Quelle  finite-orbits.g   Sprache: unbekannt

#############################################################################
##
#W  finite-orbits.g              GAP4 Package `RCWA'              Stefan Kohl
##
##  This file contains the part of the data library of groups generated by
##  3 class transpositions which concerns finite orbits of these groups.
##
##  Its contents are a record 'finiteorbits' with the following components:
##
##  - 'exceed' is a list of length 10, and exceed[k] is the list of the
##    indices of those groups which are believed to have only finite orbits,
##    but which have orbits longer than 256 which intersect nontrivially with
##    the interval [-2^k..2^k].
##
##  - 'dontexceed' is a list of length 10, and dontexceed[k] is the list of
##    the indices of those groups which are believed to have not only finite
##    orbits, but all of whose orbits which intersect nontrivially with the
##    interval [-2^k..2^k] have length <= 128.
##
##  - 'maxorbitlengths' is a list of length 10 of lists of length
##    Length(grps) = 52394. maxorbitlengths[k][i] is the length of the lon-
##    gest finite orbit of grps[i] which intersects nontrivially with the
##    interval [-2^k..2^k] if all orbits intersecting with this interval
##    have length <= 256, and unbound otherwise.
##
#############################################################################

return rec(

exceed :=
[ [ 4474,6595,11685,11689,28892,30206,32435,32700,32723,35800,
   36096,38102,38122,49005,50301,51172 ],
 [ 4474,6595,11685,11689,28892,30206,31337,32435,32700,32723,
   35800,36095,36096,36103,37818,37851,38102,38122,48509,49005,
   50300,50301,51172,51617 ],
 [ 1277,1280,1284,1286,4436,4463,4474,6595,6608,9729,11685,11689,
   16635,20096,20185,25064,27204,27212,28581,28608,28872,28892,
   30206,30211,30218,31211,31337,31472,31485,31766,32385,32414,
   32434,32435,32562,32700,32705,32718,32723,35016,35800,36095,
   36096,36103,36916,37496,37818,37851,38102,38122,38133,43598,
   44528,47815,47947,48509,49005,49356,50300,50301,51159,51172,
   51617 ],
 [ 1277,1280,1284,1286,4436,4463,4474,6595,6608,9729,11215,11685,
   11689,16635,20096,20185,20430,23437,24819,25064,26491,27204,
   27212,27508,27754,27802,28521,28581,28608,28872,28892,29039,
   29586,29909,29935,30063,30205,30206,30211,30217,30218,31211,
   31337,31472,31485,31766,31820,32168,32303,32359,32385,32414,
   32415,32434,32435,32562,32699,32700,32705,32711,32718,32723,
   33887,34712,35016,35794,35799,35800,35941,35946,36095,36096,
   36103,36835,36916,37496,37651,37818,37824,37851,37966,37971,
   38102,38107,38122,38133,43598,44528,46585,47811,47815,47827,
   47947,48509,49005,49309,49356,49364,50300,50301,51159,51160,
   51172,51617,51732 ],
 [ 1277,1280,1284,1286,4436,4455,4463,4474,6577,6594,6595,6608,
   6622,9729,11215,11441,11685,11689,14984,15138,15157,16635,
   18592,20096,20185,20236,20430,21839,23437,24767,24819,25064,
   26491,27203,27204,27212,27508,27509,27754,27802,28521,28581,
   28608,28616,28871,28872,28892,28898,29039,29586,29909,29935,
   29943,30054,30062,30063,30192,30205,30206,30211,30217,30218,
   31211,31330,31337,31472,31485,31766,31820,32168,32303,32359,
   32385,32414,32415,32434,32435,32556,32562,32563,32699,32700,
   32705,32706,32711,32718,32723,32725,33789,33790,33887,33899,
   34712,34720,35014,35016,35794,35799,35800,35826,35941,35946,
   36095,36096,36103,36107,36835,36916,36976,37037,37496,37651,
   37818,37824,37851,37852,37965,37966,37971,37972,38046,38102,
   38107,38122,38127,38128,38133,38134,43598,43726,44528,44535,
   46580,46585,46700,46705,47811,47815,47827,47947,48094,48354,
   48509,48963,49005,49013,49309,49356,49364,50288,50300,50301,
   51159,51160,51172,51617,51638,51732 ],
 [ 1277,1280,1284,1286,4436,4444,4455,4463,4474,4477,6572,6577,
   6594,6595,6608,6622,6630,9729,10451,11215,11441,11685,11689,
   14984,15138,15157,16635,17768,18592,20096,20185,20236,20430,
   20808,20830,21007,21839,23437,24767,24819,25064,25999,26016,
   26039,26491,27203,27204,27212,27506,27508,27509,27754,27802,
   28521,28581,28582,28608,28610,28616,28871,28872,28874,28892,
   28898,29039,29586,29909,29916,29935,29943,30054,30056,30062,
   30063,30192,30205,30206,30211,30217,30218,31211,31218,31330,
   31337,31472,31473,31485,31487,31766,31820,32168,32303,32359,
   32385,32414,32415,32434,32435,32443,32554,32556,32562,32563,
   32692,32693,32699,32700,32705,32706,32711,32718,32722,32723,
   32725,33789,33790,33887,33893,33899,33901,34711,34712,34720,
   35014,35016,35017,35794,35799,35800,35826,35941,35946,36084,
   36085,36095,36096,36103,36107,36108,36110,36835,36916,36976,
   36981,36983,37037,37040,37496,37651,37818,37824,37851,37852,
   37853,37965,37966,37971,37972,38046,38102,38103,38107,38122,
   38127,38128,38133,38134,43598,43606,43726,44528,44535,44541,
   46580,46585,46700,46705,47811,47815,47827,47947,48094,48354,
   48509,48963,49005,49013,49309,49356,49364,50288,50300,50301,
   51159,51160,51172,51248,51613,51617,51638,51732,51908 ],
 [ 1098,1100,1232,1235,1277,1280,1284,1286,4436,4444,4455,4463,
   4474,4477,5456,6572,6577,6594,6595,6608,6622,6630,9729,
   10451,11215,11441,11685,11689,14984,15138,15157,15359,15366,
   16635,17768,18592,20096,20185,20236,20285,20430,20520,20526,
   20808,20830,21007,21839,23437,23497,23498,24767,24819,24921,
   25064,25156,25157,25999,26016,26039,26491,27203,27204,27212,
   27415,27506,27508,27509,27754,27802,28521,28581,28582,28608,
   28610,28616,28871,28872,28874,28892,28898,28899,29039,29586,
   29909,29916,29934,29935,29943,30054,30056,30062,30063,30192,
   30198,30205,30206,30211,30217,30218,31211,31218,31329,31330,
   31337,31338,31468,31472,31473,31485,31487,31766,31820,32168,
   32303,32359,32385,32407,32409,32414,32415,32416,32434,32435,
   32436,32441,32443,32554,32556,32562,32563,32692,32693,32699,
   32700,32705,32706,32710,32711,32713,32718,32722,32723,32725,
   33737,33789,33790,33887,33893,33899,33900,33901,34711,34712,
   34720,35014,35016,35017,35794,35799,35800,35821,35826,35941,
   35946,36082,36084,36085,36091,36095,36096,36097,36098,36103,
   36107,36108,36110,36835,36916,36975,36976,36981,36983,37037,
   37040,37137,37496,37651,37818,37824,37845,37851,37852,37853,
   37965,37966,37971,37972,38046,38102,38103,38107,38109,38122,
   38127,38128,38133,38134,43598,43606,43726,43925,43943,44528,
   44535,44541,46580,46585,46700,46705,47811,47815,47827,47844,
   47888,47947,48094,48354,48509,48963,49005,49013,49063,49092,
   49309,49356,49364,50288,50300,50301,50837,51159,51160,51172,
   51208,51237,51248,51613,51617,51638,51732,51908,52023,52075,
   52105 ],
 [ 1091,1094,1095,1096,1098,1099,1100,1101,1232,1233,1234,1235,
   1238,1239,1241,1243,1277,1280,1284,1286,3443,4436,4444,4455,
   4463,4474,4477,5456,6572,6577,6594,6595,6608,6622,6630,9729,
   10451,11215,11441,11685,11689,14984,15138,15157,15206,15359,
   15366,16635,17768,18592,20096,20185,20236,20285,20291,20430,
   20520,20526,20808,20830,21007,21839,23437,23497,23498,23627,
   24767,24819,24921,24922,25064,25156,25157,25999,26016,26039,
   26491,27203,27204,27212,27415,27502,27506,27508,27509,27754,
   27802,28275,28475,28521,28581,28582,28608,28610,28616,28871,
   28872,28874,28892,28896,28898,28899,29039,29586,29907,29908,
   29909,29915,29916,29934,29935,29943,30054,30056,30062,30063,
   30192,30198,30205,30206,30211,30217,30218,31121,31211,31218,
   31329,31330,31337,31338,31402,31468,31472,31473,31485,31487,
   31766,31820,32168,32303,32359,32385,32407,32409,32414,32415,
