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 749020, 0, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 749020, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 749020, 1000000, 501961, 749020, 749020, 1000000, 749020, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 749020, 749020, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 250980, 749020, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 749020, 1000000, 1000000, 1000000, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 749020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 501961, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 749020, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 749020, 1000000, 749020, 749020, 0, 501961, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_080() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 792157, 713726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 403922, 992157, 709804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 635294, 941176, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 658824, 992157, 607843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 992157, 964706, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 513726, 996078, 996078, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 843137, 992157, 654902, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 701961, 996078, 960784, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 992157, 996078, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 854902, 992157, 662745, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 729412, 996078, 996078, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 482353, 980392, 992157, 458824, 0, 0, 286275, 721569, 796078, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 933333, 992157, 701961, 43137, 43137, 674510, 921569, 992157, 992157, 709804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 717647, 992157, 905882, 121569, 0, 588235, 992157, 929412, 976471, 992157, 556863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 996078, 992157, 243137, 0, 509804, 996078, 709804, 94118, 854902, 992157, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 537255, 1000000, 854902, 50980, 23529, 792157, 815686, 50980, 600000, 996078, 639216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 992157, 996078, 372549, 0, 352941, 992157, 494118, 749020, 980392, 721569, 47059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 992157, 996078, 329412, 196078, 886275, 992157, 996078, 992157, 866667, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 992157, 996078, 992157, 992157, 992157, 992157, 949020, 639216, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 411765, 639216, 968627, 992157, 709804, 384314, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_081() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 925490, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474510, 956863, 898039, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 956863, 996078, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 803922, 996078, 490196, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 996078, 890196, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 709804, 996078, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 972549, 996078, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 996078, 811765, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 686275, 996078, 364706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 870588, 882353, 7843, 0, 0, 0, 0, 0, 11765, 305882, 937255, 701961, 125490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243137, 996078, 878431, 0, 0, 0, 0, 0, 105882, 600000, 996078, 996078, 996078, 470588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474510, 996078, 631373, 0, 0, 0, 0, 356863, 862745, 996078, 933333, 568627, 815686, 470588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647059, 996078, 313726, 0, 0, 47059, 521569, 968627, 996078, 925490, 243137, 0, 705882, 643137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 862745, 996078, 98039, 0, 0, 764706, 996078, 996078, 733333, 50980, 0, 0, 705882, 752941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 862745, 996078, 98039, 0, 180392, 972549, 980392, 729412, 43137, 0, 0, 321569, 964706, 470588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 882353, 58824, 0, 549020, 996078, 800000, 0, 0, 0, 211765, 921569, 996078, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474510, 996078, 203922, 0, 756863, 996078, 439216, 0, 90196, 341176, 972549, 996078, 776471, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474510, 996078, 968627, 745098, 984314, 996078, 615686, 670588, 905882, 996078, 996078, 647059, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 749020, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 894118, 321569, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 415686, 603922, 976471, 996078, 996078, 835294, 509804, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_082() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 603922, 1000000, 541176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 733333, 996078, 576471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 505882, 988235, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 788235, 788235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 803922, 607843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 996078, 607843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 996078, 607843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 996078, 607843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 996078, 607843, 0, 0, 0, 0, 31373, 376471, 576471, 576471, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141176, 996078, 607843, 0, 0, 0, 31373, 647059, 996078, 996078, 996078, 827451, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 431373, 996078, 607843, 0, 0, 0, 388235, 996078, 996078, 905882, 870588, 992157, 749020, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 996078, 607843, 0, 0, 180392, 968627, 984314, 505882, 62745, 0, 690196, 996078, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 847059, 607843, 0, 0, 490196, 996078, 737255, 0, 0, 0, 741176, 996078, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 788235, 721569, 0, 0, 929412, 878431, 58824, 0, 0, 0, 964706, 996078, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572549, 992157, 517647, 274510, 992157, 819608, 0, 0, 11765, 721569, 992157, 996078, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 941176, 964706, 686275, 996078, 619608, 27451, 235294, 815686, 996078, 996078, 800000, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 945098, 996078, 996078, 921569, 874510, 996078, 996078, 996078, 952941, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368627, 956863, 996078, 996078, 996078, 996078, 917647, 545098, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 949020, 800000, 427451, 243137, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 458824, 941176, 368627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 6);