   32416,32434,32435,32436,32441,32442,32443,32554,32556,32562,
   32563,32692,32693,32697,32698,32699,32700,32705,32706,32710,
   32711,32713,32718,32722,32723,32725,33737,33789,33790,33887,
   33893,33899,33900,33901,34711,34712,34719,34720,35014,35016,
   35017,35794,35799,35800,35821,35826,35941,35946,36082,36084,
   36085,36091,36095,36096,36097,36098,36103,36107,36108,36110,
   36835,36916,36975,36976,36981,36983,37037,37040,37137,37496,
   37651,37818,37824,37844,37845,37851,37852,37853,37965,37966,
   37971,37972,38046,38102,38103,38107,38108,38109,38122,38127,
   38128,38133,38134,43598,43606,43726,43925,43943,44528,44535,
   44541,46580,46585,46700,46705,46891,47811,47815,47827,47844,
   47852,47888,47947,48094,48278,48354,48509,48963,49005,49013,
   49063,49092,49309,49356,49364,50288,50300,50301,50837,50842,
   51159,51160,51172,51208,51237,51248,51613,51617,51638,51732,
   51778,51908,52023,52024,52075,52105 ],
 [ 1091,1094,1095,1096,1098,1099,1100,1101,1232,1233,1234,1235,
   1238,1239,1241,1243,1277,1280,1284,1286,3302,3303,3307,3308,
   3313,3443,3447,3448,3449,4436,4444,4455,4463,4474,4477,5449,
   5451,5453,5456,5590,5592,5596,5597,5598,6572,6577,6594,6595,
   6608,6622,6630,9729,10451,11215,11441,11685,11689,14984,
   14998,14999,15138,15157,15206,15359,15366,16635,17768,18592,
   20096,20185,20236,20285,20291,20430,20520,20526,20808,20830,
   21007,21839,23385,23386,23437,23497,23498,23627,24767,24819,
   24921,24922,25064,25156,25157,25999,26016,26039,26491,27203,
   27204,27212,27351,27415,27502,27506,27508,27509,27754,27802,
   28275,28475,28521,28581,28582,28608,28610,28616,28871,28872,
   28874,28892,28896,28898,28899,29039,29586,29907,29908,29909,
   29915,29916,29934,29935,29943,30043,30054,30055,30056,30062,
   30063,30192,30193,30198,30205,30206,30211,30217,30218,31121,
   31211,31217,31218,31329,31330,31337,31338,31402,31468,31472,
   31473,31485,31487,31766,31820,32168,32303,32359,32385,32407,
   32409,32414,32415,32416,32434,32435,32436,32441,32442,32443,
   32554,32556,32562,32563,32692,32693,32697,32698,32699,32700,
   32705,32706,32710,32711,32713,32718,32722,32723,32725,33737,
   33789,33790,33887,33893,33899,33900,33901,34711,34712,34719,
   34720,35014,35016,35017,35794,35799,35800,35821,35826,35827,
   35941,35946,36062,36082,36084,36085,36091,36095,36096,36097,
   36098,36103,36107,36108,36109,36110,36835,36916,36975,36976,
   36981,36983,37037,37040,37137,37496,37651,37711,37756,37818,
   37824,37844,37845,37846,37851,37852,37853,37965,37966,37971,
   37972,38046,38102,38103,38107,38108,38109,38110,38122,38127,
   38128,38133,38134,43598,43606,43726,43925,43943,44528,44535,
   44541,46580,46585,46700,46705,46891,47811,47815,47827,47844,
   47852,47888,47947,48094,48278,48354,48509,48963,49005,49013,
   49063,49092,49108,49112,49309,49356,49364,49435,50288,50300,
   50301,50797,50837,50842,51159,51160,51172,51208,51237,51248,
   51613,51617,51638,51732,51778,51908,51998,52023,52024,52075,
   52096,52098,52105,52118 ],
 [ 1091,1094,1095,1096,1098,1099,1100,1101,1232,1233,1234,1235,
   1238,1239,1241,1243,1277,1280,1284,1286,3302,3303,3307,3308,
   3311,3313,3443,3446,3447,3448,3449,4436,4444,4455,4463,4474,
   4477,5449,5451,5453,5454,5456,5588,5590,5592,5596,5597,5598,
   6572,6577,6594,6595,6608,6622,6630,9729,10451,11215,11441,
   11685,11689,14984,14998,14999,15138,15157,15206,15347,15359,
   15366,16635,17768,18592,20096,20184,20185,20236,20285,20291,
   20430,20520,20526,20808,20830,21007,21839,23385,23386,23437,
   23486,23497,23498,23627,24767,24819,24921,24922,25064,25065,
   25156,25157,25999,26016,26039,26491,27203,27204,27212,27351,
   27415,27502,27506,27508,27509,27754,27802,28275,28475,28521,
   28581,28582,28608,28610,28616,28867,28871,28872,28874,28892,
   28896,28898,28899,29039,29586,29907,29908,29909,29915,29916,
   29934,29935,29943,30043,30054,30055,30056,30062,30063,30192,
   30193,30198,30205,30206,30211,30217,30218,31121,31211,31217,
   31218,31329,31330,31337,31338,31402,31468,31472,31473,31485,
   31487,31766,31820,32168,32303,32359,32376,32385,32407,32409,
   32414,32415,32416,32434,32435,32436,32441,32442,32443,32496,
   32554,32556,32562,32563,32692,32693,32697,32698,32699,32700,
   32705,32706,32710,32711,32713,32718,32722,32723,32725,33737,
   33789,33790,33887,33893,33899,33900,33901,34711,34712,34719,
   34720,35014,35016,35017,35028,35794,35799,35800,35821,35826,
   35827,35941,35946,36062,36082,36084,36085,36091,36095,36096,
   36097,36098,36103,36107,36108,36109,36110,36835,36916,36975,
   36976,36981,36983,37037,37040,37137,37496,37651,37711,37756,
   37818,37824,37844,37845,37846,37851,37852,37853,37965,37966,
   37971,37972,38046,38102,38103,38107,38108,38109,38110,38122,
   38127,38128,38133,38134,43598,43606,43726,43925,43943,44528,
   44535,44541,46580,46585,46700,46705,46891,47811,47815,47827,
   47844,47852,47888,47947,48094,48278,48354,48509,48963,49005,
   49013,49063,49092,49108,49112,49309,49356,49364,49435,50288,
   50300,50301,50797,50837,50842,51159,51160,51172,51208,51237,
   51248,51613,51617,51638,51732,51778,51908,51998,52023,52024,
   52075,52096,52098,52105,52118 ] ],

dontexceed :=
[ [ 61,63,65,66,122,123,124,125,294,295,315,316,319,324,356,
   357,377,378,381,386,536,537,557,558,561,566,651,652,672,
   673,676,681,831,832,836,839,869,870,884,885,890,891,895,
   900,936,937,941,942,943,944,947,952,970,972,973,983,996,
   997,1000,1002,1022,1023,1043,1044,1046,1047,1048,1050,1052,
   1053,1092,1093,1097,1102,1117,1130,1146,1148,1164,1177,1190,
   1191,1193,1194,1195,1196,1210,1223,1236,1237,1240,1242,1255,
   1257,1258,1268,1278,1279,1282,1287,1364,1365,1366,1367,1406,
   1407,1408,1409,1487,1488,1489,1490,1526,1527,1528,1529,1642,
   1644,1646,1647,1677,1679,1681,1682,1706,1709,1710,1712,1713,
   1714,1715,1717,1743,1744,1746,1747,1748,1749,1771,1774,1775,
   1777,1778,1779,1780,1782,1803,1804,1807,1812,1833,1834,1837,
   1842,1972,1974,1976,1977,2019,2021,2023,2024,2057,2060,2061,
   2063,2064,2065,2066,2068,2081,2082,2084,2085,2086,2087,2096,
   2099,2100,2102,2103,2104,2105,2107,2147,2150,2153,2158,2162,
   2165,2168,2173,2213,2214,2216,2220,2225,2227,2232,2234,2236,
   2241,2243,2247,2259,2261,2264,2266,2271,2272,2276,2277,2333,
   2342,2398,2407,2435,2443,2498,2506,2537,2560,2568,2589,2596,
   2599,2605,2606,2608,2611,2612,2615,2616,2617,2618,2621,2623,
   2624,2629,2633,2634,2635,2637,2639,2641,2642,2648,2653,2655,
   2657,2658,2695,2697,2699,2701,2702,2713,2717,2760,2761,2767,
   2768,2771,2774,2776,2782,2786,2787,2788,2789,2814,2826,2830,
   2883,2886,2888,2891,2896,2897,2899,2901,2923,2924,2936,2941,
   2949,3040,3041,3042,3043,3073,3081,3095,3096,3098,3125,3133,
   3147,3148,3155,3158,3196,3197,3226,3234,3254,3257,3264,3337,
   3339,3341,3343,3344,3384,3386,3388,3390,3391,3402,3406,3441,
   3461,3469,3483,3484,3489,3492,3499,3575,3617,3663,3698,3699,
   3701,3702,3703,3704,3737,3738,3740,3741,3742,3743,3888,3917,
   3918,3920,3921,3922,3923,3982,3983,3985,3986,3987,3988,4146,
   4147,4162,4171,4172,4187,4191,4211,4238,4250,4256,4258,4271,
   4279,4297,4310,4318,4332,4349,4405,4424,4427,4428,4432,4442,
   4454,4466,4469,4472,4543,4552,4580,4581,4607,4609,4650,4664,
   4705,4706,4732,4738,4741,4742,4750,4753,4754,4757,4760,4762,
   4776,4800,4801,4833,4847,4867,4892,4906,4912,4917,5027,5031,
   5033,5037,5040,5043,5051,5058,5063,5065,5068,5069,5077,5079,
   5082,5083,5086,5092,5095,5097,5099,5137,5140,5165,5166,5174,
   5188,5191,5218,5219,5270,5271,5279,5293,5297,5299,5326,5328,
   5331,5339,5342,5378,5392,5404,5406,5408,5430,5468,5469,5473,
   5486,5520,5522,5533,5536,5546,5549,5611,5613,5624,5627,5639,
   5641,5643,5677,5762,5805,5845,6002,6030,6032,6034,6035,6037,
   6038,6064,6066,6068,6069,6071,6072,6134,6135,6217,6247,6332,
   6372,6374,6376,6377,6379,6380,6415,6417,6419,6420,6422,6423,
   6459,6460,6518,6564,6565,6570,6574,6578,6591,6620,6627,6632,
   6642,6668,6669,6689,6690,6724,6728,6730,6731,6732,6734,6737,
   6743,6745,6747,6824,6831,6833,6835,6840,6841,6853,6857,6860,
   6878,6880,6913,6920,6938,6940,7055,7057,7108,7115,7117,7118,
   7121,7123,7128,7138,7144,7145,7148,7160,7165,7166,7220,7221,
   7246,7253,7254,7256,7267,7269,7299,7306,7307,7309,7320,7322,
   7323,7324,7351,7372,7406,7408,7411,7412,7415,7417,7421,7425,
   7458,7459,7460,7465,7529,7530,7553,7555,7559,7562,7568,7572,
   7600,7615,7673,7675,7687,7691,7706,7708,7757,7800,7884,7891,
   7893,7894,7963,7970,7972,7973,8021,8082,8172,8347,8387,8451,
   8458,8460,8461,8533,8540,8542,8543,8547,8668,8669,8710,8711,
   8739,8740,8746,8747,8768,8801,8802,8808,8809,8830,8982,8988,
   8990,9002,9009,9023,9025,9027,9028,9029,9037,9040,9051,9097,
   9103,9105,9117,9124,9137,9138,9142,9148,9152,9161,9164,9261,
   9262,9275,9284,9314,9315,9322,9323,9334,9336,9337,9339,9366,
   9367,9374,9376,9384,9388,9389,9393,9395,9418,9422,9424,9425,
   9426,9431,9438,9468,9472,9474,9475,9476,9477,9495,9498,9517,
   9523,9524,9526,9537,9544,9545,9564,9565,9569,9573,9578,9582,
   9584,9586,9611,9612,9616,9620,9621,9629,9631,9632,9636,9646,
   9657,9658,9662,9666,9671,9675,9678,9682,9688,9692,9703,9707,
   9709,9710,9716,9720,9723,9730,9731,9732,9746,9789,9790,9816,
   9818,9839,9840,9860,9861,9873,9881,9939,9940,9958,9960,9979,
   9981,9990,9991,9992,9993,9994,9995,9997,9998,10001,10002,
   10003,10004,10006,10007,10008,10009,10014,10016,10018,10019,
   10020,10022,10023,10024,10025,10028,10029,10030,10031,10034,
   10036,10038,10039,10040,10041,10043,10044,10046,10047,10053,
   10054,10055,10057,10058,10059,10060,10061,10062,10063,10070,
   10071,10102,10104,10106,10107,10136,10149,10158,10161,10162,
   10166,10181,10195,10196,10210,10223,10226,10227,10231,10236,
   10255,10265,10266,10286,10296,10298,10299,10300,10301,10305,
   10306,10307,10311,10314,10315,10316,10317,10318,10320,10321,
   10322,10323,10324,10417,10435,10457,10460,10500,10509,10512,
   10513,10517,10527,10537,10539,10548,10551,10552,10556,10570,
   10584,10599,10617,10665,10666,10668,10672,10677,10686,10695,
   10699,10754,10755,10761,10762,10783,10882,10883,10895,10896,
   10907,10941,10942,10954,10955,10966,10976,10980,10981,10982,
   10983,10999,11004,11013,11056,11057,11144,11146,11148,11150,
   11152,11154,11160,11168,11214,11219,11221,11223,11234,11238,
   11267,11272,11274,11275,11319,11320,11324,11326,11328,11330,
   11339,11341,11349,11352,11377,11378,11391,11392,11420,11427,
   11428,11431,11444,11449,11452,11469,11470,11476,11480,11491,
   11498,11502,11518,11525,11528,11531,11537,11538,11539,11565,
   11569,11572,11578,11584,11585,11586,11588,11595,11598,11615,
   11618,11630,11631,11634,11641,11642,11655,11656,11660,11675,
   11676,11677,11684,11686,11687,11688,11699,11704,11706,11707,
   11747,11749,11785,11789,11791,11792,11793,11795,11806,11832,
   11833,11854,11857,11886,11887,11897,11898,11911,11912,11913,
   11926,11934,11935,11936,11945,11947,11949,11950,11971,11983,
   11984,12001,12012,12023,12037,12055,12079,12081,12089,12104,
   12106,12115,12117,12125,12128,12130,12131,12132,12134,12136,
   12137,12139,12141,12143,12144,12146,12147,12148,12150,12151,
   12157,12171,12179,12180,12181,12188,12189,12191,12192,12193,
   12194,12195,12196,12197,12199,12201,12202,12206,12207,12208,
   12209,12210,12212,12213,12214,12215,12217,12218,12219,12222,
   12223,12224,12225,12226,12229,12231,12234,12236,12238,12239,
   12240,12241,12242,12244,12245,12246,12247,12248,12261,12266,
   12269,12316,12341,12342,12359,12365,12367,12369,12384,12403,
   12405,12421,12425,12426,12436,12464,12468,12469,12496,12504,
   12508,12514,12523,12531,12541,12549,12555,12556,12557,12558,
   12559,12561,12640,12641,12643,12648,12649,12651,12657,12663,
   12669,12690,12691,12693,12698,12700,12701,12703,12706,12708,
   12714,12720,12722,12766,12774,12780,12786,12803,12825,12832,
   12833,12846,12867,12872,12873,12880,12883,12884,12894,12895,
   12898,12905,12940,12948,12954,12960,12977,13105,13106,13113,
   13116,13127,13130,13158,13159,13165,13166,13168,13169,13178,
   13180,13183,13184,13210,13211,13232,13261,13268,13269,13271,
   13279,13282,13318,13319,13360,13368,13370,13371,13380,13381,
   13382,13389,13408,13416,13419,13422,13424,13426,13473,13475,
   13476,13508,13515,13517,13521,13532,13567,13568,13590,13598,
   13633,13634,13660,13666,13723,13724,13744,13748,13756,13764,
   13834,13835,13841,13844,13845,13846,13847,13848,13849,13850,
   13851,13855,13860,13862,13866,13867,13868,13869,13870,13899,
   13914,14079,14100,14111,14113,14114,14115,14116,14117,14118,
   14119,14122,14129,14130,14133,14135,14136,14137,14138,14179,
   14207,14236,14275,14285,14296,14297,14301,14307,14317,14318,
   14438,14446,14494,14580,14583,14587,14590,14598,14609,14610,
   14616,14617,14639,14649,14662,14665,14667,14675,14697,14707,
   14720,14723,14725,14733,14754,14757,14761,14764,14777,14920,
   14921,14922,14925,14926,14927,14928,14929,14930,14931,14932,
   14933,14934,14935,14936,14937,14938,14939,14941,14942,14945,
   14946,14947,14948,14949,14952,14953,14955,14956,14958,14962,
   14963,14967,14969,14970,14971,14973,14974,14975,14976,14981,
   14982,14988,14990,14991,14994,14996,15005,15006,15007,15015,
   15020,15035,15040,15041,15042,15048,15051,15054,15056,15058,
   15059,15060,15062,15063,15079,15081,15082,15083,15084,15085,
   15086,15087,15088,15089,15090,15092,15093,15094,15095,15097,
   15098,15099,15101,15102,15103,15104,15105,15107,15108,15109,
   15110,15111,15112,15118,15123,15124,15125,15126,15127,15128,
   15129,15135,15141,15148,15149,15151,15160,15179,15188,15190,
   15191,15196,15197,15198,15200,15201,15224,15229,15232,15234,
   15240,15249,15250,15251,15252,15254,15255,15256,15257,15258,
   15259,15260,15265,15270,15271,15279,15287,15289,15295,15296,
   15297,15303,15305,15306,15307,15321,15324,15329,15337,15345,
   15354,15363,15371,15373,15380,15386,15387,15388,15390,15395,
   15396,15397,15398,15399,15415,15416,15417,15420,15422,15423,
   15427,15428,15430,15432,15433,15434,15436,15438,15440,15441,
   15447,15448,15452,15454,15455,15456,15457,15459,15465,15481,
   15507,15516,15519,15521,15548,15549,15596,15597,15665,15671,
   15679,15702,15739,15744,15747,15748,15749,15750,15752,15753,
   15754,15755,15756,15757,15758,15759,15763,15768,15769,15770,
   15772,15773,15781,15880,15881,15947,15999,16008,16031,16032,
   16033,16037,16038,16054,16061,16086,16087,16102,16108,16124,
   16126,16152,16153,16157,16210,16212,16234,16245,16247,16258,
   16262,16266,16279,16288,16294,16432,16433,16445,16446,16457,
   16540,16548,16554,16560,16577,16639,16641,16642,16643,16645,
   16666,16671,16706,16710,16714,16719,16725,16726,16727,16728,
   16729,16758,16765,16766,16767,16772,16778,16780,16810,16811,
   16820,16824,16830,16831,16832,16833,16848,16862,16866,16868,
   16871,16875,16877,16879,16881,16882,16885,16918,16919,16925,
   16931,16933,16944,16948,16960,16969,16970,16974,16980,16981,
   16982,16983,16993,16998,17017,17022,17024,17026,17028,17029,
   17056,17060,17062,17069,17071,17073,17075,17076,17078,17080,