}

#[test]
fn test_main_083() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 313726, 764706, 996078, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 419608, 870588, 996078, 996078, 996078, 988235, 580392, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 937255, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 760784, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 886275, 996078, 996078, 996078, 996078, 682353, 776471, 666667, 972549, 996078, 980392, 184314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352941, 996078, 996078, 996078, 996078, 635294, 0, 0, 0, 196078, 925490, 996078, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 996078, 996078, 996078, 917647, 54902, 0, 0, 0, 196078, 925490, 996078, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 996078, 996078, 964706, 223529, 74510, 0, 31373, 392157, 972549, 996078, 862745, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294118, 996078, 996078, 952941, 662745, 921569, 760784, 823529, 996078, 996078, 780392, 101961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 988235, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 890196, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 996078, 996078, 996078, 996078, 996078, 996078, 996078, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 996078, 996078, 996078, 996078, 584314, 976471, 996078, 925490, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 921569, 996078, 996078, 972549, 258824, 0, 223529, 976471, 996078, 352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576471, 996078, 996078, 870588, 160784, 0, 0, 0, 847059, 996078, 800000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 905882, 996078, 901961, 58824, 0, 0, 0, 98039, 917647, 996078, 513726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 858824, 996078, 592157, 0, 0, 0, 0, 50980, 941176, 996078, 423529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 858824, 996078, 309804, 0, 0, 0, 43137, 611765, 996078, 964706, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 858824, 996078, 713726, 27451, 3922, 223529, 858824, 996078, 996078, 752941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 835294, 996078, 996078, 811765, 764706, 996078, 1000000, 996078, 952941, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 988235, 996078, 996078, 996078, 996078, 996078, 627451, 137255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 686275, 756863, 984314, 650980, 309804, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_084() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 443137, 690196, 992157, 992157, 929412, 443137, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 298039, 760784, 894118, 988235, 992157, 988235, 988235, 988235, 988235, 945098, 698039, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 964706, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 341176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 913725, 282353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 874510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 639216, 992157, 698039, 549020, 309804, 0, 125490, 549020, 549020, 1000000, 992157, 992157, 882353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 105882, 35294, 0, 0, 0, 0, 0, 0, 501961, 988235, 988235, 976471, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 478431, 988235, 988235, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 698039, 988235, 988235, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 882353, 988235, 988235, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 992157, 992157, 992157, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 333333, 933333, 988235, 988235, 988235, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 223529, 776471, 772549, 345098, 611765, 988235, 992157, 988235, 988235, 988235, 556863, 223529, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 113725, 541176, 878431, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 694118, 662745, 282353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 443137, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 937255, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 690196, 992157, 992157, 992157, 992157, 1000000, 992157, 992157, 992157, 992157, 1000000, 992157, 992157, 992157, 992157, 1000000, 992157, 992157, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 776471, 215686, 219608, 215686, 215686, 215686, 215686, 466667, 964706, 988235, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 929412, 988235, 988235, 988235, 988235, 941176, 874510, 447059, 109804, 0, 0, 0, 0, 0, 0, 0, 478431, 964706, 988235, 925490, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 929412, 988235, 925490, 439216, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 772549, 988235, 439216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_085() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125490, 654902, 764706, 992157, 992157, 992157, 749020, 247059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 784314, 972549, 988235, 988235, 988235, 992157, 949020, 262745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 376471, 376471, 827451, 992157, 988235, 933333, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 584314, 988235, 988235, 419608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 686275, 988235, 933333, 203922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 988235, 988235, 282353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 988235, 835294, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 729412, 988235, 800000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 988235, 988235, 882353, 325490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 517647, 988235, 988235, 988235, 752941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 435294, 517647, 517647, 745098, 1000000, 992157, 992157, 984314, 498039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137255, 890196, 988235, 988235, 988235, 988235, 992157, 988235, 976471, 498039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90196, 376471, 756863, 847059, 847059, 984314, 992157, 976471, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 945098, 992157, 894118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 945098, 992157, 780392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 980392, 980392, 301961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 972549, 988235, 560784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 988235, 988235, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 988235, 988235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 