   17087,17091,17101,17108,17109,17117,17121,17125,17126,17133,
   17138,17146,17151,17153,17154,17155,17166,17168,17169,17178,
   17180,17182,17183,17204,17206,17210,17211,17214,17240,17247,
   17253,17254,17285,17289,17295,17296,17330,17332,17336,17340,
   17370,17376,17377,17378,17409,17415,17416,17418,17447,17453,
   17470,17484,17490,17491,17503,17520,17522,17524,17526,17527,
   17538,17542,17555,17557,17577,17578,17595,17596,17597,17598,
   17608,17609,17611,17613,17621,17624,17629,17640,17644,17645,
   17660,17661,17662,17663,17673,17674,17676,17678,17684,17685,
   17691,17692,17703,17715,17716,17736,17738,17744,17747,17749,
   17750,17751,17772,17779,17781,17831,17832,17850,17856,17857,
   17860,17868,17870,17875,17876,17878,17879,17881,17885,17887,
   17888,17889,17890,17892,17893,17894,17895,17896,17897,17898,
   17903,17907,17917,17920,17923,17926,17932,17937,17941,17942,
   17947,17959,17960,17962,17964,17970,17978,17980,17983,17986,
   17998,17999,18001,18003,18004,18005,18006,18008,18010,18011,
   18012,18013,18014,18015,18016,18017,18019,18020,18021,18022,
   18023,18024,18027,18030,18031,18032,18033,18034,18036,18038,
   18049,18059,18069,18077,18079,18082,18155,18157,18160,18162,
   18167,18168,18172,18173,18178,18188,18201,18204,18206,18214,
   18252,18258,18260,18272,18279,18292,18294,18296,18297,18302,
   18304,18309,18314,18316,18319,18328,18333,18346,18352,18354,
   18356,18359,18361,18367,18377,18382,18383,18386,18423,18425,
   18426,18437,18439,18440,18442,18469,18476,18477,18490,18492,
   18494,18521,18522,18544,18573,18577,18579,18580,18582,18588,
   18593,18596,18597,18629,18630,18672,18679,18680,18682,18697,
   18704,18724,18726,18729,18739,18740,18743,18771,18773,18786,
   18787,18812,18813,18817,18819,18833,18836,18837,18844,18857,
   18862,18908,18911,18922,18951,18965,18993,19007,19034,19035,
   19056,19064,19113,19115,19117,19127,19129,19136,19144,19151,
   19169,19179,19233,19237,19238,19248,19253,19259,19273,19340,
   19343,19353,19358,19372,19390,19391,19392,19394,19397,19402,
   19403,19405,19407,19408,19409,19410,19411,19412,19414,19416,
   19419,19420,19444,19451,19462,19468,19469,19481,19489,19496,
   19503,19542,19543,19715,19726,19728,19734,19735,19737,19738,
   19739,19741,19742,19743,19747,19749,20056,20057,20058,20060,
   20063,20065,20066,20067,20069,20070,20071,20072,20073,20074,
   20076,20079,20080,20081,20084,20089,20090,20097,20098,20099,
   20101,20103,20111,20112,20120,20131,20133,20134,20144,20149,
   20161,20163,20164,20171,20174,20175,20189,20190,20193,20196,
   20203,20214,20221,20227,20231,20232,20237,20238,20243,20244,
   20246,20248,20259,20264,20269,20279,20282,20286,20287,20290,
   20297,20305,20314,20315,20317,20318,20320,20321,20322,20324,
   20325,20326,20327,20328,20330,20331,20333,20334,20335,20336,
   20337,20339,20342,20343,20345,20347,20351,20352,20353,20354,
   20355,20356,20357,20358,20359,20365,20366,20368,20369,20370,
   20373,20374,20375,20376,20377,20378,20381,20382,20386,20388,
   20389,20390,20393,20399,20401,20403,20404,20405,20406,20407,
   20421,20423,20429,20431,20435,20437,20439,20440,20450,20507,
   20510,20511,20512,20514,20515,20521,20525,20528,20532,20566,
   20574,20649,20651,20692,20732,20809,20846,20861,20863,20867,
   20916,20917,20920,20921,21014,21020,21045,21047,21055,21104,
   21106,21114,21121,21134,21135,21138,21142,21143,21161,21165,
   21166,21171,21190,21195,21196,21198,21202,21203,21204,21205,
   21207,21208,21209,21216,21286,21345,21374,21377,21381,21396,
   21413,21427,21541,21542,21546,21564,21568,21666,21672,21674,
   21676,21685,21687,21692,21725,21726,21727,21736,21739,21740,
   21741,21746,21756,21770,21771,21778,21791,21793,21807,21821,
   21826,21828,21829,21835,21844,21856,21858,21872,21876,21878,
   21879,21880,21882,21885,21887,21891,21893,21895,21897,21898,
   21907,21931,21969,21973,21976,21982,21984,21988,21992,22004,
   22015,22022,22031,22033,22035,22036,22043,22106,22107,22111,
   22126,22127,22128,22133,22142,22157,22220,22228,22230,22272,
   22273,22304,22313,22409,22425,22430,22454,22457,22494,22502,
   22504,22515,22517,22562,22571,22604,22628,22636,22638,22659,
   22673,22698,22728,22765,22824,22831,22855,22906,22913,22921,
   22923,22941,22960,22963,22977,22979,22986,22988,22989,23003,
   23029,23076,23077,23078,23086,23087,23088,23131,23133,23134,
   23195,23200,23201,23210,23211,23214,23217,23218,23224,23228,
   23229,23231,23234,23236,23241,23245,23246,23247,23251,23252,
   23254,23255,23256,23258,23259,23260,23261,23262,23264,23265,
   23266,23267,23270,23271,23273,23275,23277,23281,23283,23284,
   23285,23286,23287,23288,23289,23293,23294,23296,23300,23304,
   23310,23311,23314,23315,23333,23334,23335,23337,23349,23351,
   23352,23354,23356,23359,23367,23368,23373,23374,23378,23380,
   23382,23384,23390,23397,23408,23418,23419,23423,23430,23432,
   23436,23446,23450,23453,23463,23469,23477,23478,23489,23499,
   23501,23502,23503,23504,23505,23506,23508,23510,23512,23514,
   23516,23517,23521,23523,23526,23528,23529,23531,23532,23535,
   23537,23543,23544,23545,23546,23550,23556,23557,23560,23562,
   23564,23573,23574,23575,23576,23578,23579,23581,23604,23608,
   23609,23618,23621,23622,23626,23631,23640,23643,23646,23647,
   23648,23650,23651,23655,23664,23665,23670,23671,23702,23735,
   23738,23739,23740,23742,23745,23746,23751,23752,23753,23754,
   23756,23757,23759,23760,23763,23764,23769,23787,23828,23868,
   23881,23945,23960,23962,23970,23982,24018,24019,24029,24132,
   24134,24139,24164,24166,24183,24192,24197,24213,24242,24243,
   24253,24257,24260,24324,24332,24334,24336,24337,24338,24339,
   24340,24341,24347,24348,24349,24360,24362,24450,24451,24470,
   24477,24482,24526,24555,24557,24558,24561,24571,24677,24681,
   24682,24683,24685,24687,24688,24690,24694,24696,24699,24702,
   24703,24704,24705,24707,24710,24712,24713,24716,24719,24720,
   24721,24722,24723,24724,24726,24728,24733,24734,24735,24737,
   24738,24739,24743,24751,24756,24760,24761,24762,24766,24773,
   24785,24787,24790,24795,24799,24818,24820,24828,24838,24840,
   24849,24851,24860,24870,24882,24886,24888,24890,24895,24900,
   24901,24908,24911,24920,24930,24985,24987,24988,24990,24991,
   24993,24996,24997,25006,25008,25013,25014,25015,25017,25018,
   25022,25025,25027,25029,25030,25032,25037,25039,25045,25055,
   25059,25060,25061,25066,25072,25079,25080,25081,25082,25083,
   25084,25085,25086,25089,25094,25098,25099,25100,25101,25103,
   25104,25105,25106,25107,25109,25110,25111,25115,25116,25117,
   25118,25119,25120,25122,25123,25124,25126,25128,25130,25135,
   25136,25146,25151,25152,25153,25154,25155,25172,25175,25178,
   25183,25187,25188,25189,25190,25193,25195,25196,25199,25200,
   25204,25206,25207,25209,25212,25314,25316,25356,25365,25367,
   25395,25443,25447,25575,25608,25617,25624,25640,25649,25651,
   25730,25836,25841,25846,25888,25889,25892,25894,25898,25900,
   25902,25904,25905,25906,25936,25937,25960,26000,26002,26004,
   26009,26054,26056,26174,26175,26182,26183,26185,26196,26197,
   26226,26227,26234,26235,26237,26248,26249,26278,26282,26284,
   26286,26287,26288,26298,26300,26301,26328,26334,26335,26338,
   26350,26353,26377,26383,26384,26387,26399,26402,26425,26433,
   26438,26440,26442,26444,26447,26450,26472,26476,26480,26482,
   26489,26492,26494,26495,26497,26517,26518,26522,26526,26539,
   26542,26562,26563,26567,26571,26584,26587,26628,26629,26630,
   26649,26650,26658,26672,26673,26675,26692,26699,26700,26702,
   26713,26715,26733,26741,26743,26755,26758,26772,26781,26795,
   26798,26812,26818,26820,26822,26832,26834,26835,26850,26858,
   26860,26871,26878,26882,26888,26889,26890,26891,26892,26896,
   26898,26899,26900,26901,26902,26903,26904,26905,26906,26907,
   26908,26909,26911,26913,26914,26915,26917,26918,26919,26920,
   26921,26922,26923,26924,26931,26933,26942,26943,26945,26948,
   26966,26967,26968,26980,26983,26996,26999,27000,27014,27017,
   27035,27047,27048,27055,27056,27067,27076,27079,27080,27082,
   27096,27097,27107,27110,27113,27119,27125,27126,27146,27158,
   27159,27160,27161,27162,27163,27164,27165,27166,27167,27168,
   27169,27171,27172,27173,27175,27176,27177,27179,27180,27181,
   27182,27183,27184,27205,27213,27214,27216,27217,27218,27219,
   27221,27229,27231,27233,27235,27236,27237,27247,27250,27253,
   27273,27275,27276,27278,27295,27299,27302,27310,27312,27321,
   27322,27325,27338,27339,27360,27365,27367,27368,27396,27401,
   27408,27411,27416,27420,27422,27425,27433,27435,27439,27440,
   27442,27448,27455,27458,27465,27467,27470,27471,27474,27475,
   27476,27477,27478,27480,27482,27483,27485,27487,27488,27491,
   27493,27495,27499,27507,27513,27515,27517,27522,27527,27604,
   27605,27612,27613,27615,27626,27627,27655,27660,27662,27663,
   27665,27676,27677,27680,27705,27710,27712,27713,27715,27726,
   27727,27730,27762,27764,27765,27776,27779,27810,27813,27816,
   27820,27822,27824,27826,27827,27849,27854,27857,27867,27869,
   27870,27874,27895,27900,27903,27913,27915,27916,27920,27940,
   27945,27948,27961,27962,27965,27984,27992,28006,28007,28009,
   28027,28028,28070,28077,28078,28080,28091,28094,28095,28117,
   28118,28132,28150,28158,28171,28172,28175,28189,28197,28211,
   28214,28228,28229,28230,28231,28232,28233,28234,28235,28236,
   28238,28239,28240,28241,28242,28244,28245,28246,28247,28249,
   28251,28252,28253,28254,28256,28257,28258,28259,28260,28261,
   28262,28263,28265,28272,28286,28287,28289,28291,28308,28322,
   28325,28340,28342,28345,28357,28377,28389,28391,28394,28410,
   28424,28427,28433,28442,28456,28459,28473,28487,28490,28497,
   28502,28504,28505,28507,28508,28509,28510,28512,28513,28514,
   28518,28519,28522,28523,28524,28525,28526,28527,28529,28530,
   28531,28532,28533,28538,28541,28543,28549,28554,28558,28573,
   28574,28588,28602,28627,28630,28652,28654,28655,28669,28673,
   28679,28688,28690,28695,28698,28699,28700,28745,28765,28774,
   28777,28784,28792,28793,28797,28799,28813,28816,28826,28829,
   28833,28836,28837,28838,28840,28842,28843,28844,28845,28847,
   28848,28851,28852,28855,28878,28879,28880,28882,28883,28885,
   28887,28888,28890,28914,28918,28923,28927,28932,28958,28981,
   28982,28988,28991,29002,29003,29004,29031,29032,29038,29053,
   29054,29080,29081,29087,29090,29101,29102,29103,29128,29129,
   29139,29142,29144,29146,29148,29150,29151,29152,29175,29176,
   29180,29193,29195,29196,29197,29198,29221,29222,29243,29244,
   29245,29246,29266,29267,29271,29284,29286,29287,29288,29289,
   29310,29318,29332,29333,29334,29335,29340,29343,29353,29354,
   29362,29376,29379,29380,29382,29396,29417,29437,29452,29458,
   29459,29464,29476,29497,29498,29499,29515,29516,29536,29537,
   29538,29547,29554,29555,29556,29557,29558,29559,29560,29561,
   29562,29564,29565,29566,29568,29569,29570,29571,29572,29575,
   29577,29579,29580,29582,29583,29584,29585,29587,29588,29589,
   29590,29591,29592,29593,29594,29595,29596,29598,29600,29601,
   29602,29603,29605,29606,29607,29608,29609,29610,29611,29612,
   29613,29614,29615,29617,29618,29619,29621,29622,29623,29624,
   29625,29626,29627,29637,29648,29649,29666,29683,29684,29700,
   29702,29704,29705,29715,29717,29718,29726,29739,29749,29750,
   29751,29754,29761,29780,29782,29783,29813,29814,29844,29846,
   29848,29872,29873,29883,29893,29899,29900,29911,29919,29920,
   29924,29927,29928,29937,29939,29940,29953,29954,29978,29979,
   30021,30025,30026,30038,30047,30064,30067,30069,30088,30107,
   30119,30125,30126,30142,30143,30158,30159,30162,30164,30166,
   30167,30168,30169,30170,30171,30174,30175,30176,30177,30178,
   30180,30181,30182,30183,30184,30187,30188,30189,30202,30208,
   30214,30219,30222,30223,30306,30311,30313,30314,30316,30327,
   30328,30331,30355,30356,30362,30365,30376,30377,30378,30404,
   30408,30410,30414,30417,30419,30421,30423,30424,30427,30451,
   30455,30457,30461,30464,30466,30468,30470,30471,30474,30501,
   30503,30506,30517,30520,30521,30541,30546,30548,30551,30562,
   30563,30590,30592,30595,30606,30633,30635,30638,30649,30675,
   30677,30680,30681,30691,30716,30718,30719,30756,30759,30772,
   30773,30776,30790,30795,30797,30799,30808,30811,30813,30831,
   30833,30853,30857,30866,30869,30870,30876,30886,30892,30921,
   30922,30941,30943,30946,30957,30975,30977,30980,30991,31011,
   31015,31016,31017,31018,31019,31020,31021,31023,31024,31025,
   31028,31031,31032,31033,31034,31035,31037,31038,31039,31040,
   31041,31042,31045,31049,31056,31074,31075,31077,31078,31079,
   31080,31081,31082,31083,31084,31085,31086,31087,31088,31089,
   31091,31093,31094,31095,31096,31098,31099,31100,31101,31102,
   31103,31104,31106,31117,31124,31125,31135,31139,31144,31146,
   31152,31155,31165,31166,31167,31168,31169,31170,31172,31173,
   31174,31175,31176,31180,31184,31186,31187,31188,31189,31190,
   31191,31201,31209,31210,31224,31226,31227,31245,31247,31251,
   31252,31255,31271,31274,31276,31285,31289,31291,31299,31318,
   31321,31336,31342,31361,31365,31375,31377,31381,31390,31391,
   31395,31399,31412,31414,31417,31418,31419,31422,31424,31425,
   31426,31427,31428,31429,31430,31431,31433,31444,31454,31456,
   31474,31480,31542,31545,31547,31551,31553,31565,31581,31587,
   31588,31591,31603,31606,31635,31636,31644,31646,31648,31652,
   31680,31682,31683,31693,31695,31696,31728,31729,31737,31739,
   31741,31745,31771,31773,31774,31787,31788,31817,31818,31826,
   31848,31860,31874,31886,31890,31902,31903,31904,31941,31943,
   31944,31958,31965,31968,31984,32016,32020,32022,32023,32024,
   32026,32035,32045,32055,32060,32061,32078,32085,32098,32105,
   32109,32128,32134,32154,32157,32202,32203,32222,32231,32236,
   32247,32252,32256,32267,32268,32299,32300,32301,32302,32304,
   32305,32306,32307,32308,32309,32310,32311,32312,32313,32316,
   32318,32319,32320,32321,32323,32324,32325,32326,32327,32328,
   32329,32330,32331,32333,32334,32335,32336,32338,32340,32342,
   32344,32345,32346,32347,32348,32349,32350,32351,32352,32353,
   32355,32356,32357,32358,32360,32378,32399,32405,32427,32433,
   32440,32456,32466,32470,32495,32505,32517,32518,32523,32525,
   32527,32537,32561,32605,32607,32637,32638,32649,32673,32702,
   32703,32714,32809,32814,32818,32824,32825,32826,32856,32861,
   32862,32869,32871,32872,32907,32922,32947,32952,32956,32962,
   32963,32964,32993,32996,33039,33081,33082,33092,33123,33135,
   33162,33163,33178,33202,33219,33229,33242,33261,33266,33268,
   33272,33276,33277,33298,33313,33347,33348,33359,33381,33404,
   33415,33443,33446,33447,33477,33478,33494,33503,33509,33513,
   33524,33536,33552,33565,33566,33567,33569,33570,33571,33572,
   33574,33576,33577,33581,33583,33587,33588,33589,33592,33593,
   33596,33601,33602,33604,33609,33610,33613,33615,33627,33629,
   33648,33690,33708,33719,33731,33742,33799,33813,33830,33846,
   33849,33864,33898,33916,33920,33925,33929,33960,33980,33984,
   33986,33990,33993,33995,33997,33999,34000,34003,34032,34033,
   34041,34043,34045,34049,34075,34080,34084,34090,34091,34092,