945098, 760784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_086() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 725490, 996078, 996078, 1000000, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 992157, 992157, 454902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 992157, 992157, 803922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 992157, 992157, 803922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 992157, 992157, 992157, 992157, 396078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 419608, 992157, 992157, 992157, 992157, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 992157, 992157, 992157, 992157, 992157, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 992157, 992157, 992157, 992157, 992157, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 760784, 992157, 992157, 992157, 992157, 917647, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592157, 992157, 992157, 992157, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592157, 992157, 992157, 992157, 992157, 733333, 121569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 301961, 949020, 992157, 992157, 992157, 858824, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 992157, 992157, 992157, 843137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 333333, 992157, 992157, 992157, 992157, 843137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 945098, 992157, 992157, 992157, 992157, 156863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 992157, 992157, 992157, 992157, 992157, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596078, 992157, 992157, 992157, 992157, 545098, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 992157, 992157, 992157, 992157, 501961, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 670588, 992157, 992157, 992157, 686275, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 690196, 992157, 713726, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_087() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 815686, 1000000, 356863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 415686, 992157, 992157, 717647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 905882, 992157, 992157, 717647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 501961, 988235, 992157, 992157, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 513726, 992157, 992157, 992157, 576471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 776471, 992157, 992157, 992157, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 317647, 976471, 992157, 686275, 894118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 780392, 901961, 556863, 23529, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82353, 776471, 819608, 129412, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 701961, 992157, 478431, 0, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 686275, 901961, 50980, 0, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 705882, 992157, 145098, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 427451, 427451, 596078, 992157, 992157, 992157, 956863, 427451, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 831373, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568627, 992157, 678431, 388235, 388235, 388235, 388235, 388235, 388235, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_088() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 447059, 749020, 168627, 509804, 1000000, 992157, 992157, 717647, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 482353, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 886275, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 925490, 988235, 988235, 988235, 956863, 666667, 184314, 156863, 988235, 988235, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 580392, 988235, 968627, 466667, 192157, 0, 0, 86275, 988235, 988235, 517647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 580392, 850980, 184314, 0, 0, 0, 0, 600000, 988235, 988235, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 615686, 992157, 992157, 992157, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 615686, 988235, 988235, 988235, 537255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43137, 498039, 843137, 992157, 988235, 984314, 525490, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 988235, 988235, 992157, 905882, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 988235, 988235, 992157, 658824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 827451, 658824, 815686, 360784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 607843, 933333, 250980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 882353, 968627, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 396078, 988235, 541176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 988235, 988235, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 992157, 992157, 419608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 623529, 505882, 333333, 333333, 333333, 54902, 196078, 333333, 556863, 988235, 988235, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 960784, 988235, 988235, 988235, 925490, 960784, 988235, 988235, 988235, 956863, 207843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 823529, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 301961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 576471, 988235, 988235, 992157, 988235, 956863, 474510, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_089() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 70588, 235294, 729412, 996078, 1000000, 996078, 564706, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 321569, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 690196, 164706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 454902, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 619608, 0, 0, 0, 39216, 329412, 670588, 192157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 894118, 992157, 992157, 992157, 745098, 490196, 254902, 717647, 992157, 992157, 278431, 0, 274510, 549020, 788235, 992157, 992157, 894118, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 992157, 992157, 992157, 545098, 23529, 0, 0, 192157, 643137, 772549, 380392, 552941, 988235, 992157, 992157, 992157, 992157, 854902, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 992157, 992157, 992157, 184314, 0, 0, 0, 70588, 419608, 862745, 992157, 992157, 992157, 992157, 992157, 992157, 662745, 133333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3922, 607843, 992157, 992157, 631373, 15686, 23529, 749020, 956863, 992157, 992157, 992157, 992157, 992157, 917647, 423529, 43137, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 964706, 992157, 992157, 807843, 772549, 992157, 992157, 992157, 992157, 992157, 909804, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 952941, 992157, 992157, 992157, 992157, 992157, 992157, 866667, 443137, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 741176, 992157, 992157, 992157, 992157, 772549, 298039, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 305882, 937255, 992157, 992157, 992157, 992157, 368627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 941176, 992157, 992157, 992157, 992157, 992157, 541176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 992157, 992157, 992157, 992157, 992157, 992157, 831373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 984314, 992157, 992157, 415686, 431373, 992157, 992157, 913725, 176471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 992157, 992157, 831373, 78431, 474510, 992157, 992157, 992157, 760784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 992157, 992157, 898039, 650980, 952941, 992157, 992157, 992157, 458824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 756863, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 533333, 992157, 992157, 992157, 992157, 992157, 992157, 768627, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352941, 992157, 992157, 992157, 992157, 992157, 392157, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 415686, 992157, 992157, 666667, 66667, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_090() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 588235, 992157, 1000000, 996078, 874510, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 909804, 992157, 992157, 992157, 992157, 882353, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 988235, 992157, 992157, 788235, 858824, 992157, 627451, 0, 0, 66667, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47059, 905882, 992157, 925490, 509804, 7843, 639216, 454902, 74510, 0, 333333, 850980, 827451, 435294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270588, 992157, 992157, 415686, 0, 0, 35294, 0, 0, 0, 505882, 992157, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 470588, 992157, 992157, 384314, 0, 0, 0, 0, 0, 294118, 898039, 992157, 992157, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 992157, 992157, 572549, 0, 0, 0, 278431, 760784, 980392, 992157, 992157, 580392, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 768627, 992157, 839216, 50980, 243137, 552941, 972549, 992157, 992157, 929412, 552941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 643137, 992157, 992157, 866667, 992157, 992157, 992157, 988235, 741176, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 329412, 992157, 992157, 992157, 992157, 992157, 752941, 266667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 784314, 992157, 992157, 992157, 929412, 466667, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 450980, 937255, 992157, 992157, 992157, 992157, 431373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 745098, 992157, 992157, 992157, 850980, 992157, 992157, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129412, 847059, 992157, 992157, 862745, 200000, 439216, 992157, 992157, 427451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 854902, 992157, 960784, 407843, 35294, 0, 431373, 992157, 992157, 301961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 752941, 992157, 968627, 321569, 0, 0, 23529, 639216, 992157, 992157, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 992157, 992157, 556863, 0, 0, 19608, 611765, 992157, 992157, 890196, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 941176, 992157, 937255, 486275, 450980, 450980, 815686, 992157, 992157, 784314, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 623529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 423529, 584314, 811765, 992157, 615686, 584314, 584314, 321569, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_091() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 462745, 337255, 133333, 541176, 337255, 541176, 749020, 792157, 992157, 870588, 541176, 541176, 501961, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 894118, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 988235, 988235, 988235, 988235, 992157, 925490, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 917647, 988235, 988235, 992157, 988235, 988235, 890196, 717647, 721569, 717647, 717647, 717647, 964706, 992157, 988235, 596078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 627451, 627451, 180392, 176471, 176471, 113725, 0, 0, 0, 0, 0, 698039, 992157, 988235, 717647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 901961, 992157, 988235, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 407843, 992157, 1000000, 768627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 925490, 988235, 854902, 129412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50980, 796078, 988235, 988235, 454902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 682353, 988235, 988235, 823529, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 709804, 988235, 988235, 823529, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 298039, 1000000, 992157, 843137, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 650980, 988235, 992157, 956863, 384314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325490, 941176, 988235, 992157, 482353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 317647, 941176, 988235, 988235, 384314, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 956863, 988235, 988235, 576471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 290196, 1000000, 992157, 992157, 631373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 317647, 956863, 992157, 988235, 941176, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 811765, 988235, 992157, 988235, 392157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 811765, 988235, 960784, 545098, 50980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 811765, 988235, 698039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_092() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196078, 247059, 788235, 996078, 1000000, 580392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7843, 231373, 552941, 968627, 996078, 996078, 996078, 964706, 921569, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 537255, 996078, 996078, 996078, 996078, 996078, 709804, 192157, 133333, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 494118, 960784, 996078, 996078, 996078, 984314, 658824, 50980, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 341176, 196078, 400000, 996078, 996078, 996078, 964706, 549020, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 917647, 682353, 454902, 996078, 996078, 698039, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 207843, 866667, 996078, 788235, 654902, 925490, 501961, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54902, 509804, 988235, 996078, 941176, 239216, 78431, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 996078, 996078, 686275, 86275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 996078, 996078, 309804, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 560784, 964706, 996078, 733333, 39216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192157, 780392, 996078, 807843, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 670588, 996078, 933333, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 427451, 909804, 929412, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325490, 909804, 858824, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 498039, 996078, 443137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 729412, 988235, 643137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 403922, 458824, 266667, 266667, 66667, 533333, 501961, 800000, 996078, 858824, 462745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572549, 996078, 996078, 996078, 909804, 996078, 968627, 517647, 254902, 109804, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 247059, 709804, 858824, 701961, 996078, 721569, 349020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 5);