   34128,34130,34132,34134,34138,34157,34158,34171,34173,34175,
   34177,34181,34210,34213,34215,34217,34219,34223,34251,34254,
   34256,34258,34260,34264,34294,34296,34298,34300,34304,34324,
   34333,34335,34337,34339,34343,34358,34368,34371,34372,34373,
   34375,34377,34386,34402,34405,34408,34410,34411,34412,34413,
   34414,34418,34421,34441,34444,34446,34448,34450,34451,34476,
   34479,34481,34483,34486,34506,34513,34515,34517,34519,34521,
   34544,34545,34546,34548,34550,34552,34553,34563,34567,34570,
   34574,34578,34580,34582,34584,34587,34608,34609,34627,34639,
   34640,34641,34643,34654,34660,34668,34670,34672,34673,34674,
   34681,34684,34695,34696,34698,34700,34702,34713,34721,34722,
   34724,34725,34726,34727,34729,34730,34731,34741,34743,34744,
   34745,34753,34755,34774,34776,34780,34781,34784,34799,34800,
   34802,34803,34805,34807,34810,34811,34812,34814,34815,34816,
   34817,34818,34819,34820,34821,34822,34825,34827,34831,34846,
   34847,34856,34861,34862,34865,34868,34870,34874,34890,34892,
   34897,34901,34902,34903,34904,34905,34906,34907,34908,34909,
   34919,34923,34925,34927,34928,34929,34930,34932,34933,34934,
   34935,34936,34937,34938,34939,34940,34941,34942,34943,34944,
   34945,34948,34955,34956,34964,34973,34979,34985,34998,35003,
   35006,35007,35015,35090,35106,35111,35114,35124,35126,35127,
   35131,35151,35152,35156,35169,35171,35172,35173,35174,35200,
   35213,35215,35216,35243,35256,35258,35259,35262,35285,35298,
   35300,35301,35326,35339,35341,35347,35358,35366,35379,35381,
   35382,35383,35405,35418,35420,35421,35423,35424,35425,35438,
   35441,35443,35444,35453,35456,35458,35460,35463,35473,35479,
   35480,35492,35493,35495,35496,35525,35527,35529,35531,35532,
   35543,35547,35551,35564,35567,35585,35588,35594,35598,35600,
   35601,35602,35605,35613,35621,35625,35626,35627,35628,35629,
   35630,35631,35632,35633,35634,35635,35636,35637,35638,35639,
   35642,35643,35644,35646,35647,35648,35650,35651,35663,35665,
   35666,35668,35686,35688,35689,35690,35694,35696,35697,35712,
   35724,35727,35759,35775,35781,35783,35790,35797,35802,35808,
   35810,35811,35818,35834,35836,35837,35847,35850,35855,35861,
   35862,35881,35883,35886,35896,35901,35906,35908,35909,35917,
   35928,35931,35932,35937,35939,35942,35947,35948,35949,35951,
   35952,35971,35973,35975,35978,35979,35980,35982,35983,35984,
   35985,35986,35987,35988,35990,35991,35994,36000,36009,36010,
   36011,36012,36013,36014,36015,36016,36017,36018,36019,36020,
   36021,36022,36023,36024,36025,36026,36027,36028,36029,36031,
   36032,36033,36034,36035,36036,36037,36038,36039,36040,36041,
   36043,36045,36052,36079,36080,36088,36094,36186,36187,36191,
   36195,36208,36211,36235,36237,36254,36255,36293,36297,36336,
   36340,36341,36374,36380,36401,36421,36460,36467,36486,36497,
   36503,36516,36535,36571,36597,36605,36606,36640,36646,36673,
   36676,36678,36680,36705,36737,36747,36753,36758,36768,36777,
   36800,36817,36829,36876,36900,36901,36925,36947,36958,36960,
   36963,36974,36982,36986,36990,36991,37010,37011,37014,37042,
   37047,37048,37052,37068,37069,37080,37097,37110,37114,37117,
   37119,37122,37124,37128,37129,37130,37133,37134,37136,37144,
   37187,37190,37192,37198,37210,37220,37225,37228,37242,37243,
   37244,37258,37263,37264,37268,37284,37287,37296,37300,37310,
   37325,37326,37327,37351,37375,37378,37386,37391,37404,37407,
   37408,37425,37430,37447,37450,37455,37464,37465,37466,37467,
   37468,37469,37471,37472,37474,37476,37483,37485,37487,37488,
   37489,37490,37492,37493,37494,37495,37499,37500,37501,37504,
   37505,37511,37513,37521,37522,37524,37527,37531,37547,37556,
   37557,37558,37564,37567,37576,37592,37593,37594,37610,37612,
   37613,37614,37619,37621,37625,37626,37627,37631,37632,37641,
   37649,37650,37652,37653,37654,37655,37656,37657,37658,37659,
   37660,37661,37663,37664,37665,37666,37667,37668,37669,37670,
   37671,37672,37673,37674,37675,37676,37692,37713,37720,37722,
   37750,37782,37803,37809,37810,37819,37822,37826,37827,37835,
   37836,37849,37859,37862,37863,37876,37887,37888,37911,37934,
   37935,37947,37953,37956,37957,37963,37968,37977,37998,38005,
   38010,38017,38034,38035,38037,38049,38052,38054,38057,38058,
   38059,38061,38062,38063,38064,38065,38066,38069,38070,38072,
   38073,38074,38077,38078,38079,38080,38081,38082,38083,38084,
   38087,38091,38093,38105,38115,38118,38123,38131,38137,38236,
   38278,38362,38401,38578,38584,38616,38643,38649,38657,38807,
   38833,38852,38872,38911,38919,38932,38940,38971,38979,38993,
   39054,39181,39224,39264,39453,39487,39636,39666,39775,39791,
   39799,39834,39842,39937,39989,39993,39997,40084,40163,40221,
   40519,40547,40636,40658,40663,40740,40945,40983,41098,41133,
   41200,41374,41433,41456,41480,41502,41543,41577,41637,41658,
   41683,41688,41692,41697,41765,41877,41946,42066,42096,42171,
   42357,42539,42615,42619,42713,42749,42753,42779,42838,42896,
   42912,42955,43084,43167,43202,43221,43227,43645,43680,43877,
   43880,43898,43949,43967,44057,44090,44101,44257,44281,44307,
   44467,44653,44686,44748,44752,44837,44911,44912,44927,44936,
   44937,44952,44976,45003,45021,45062,45097,45114,45170,45207,
   45231,45237,45283,45356,45520,45551,45571,45572,45592,45616,
   45617,45876,45903,45909,46025,46078,46083,46093,46172,46177,
   46193,46198,46333,46339,46348,46353,46384,46398,46581,46607,
   46621,46624,46632,46634,46656,46679,46701,46722,46742,46771,
   46796,46798,46843,46847,46877,46911,46919,46920,46922,46941,
   47048,47049,47054,47056,47075,47076,47105,47106,47117,47136,
   47183,47201,47203,47259,47260,47339,47364,47482,47556,47742,
   47862,47871,47955,48056,48079,48111,48283,48325,48351,48362,
   48397,48404,48423,48429,48453,48462,48498,48501,48518,48539,
   48558,48567,48576,48593,48624,48677,48679,48681,48683,48685,
   48775,48848,48864,48947,48958,48961,48979,48982,49083,49117,
   49126,49137,49142,49152,49200,49230,49236,49251,49257,49290,
   49298,49312,49314,49346,49434,49476,49477,49492,49537,49577,
   49582,49598,49619,49620,49624,49629,49630,49633,49635,49637,
   49639,49641,49724,49725,49840,49923,49924,49927,49935,49937,
   49944,49946,49947,49950,49951,49952,49954,49956,49977,49997,
   49999,50115,50119,50137,50139,50178,50188,50197,50232,50263,
   50289,50290,50302,50313,50332,50340,50353,50362,50365,50368,
   50404,50412,50449,50466,50528,50583,50614,50616,50636,50642,
   50662,50852,50853,50885,50893,50897,50947,50968,50969,50975,
   50981,50982,50983,50987,50995,51157,51173,51251,51330,51331,
   51344,51393,51394,51419,51422,51438,51519,51529,51559,51570,
   51571,51686,51691,51695,51738,51757,51763,51936,51960,52011,
   52016,52050,52094,52116 ],
 [ 122,123,124,125,831,832,836,839,869,870,884,885,890,891,
   895,900,936,937,941,942,943,944,947,952,970,972,973,983,
   996,997,1000,1002,1022,1023,1043,1044,1046,1047,1048,1050,
   1052,1053,1092,1093,1097,1102,1117,1130,1146,1148,1164,1177,
   1190,1191,1193,1194,1195,1196,1236,1237,1240,1242,1257,1258,
   1278,1279,1282,1287,1364,1365,1366,1367,1406,1407,1408,1409,
   1487,1488,1489,1490,1526,1527,1528,1529,1706,1709,1710,1712,
   1713,1714,1715,1717,1743,1746,1747,1748,1771,1774,1775,1777,
   1778,1779,1780,1782,1803,1804,1807,1812,1833,1834,1837,1842,
   2057,2060,2061,2063,2064,2065,2066,2068,2081,2084,2085,2086,
   2096,2099,2100,2102,2103,2104,2105,2107,2147,2150,2153,2158,
   2162,2165,2168,2173,2213,2214,2216,2220,2225,2234,2243,2247,
   2264,2266,2272,2277,2589,2596,2767,2768,2786,2788,2789,2814,