}

#[test]
fn test_main_093() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 529412, 996078, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 407843, 980392, 858824, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 937255, 992157, 407843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 937255, 992157, 682353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 937255, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 937255, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 937255, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 992157, 992157, 211765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352941, 992157, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145098, 854902, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 768627, 996078, 588235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760784, 992157, 584314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760784, 992157, 854902, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 992157, 996078, 450980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 992157, 996078, 827451, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176471, 992157, 996078, 992157, 349020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 776471, 996078, 992157, 349020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380392, 1000000, 992157, 901961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 894118, 992157, 980392, 403922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 415686, 992157, 992157, 521569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 1);
}

#[test]
fn test_main_094() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 701961, 996078, 996078, 400000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 462745, 996078, 992157, 992157, 631373, 0, 0, 7843, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 427451, 850980, 992157, 996078, 552941, 305882, 23529, 0, 0, 23529, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 658824, 992157, 992157, 992157, 662745, 11765, 0, 0, 62745, 482353, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760784, 992157, 992157, 929412, 462745, 0, 0, 0, 0, 529412, 815686, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 819608, 1000000, 996078, 717647, 176471, 0, 0, 0, 0, 623529, 996078, 298039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 482353, 992157, 996078, 568627, 47059, 0, 0, 0, 7843, 607843, 968627, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 682353, 992157, 717647, 47059, 0, 0, 0, 0, 462745, 992157, 572549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 329412, 992157, 772549, 82353, 0, 0, 0, 243137, 921569, 764706, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94118, 901961, 996078, 709804, 266667, 0, 298039, 996078, 992157, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 447059, 1000000, 996078, 996078, 847059, 996078, 1000000, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 745098, 992157, 992157, 992157, 996078, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 992157, 992157, 992157, 996078, 819608, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 894118, 992157, 968627, 690196, 996078, 992157, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149020, 905882, 992157, 992157, 396078, 0, 996078, 992157, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184314, 905882, 1000000, 996078, 454902, 39216, 525490, 1000000, 976471, 235294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 858824, 992157, 996078, 568627, 70588, 513726, 992157, 996078, 705882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 968627, 992157, 996078, 411765, 662745, 992157, 992157, 921569, 105882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 309804, 992157, 992157, 996078, 992157, 992157, 968627, 690196, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70588, 639216, 992157, 996078, 992157, 725490, 219608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_095() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372549, 470588, 1000000, 996078, 996078, 996078, 996078, 568627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 231373, 784314, 980392, 992157, 992157, 992157, 992157, 992157, 992157, 929412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321569, 733333, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 964706, 313726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 545098, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 980392, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 462745, 839216, 764706, 239216, 239216, 239216, 603922, 992157, 992157, 992157, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 992157, 992157, 992157, 149020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 964706, 992157, 992157, 560784, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168627, 992157, 992157, 949020, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160784, 847059, 992157, 992157, 615686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 490196, 992157, 992157, 992157, 329412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11765, 407843, 964706, 992157, 992157, 745098, 98039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180392, 486275, 486275, 486275, 545098, 992157, 992157, 992157, 756863, 62745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 274510, 623529, 917647, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 505882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 431373, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 831373, 133333, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000000, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 631373, 454902, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 850980, 992157, 992157, 992157, 992157, 992157, 764706, 384314, 749020, 823529, 992157, 992157, 992157, 992157, 992157, 866667, 454902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 968627, 992157, 992157, 968627, 627451, 23529, 0, 0, 109804, 415686, 960784, 988235, 992157, 992157, 992157, 980392, 635294, 505882, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 568627, 568627, 137255, 0, 0, 0, 0, 0, 0, 0, 501961, 850980, 992157, 992157, 992157, 992157, 992157, 643137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121569, 176471, 690196, 913725, 992157, 945098, 780392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250980, 388235, 305882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 2);