   2830,2883,2888,2891,2896,2897,2899,2901,2936,2941,2949,3042,
   3043,3073,3081,3095,3096,3098,3125,3133,3147,3148,3155,3158,
   3196,3197,3226,3234,3254,3257,3264,3337,3339,3341,3343,3344,
   3384,3388,3390,3391,3402,3406,3441,3461,3469,3483,3484,3489,
   3492,3499,3698,3699,3701,3702,3703,3704,3737,3738,3740,3741,
   3742,3743,3917,3918,3920,3921,3922,3923,3982,3983,3985,3986,
   3987,3988,4258,4271,4279,4310,4318,4405,4424,4427,4432,4442,
   4454,4469,4607,4609,4650,4664,4705,4706,4732,4738,4741,4742,
   4750,4753,4754,4757,4776,4800,4801,4912,4917,5027,5031,5033,
   5037,5095,5097,5099,5137,5140,5165,5166,5174,5188,5191,5218,
   5219,5270,5271,5279,5293,5297,5299,5326,5328,5331,5339,5342,
   5378,5392,5404,5406,5408,5430,5473,5486,5520,5522,5533,5536,
   5546,5549,5611,5613,5624,5627,5639,5641,5643,5677,5762,5805,
   5845,6030,6032,6034,6035,6037,6038,6064,6066,6068,6069,6071,
   6072,6134,6135,6247,6372,6374,6376,6377,6379,6380,6415,6417,
   6419,6420,6422,6423,6459,6460,6565,6570,6574,6578,6591,6620,
   6627,6632,6730,6737,6831,6835,6857,6878,6880,6913,6920,7055,
   7057,7123,7128,7246,7253,7254,7256,7267,7299,7306,7307,7309,
   7320,7351,7372,7406,7408,7415,7421,7425,7458,7459,7460,7465,
   7529,7530,7553,7555,7562,7568,7572,7600,7615,7673,7675,7687,
   7691,7706,7708,7757,7800,7884,7891,7963,7970,8021,8347,8451,
   8458,8533,8540,8740,8746,8768,8802,8808,8830,8982,9023,9025,
   9027,9028,9029,9040,9051,9097,9137,9138,9142,9164,9262,9275,
   9284,9322,9334,9336,9337,9367,9374,9376,9384,9388,9389,9393,
   9395,9418,9422,9424,9425,9438,9468,9472,9474,9475,9495,9498,
   9517,9523,9524,9526,9537,9544,9545,9565,9569,9578,9582,9584,
   9586,9612,9616,9629,9631,9632,9636,9646,9658,9662,9671,9675,
   9678,9688,9692,9703,9707,9709,9710,9716,9720,9723,9730,9731,
   9732,9816,9818,9860,9861,9873,9939,9940,9979,9981,10028,
   10029,10030,10031,10034,10036,10038,10039,10040,10041,10043,
   10044,10046,10047,10053,10054,10055,10057,10058,10060,10061,
   10062,10063,10136,10149,10158,10161,10162,10166,10181,10195,
   10223,10226,10227,10231,10255,10286,10500,10509,10512,10513,
   10517,10537,10539,10548,10551,10552,10556,10570,10584,10599,
   10617,10665,10666,10668,10672,10677,10686,10695,10699,10755,
   10761,10783,10976,10980,10981,10982,10983,10999,11004,11144,
   11146,11150,11152,11214,11221,11223,11234,11267,11319,11320,
   11326,11328,11349,11352,11377,11391,11420,11427,11431,11444,
   11449,11452,11469,11470,11476,11480,11498,11502,11518,11531,
   11537,11538,11578,11584,11585,11595,11598,11630,11631,11634,
   11641,11642,11655,11656,11675,11676,11684,11686,11687,11688,
   11706,11749,11791,11854,11857,11897,11898,11911,11913,11934,
   11935,11936,11949,11971,12012,12079,12081,12115,12117,12179,
   12180,12181,12189,12191,12192,12193,12194,12195,12196,12197,
   12199,12201,12206,12207,12209,12210,12212,12213,12214,12215,
   12218,12269,12341,12359,12403,12421,12425,12426,12464,12468,
   12469,12504,12508,12523,12541,12640,12641,12643,12648,12649,
   12651,12657,12663,12669,12690,12691,12693,12698,12701,12703,
   12720,12722,12786,12825,12833,12867,12872,12873,12880,12883,
   12884,12894,12895,12898,12905,12960,13105,13106,13113,13116,
   13127,13130,13158,13159,13165,13166,13168,13169,13178,13180,
   13211,13232,13261,13268,13269,13271,13279,13282,13318,13360,
   13368,13370,13371,13380,13381,13382,13389,13422,13426,13473,
   13475,13476,13508,13515,13517,13521,13532,13567,13568,13633,
   13634,13660,13666,13723,13724,13744,13748,13756,13764,13834,
   13844,13845,13846,13847,13848,13849,13850,13851,13855,13860,
   13862,13866,13867,13868,13899,14079,14100,14111,14113,14114,
   14115,14116,14117,14118,14119,14122,14129,14130,14133,14135,
   14136,14138,14179,14207,14275,14297,14301,14317,14318,14446,
   14580,14583,14587,14610,14754,14757,14920,14921,14925,14926,
   14927,14928,14930,14931,14932,14934,14935,14936,14938,14939,
   14946,14947,14949,14952,14962,14963,14967,14970,14973,14974,
   14975,14976,14981,14991,14994,15005,15006,15007,15015,15020,
   15035,15041,15048,15051,15054,15056,15058,15062,15063,15079,
   15083,15084,15086,15087,15088,15090,15094,15095,15098,15099,
   15101,15103,15107,15108,15109,15111,15112,15118,15123,15124,
   15125,15126,15127,15128,15141,15148,15151,15160,15179,15188,
   15190,15191,15196,15197,15198,15224,15234,15251,15252,15255,
   15257,15270,15289,15295,15297,15303,15306,15307,15321,15324,
   15329,15337,15345,15354,15363,15371,15373,15380,15386,15388,
   15390,15395,15398,15399,15516,15521,15781,15880,15881,16031,
   16032,16033,16037,16038,16152,16153,16157,16258,16279,16560,
   16639,16642,16643,16671,16706,16710,16714,16719,16725,16727,
   16728,16758,16765,16766,16767,16772,16778,16780,16810,16811,
   16820,16824,16830,16832,16833,16848,16862,16866,16868,16879,
   16918,16919,16925,16931,16933,16944,16948,16960,16969,16974,
   16980,16982,16983,16993,16998,17017,17026,17060,17062,17073,
   17075,17078,17080,17087,17091,17101,17108,17109,17121,17126,
   17133,17138,17146,17153,17154,17155,17166,17168,17169,17178,
   17180,17182,17183,17204,17210,17247,17253,17289,17295,17330,
   17336,17370,17376,17409,17415,17447,17453,17470,17484,17490,
   17503,17595,17597,17598,17608,17609,17611,17613,17644,17660,
   17662,17663,17673,17674,17676,17678,17684,17685,17691,17703,
   17715,17716,17736,17738,17744,17747,17749,17750,17772,17850,
   17875,17879,17885,17887,17888,17889,17890,17892,17893,17894,
   17897,17898,17959,17960,17962,17964,17980,17998,17999,18001,
   18003,18005,18006,18008,18010,18011,18012,18013,18015,18016,
   18019,18020,18021,18049,18059,18069,18160,18162,18168,18173,
   18252,18292,18294,18296,18297,18346,18425,18439,18469,18477,
   18492,18494,18521,18522,18544,18573,18577,18580,18588,18596,
   18597,18630,18672,18679,18680,18697,18704,18724,18729,18739,
   18743,18771,18786,18812,18813,18817,18837,18844,18857,18862,
   19179,19353,19444,19469,19726,20056,20057,20058,20060,20065,
   20066,20067,20069,20070,20071,20072,20073,20074,20080,20081,
   20090,20097,20098,20099,20101,20111,20112,20120,20131,20133,
   20134,20144,20149,20161,20163,20164,20171,20174,20175,20189,
   20190,20193,20196,20203,20214,20221,20227,20231,20232,20237,
   20238,20243,20244,20246,20259,20264,20269,20279,20286,20287,
   20290,20297,20305,20314,20315,20317,20318,20320,20321,20322,
   20324,20325,20326,20327,20330,20331,20333,20334,20335,20336,
   20337,20339,20342,20343,20345,20347,20351,20352,20353,20354,
   20355,20356,20357,20358,20359,20365,20366,20368,20369,20373,
   20374,20375,20376,20377,20378,20386,20388,20389,20390,20393,
   20399,20401,20403,20404,20405,20406,20407,20421,20423,20437,
   20440,20450,20507,20510,20511,20512,20514,20515,20521,20525,
   20528,20532,20566,20649,20651,20692,20732,20809,20846,20861,
   20863,20867,20916,20921,21014,21020,21047,21106,21134,21143,
   21161,21165,21166,21171,21196,21198,21203,21204,21205,21207,
   21208,21286,21345,21396,21413,21542,21546,21666,21672,21674,
   21676,21685,21687,21692,21725,21727,21736,21739,21740,21741,
   21746,21756,21770,21771,21778,21791,21793,21807,21821,21826,
   21828,21829,21835,21844,21856,21858,21872,21876,21879,21880,
   21882,21885,21887,21891,21893,21895,21897,21898,21907,21969,
   21973,21976,21988,21992,22004,22015,22022,22033,22035,22036,
   22043,22106,22107,22111,22126,22127,22128,22133,22142,22220,
   22228,22230,22409,22425,22430,22454,22457,22494,22502,22504,
   22562,22571,22604,22628,22636,22638,22659,22698,22728,22765,
   22855,22913,22921,22923,22941,22979,22986,22988,22989,23003,