}

#[test]
fn test_main_096() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133333, 678431, 996078, 996078, 901961, 415686, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 866667, 992157, 992157, 992157, 992157, 992157, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 996078, 992157, 992157, 749020, 537255, 992157, 988235, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27451, 278431, 996078, 819608, 305882, 19608, 11765, 788235, 992157, 803922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 643137, 992157, 968627, 235294, 0, 0, 0, 780392, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 647059, 992157, 992157, 188235, 0, 0, 0, 0, 780392, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 650980, 992157, 847059, 329412, 0, 0, 0, 0, 0, 556863, 988235, 980392, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39216, 647059, 992157, 964706, 384314, 0, 0, 0, 0, 0, 0, 0, 721569, 992157, 690196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352941, 992157, 980392, 384314, 0, 0, 0, 0, 0, 0, 0, 0, 909804, 992157, 556863, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 458824, 949020, 992157, 384314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 909804, 992157, 258824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 282353, 980392, 968627, 376471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 960784, 898039, 113725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 823529, 992157, 776471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 835294, 992157, 819608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 890196, 992157, 419608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 392157, 992157, 803922, 309804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 262745, 992157, 909804, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 313726, 980392, 992157, 482353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 992157, 811765, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 831373, 992157, 670588, 31373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 694118, 992157, 474510, 0, 0, 0, 0, 0, 0, 0, 243137, 792157, 992157, 917647, 141176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 988235, 686275, 15686, 0, 0, 0, 0, 39216, 537255, 968627, 992157, 874510, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 823529, 992157, 647059, 39216, 0, 31373, 309804, 945098, 1000000, 949020, 647059, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384314, 980392, 992157, 792157, 737255, 780392, 992157, 992157, 823529, 321569, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 349020, 654902, 803922, 784314, 486275, 129412, 129412, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}

#[test]
fn test_main_097() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 592157, 937255, 917647, 364706, 0, 0, 0, 133333, 552941, 592157, 576471, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 921569, 996078, 996078, 996078, 607843, 0, 0, 564706, 937255, 996078, 996078, 984314, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 847059, 996078, 996078, 996078, 886275, 105882, 211765, 862745, 996078, 996078, 996078, 960784, 486275, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109804, 839216, 996078, 996078, 682353, 262745, 278431, 490196, 992157, 996078, 996078, 898039, 470588, 196078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 537255, 996078, 996078, 690196, 27451, 54902, 776471, 996078, 996078, 996078, 682353, 172549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101961, 917647, 996078, 1000000, 121569, 70588, 592157, 996078, 996078, 952941, 403922, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172549, 996078, 996078, 721569, 19608, 627451, 996078, 996078, 972549, 282353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 996078, 996078, 639216, 462745, 996078, 996078, 949020, 294118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376471, 992157, 996078, 996078, 996078, 996078, 996078, 615686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486275, 996078, 996078, 996078, 996078, 996078, 760784, 290196, 3922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 937255, 996078, 996078, 996078, 996078, 996078, 996078, 337255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 392157, 996078, 996078, 894118, 427451, 600000, 933333, 996078, 996078, 239216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254902, 933333, 996078, 898039, 180392, 0, 0, 305882, 996078, 996078, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 768627, 996078, 945098, 333333, 0, 0, 0, 207843, 996078, 996078, 576471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 392157, 988235, 996078, 768627, 0, 0, 0, 0, 501961, 996078, 996078, 243137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776471, 996078, 835294, 82353, 0, 0, 0, 254902, 960784, 996078, 984314, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776471, 996078, 670588, 0, 0, 19608, 533333, 945098, 996078, 996078, 725490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776471, 996078, 952941, 647059, 564706, 866667, 996078, 996078, 996078, 803922, 66667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 988235, 996078, 996078, 996078, 996078, 996078, 992157, 690196, 74510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 721569, 996078, 996078, 803922, 321569, 180392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 8);
}

#[test]
fn test_main_098() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 1000000, 1000000, 1000000, 913725, 509804, 509804, 156863, 27451, 19608, 0, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560784, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 858824, 533333, 760784, 533333, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286275, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 823529, 90196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31373, 694118, 894118, 894118, 960784, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258824, 482353, 525490, 741176, 870588, 870588, 909804, 992157, 992157, 992157, 627451, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 886275, 992157, 992157, 992157, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 827451, 992157, 992157, 992157, 70588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219608, 941176, 992157, 992157, 913725, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 552941, 992157, 992157, 992157, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215686, 811765, 992157, 992157, 992157, 223529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 427451, 992157, 992157, 992157, 992157, 94118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 356863, 945098, 992157, 992157, 886275, 274510, 23529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200000, 949020, 992157, 992157, 992157, 627451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78431, 501961, 992157, 992157, 992157, 874510, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400000, 992157, 992157, 992157, 992157, 474510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600000, 960784, 992157, 992157, 992157, 286275, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156863, 964706, 992157, 992157, 992157, 729412, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388235, 992157, 992157, 992157, 992157, 490196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 435294, 992157, 992157, 992157, 639216, 117647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 411765, 992157, 886275, 388235, 7843, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 7);
}

#[test]
fn test_main_099() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 70588, 513726, 533333, 827451, 996078, 996078, 1000000, 996078, 301961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98039, 490196, 921569, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 952941, 58824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 494118, 890196, 992157, 921569, 784314, 784314, 521569, 321569, 321569, 321569, 572549, 992157, 992157, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 419608, 992157, 992157, 784314, 466667, 0, 0, 0, 0, 0, 0, 501961, 992157, 992157, 415686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 913725, 992157, 756863, 164706, 0, 0, 0, 0, 0, 0, 270588, 890196, 992157, 956863, 78431, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 772549, 509804, 39216, 0, 0, 0, 0, 0, 70588, 525490, 968627, 992157, 992157, 341176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19608, 0, 0, 0, 0, 0, 11765, 286275, 788235, 992157, 992157, 992157, 992157, 498039, 490196, 184314, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 749020, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 882353, 192157, 15686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 952941, 992157, 992157, 992157, 866667, 831373, 831373, 831373, 850980, 992157, 992157, 992157, 494118, 11765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 729412, 717647, 298039, 298039, 70588, 0, 0, 0, 35294, 388235, 760784, 945098, 992157, 501961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 788235, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 788235, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 788235, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 788235, 992157, 992157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 117647, 43137, 0, 0, 0, 0, 0, 0, 23529, 454902, 909804, 992157, 937255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66667, 188235, 800000, 976471, 301961, 0, 0, 0, 0, 0, 109804, 552941, 992157, 992157, 917647, 215686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74510, 729412, 992157, 992157, 564706, 0, 0, 0, 98039, 258824, 498039, 878431, 992157, 992157, 909804, 447059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188235, 933333, 992157, 992157, 878431, 788235, 788235, 788235, 866667, 992157, 992157, 992157, 933333, 666667, 235294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 627451, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 788235, 545098, 109804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23529, 66667, 66667, 66667, 145098, 529412, 529412, 529412, 109804, 35294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 3);
}

#[test]
fn test_main_100() {
  let sample = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 654902, 996078, 592157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 490196, 996078, 992157, 949020, 235294, 27451, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 584314, 996078, 992157, 992157, 992157, 498039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 584314, 996078, 992157, 992157, 992157, 698039, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105882, 400000, 945098, 996078, 992157, 992157, 992157, 960784, 431373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 117647, 776471, 992157, 992157, 949020, 972549, 992157, 992157, 992157, 956863, 333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117647, 992157, 992157, 992157, 678431, 278431, 388235, 498039, 992157, 992157, 992157, 745098, 345098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 490196, 945098, 992157, 866667, 192157, 23529, 0, 0, 39216, 807843, 992157, 992157, 992157, 764706, 82353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86275, 901961, 992157, 992157, 639216, 0, 0, 0, 0, 0, 109804, 905882, 992157, 992157, 992157, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35294, 776471, 992157, 992157, 992157, 639216, 0, 0, 0, 0, 0, 0, 878431, 992157, 992157, 992157, 231373, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647059, 996078, 996078, 996078, 996078, 403922, 0, 0, 0, 0, 0, 0, 643137, 996078, 996078, 643137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 725490, 992157, 992157, 964706, 447059, 11765, 0, 0, 0, 0, 0, 113725, 807843, 992157, 866667, 145098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 992157, 992157, 992157, 494118, 0, 0, 0, 0, 0, 0, 39216, 807843, 992157, 992157, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 992157, 992157, 992157, 290196, 0, 0, 0, 0, 0, 113725, 501961, 992157, 992157, 992157, 466667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 992157, 992157, 992157, 462745, 0, 0, 0, 176471, 886275, 905882, 992157, 992157, 992157, 886275, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235294, 992157, 992157, 992157, 890196, 117647, 117647, 568627, 874510, 996078, 992157, 992157, 992157, 713726, 254902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113725, 807843, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 996078, 992157, 647059, 466667, 54902, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 439216, 992157, 992157, 992157, 992157, 992157, 992157, 992157, 1000000, 560784, 19608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15686, 505882, 815686, 941176, 992157, 992157, 992157, 886275, 576471, 43137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360784, 992157, 992157, 541176, 168627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  assert(main(sample) == 0);
}