   23029,23076,23077,23078,23087,23133,23195,23201,23211,23214,
   23218,23224,23234,23245,23246,23247,23251,23252,23256,23258,
   23259,23260,23262,23264,23266,23270,23271,23273,23281,23283,
   23285,23286,23287,23288,23289,23293,23296,23300,23304,23310,
   23314,23315,23333,23335,23337,23349,23351,23352,23354,23359,
   23367,23373,23374,23378,23380,23384,23390,23397,23408,23419,
   23423,23430,23432,23436,23446,23450,23453,23463,23469,23477,
   23478,23489,23499,23501,23502,23505,23506,23510,23512,23514,
   23521,23523,23528,23532,23537,23543,23544,23545,23557,23560,
   23562,23564,23573,23575,23578,23579,23604,23608,23609,23618,
   23621,23622,23631,23640,23643,23648,23650,23651,23655,23664,
   23665,23671,23702,23787,23828,23868,23881,23945,23970,23982,
   24139,24183,24197,24213,24332,24336,24337,24338,24339,24348,
   24349,24450,24451,24470,24677,24681,24682,24683,24685,24687,
   24688,24690,24694,24696,24699,24702,24703,24707,24710,24712,
   24713,24716,24719,24720,24721,24722,24723,24726,24728,24733,
   24734,24735,24738,24739,24743,24751,24756,24760,24762,24766,
   24773,24785,24787,24790,24795,24799,24818,24828,24838,24851,
   24860,24870,24882,24895,24900,24901,24908,24920,24930,24988,
   24990,24991,24996,24997,25006,25013,25014,25015,25025,25027,
   25029,25030,25032,25037,25039,25045,25059,25060,25061,25066,
   25072,25079,25081,25082,25083,25084,25085,25086,25089,25094,
   25098,25099,25103,25104,25106,25107,25109,25111,25115,25116,
   25117,25118,25119,25120,25122,25123,25124,25126,25128,25130,
   25135,25136,25151,25152,25153,25154,25155,25365,25367,25649,
   25651,25936,25937,26000,26004,26009,26054,26056,26174,26175,
   26182,26183,26185,26196,26197,26226,26227,26234,26235,26237,
   26248,26249,26278,26282,26284,26286,26287,26288,26298,26300,
   26328,26334,26335,26338,26350,26353,26377,26383,26384,26387,
   26399,26402,26425,26433,26438,26440,26442,26444,26447,26450,
   26472,26476,26480,26482,26489,26492,26494,26497,26517,26518,
   26522,26526,26539,26542,26562,26563,26567,26571,26584,26587,
   26628,26629,26649,26650,26658,26672,26675,26692,26699,26700,
   26702,26713,26733,26741,26743,26755,26758,26772,26781,26795,
   26798,26812,26818,26820,26822,26850,26858,26860,26871,26878,
   26882,26888,26889,26890,26891,26892,26896,26898,26899,26900,
   26901,26902,26903,26904,26905,26906,26907,26908,26909,26911,
   26913,26914,26915,26917,26918,26919,26920,26921,26923,26924,
   26931,26933,26945,26948,26966,26968,26980,26983,26996,26999,
   27000,27014,27017,27055,27067,27076,27079,27096,27119,27125,
   27126,27146,27158,27159,27160,27161,27162,27163,27165,27166,
   27167,27168,27169,27171,27175,27176,27177,27179,27180,27181,
   27182,27183,27184,27213,27214,27216,27221,27229,27231,27233,
   27236,27250,27253,27275,27278,27295,27299,27302,27310,27321,
   27322,27325,27360,27365,27367,27368,27396,27401,27408,27411,
   27416,27422,27435,27448,27455,27458,27465,27467,27470,27474,
   27475,27476,27477,27478,27480,27482,27483,27485,27507,27513,
   27515,27522,27527,27604,27605,27612,27613,27615,27626,27627,
   27655,27660,27662,27663,27665,27676,27677,27680,27705,27710,
   27712,27713,27715,27726,27727,27730,27762,27764,27765,27776,
   27779,27810,27816,27820,27822,27824,27826,27827,27849,27854,
   27857,27869,27870,27895,27900,27903,27915,27916,27940,27945,
   27948,27961,27962,27965,27984,27992,28006,28007,28009,28027,
   28028,28070,28077,28078,28080,28091,28117,28118,28132,28150,
   28158,28171,28172,28175,28189,28197,28211,28214,28228,28229,
   28230,28231,28232,28233,28234,28235,28236,28238,28239,28240,
   28241,28244,28246,28247,28249,28251,28254,28256,28257,28258,
   28259,28260,28261,28262,28263,28265,28272,28286,28287,28289,
   28291,28308,28322,28325,28340,28342,28345,28357,28377,28389,
   28391,28394,28410,28424,28427,28433,28442,28456,28459,28473,
   28487,28497,28502,28504,28505,28507,28508,28509,28510,28512,
   28513,28514,28518,28522,28523,28524,28525,28526,28527,28530,
   28532,28533,28538,28541,28543,28549,28554,28558,28573,28574,
   28588,28602,28627,28630,28652,28655,28669,28673,28679,28688,
   28698,28699,28700,28745,28774,28777,28784,28792,28793,28797,
   28799,28813,28816,28826,28829,28833,28836,28837,28838,28840,
   28842,28843,28844,28845,28847,28848,28852,28855,28879,28880,
   28882,28883,28885,28890,28914,28918,28923,28927,28932,28958,
   28981,28982,28988,28991,29002,29003,29031,29032,29038,29053,
   29054,29080,29081,29087,29090,29101,29102,29128,29129,29142,
   29144,29146,29148,29150,29151,29152,29175,29176,29180,29193,
   29195,29196,29197,29198,29221,29222,29243,29244,29245,29246,
   29266,29267,29271,29284,29286,29287,29288,29289,29310,29318,
   29332,29333,29335,29340,29343,29353,29354,29362,29376,29379,
   29380,29382,29396,29417,29437,29452,29458,29459,29464,29476,
   29497,29498,29499,29515,29516,29536,29537,29538,29547,29554,
   29555,29556,29557,29558,29559,29560,29561,29562,29564,29565,
   29566,29568,29569,29570,29571,29572,29575,29577,29579,29580,
   29582,29583,29584,29585,29587,29589,29590,29591,29592,29593,
   29596,29598,29600,29601,29602,29603,29605,29606,29607,29608,
   29609,29611,29612,29613,29615,29617,29618,29619,29622,29624,
   29625,29627,29637,29648,29649,29666,29683,29684,29702,29704,
   29705,29718,29726,29749,29750,29751,29761,29780,29782,29783,
   29813,29814,29844,29846,29848,29872,29873,29883,29893,29899,
   29900,29911,29919,29920,29924,29927,29928,29937,29939,29940,
   29953,29954,29978,29979,30021,30025,30026,30038,30047,30064,
   30067,30069,30088,30107,30119,30126,30142,30143,30158,30159,
   30162,30164,30166,30167,30168,30169,30170,30171,30174,30175,
   30176,30178,30180,30181,30182,30183,30184,30187,30188,30189,
   30202,30208,30214,30219,30222,30223,30306,30311,30313,30314,
   30316,30327,30328,30331,30355,30356,30362,30365,30376,30377,
   30408,30410,30417,30421,30423,30424,30427,30455,30457,30464,
   30468,30470,30471,30474,30501,30503,30506,30517,30520,30521,
   30541,30546,30548,30551,30562,30563,30590,30592,30595,30606,
   30633,30635,30638,30649,30675,30677,30680,30691,30716,30718,
   30719,30756,30759,30772,30773,30776,30790,30795,30797,30799,
   30808,30831,30833,30853,30857,30866,30869,30870,30886,30892,
   30921,30922,30941,30943,30946,30957,30975,30977,30980,30991,
   31011,31015,31016,31018,31019,31020,31021,31023,31024,31025,
   31028,31031,31032,31033,31034,31037,31038,31039,31040,31041,
   31042,31045,31049,31056,31074,31075,31077,31078,31079,31080,
   31081,31082,31083,31084,31085,31086,31087,31088,31089,31091,
   31093,31094,31095,31096,31098,31099,31100,31101,31102,31103,
   31106,31117,31124,31125,31139,31144,31155,31165,31166,31168,
   31169,31170,31172,31173,31174,31175,31180,31184,31186,31187,
   31188,31190,31201,31209,31224,31227,31245,31247,31251,31255,
   31274,31285,31289,31299,31321,31342,31361,31365,31375,31377,
   31381,31390,31391,31395,31399,31414,31417,31419,31422,31424,
   31425,31426,31427,31428,31429,31430,31431,31444,31454,31456,
   31480,31542,31545,31547,31551,31553,31565,31581,31587,31588,
   31591,31603,31606,31635,31636,31644,31646,31648,31680,31682,
   31683,31693,31695,31696,31728,31729,31737,31739,31741,31771,
   31773,31774,31787,31788,31817,31818,31848,31860,31874,31886,
   31890,31902,31903,31904,31941,31943,31944,31958,31965,31968,
   31984,32016,32020,32023,32026,32035,32045,32055,32060,32061,
   32078,32085,32098,32105,32109,32128,32134,32154,32157,32202,
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