#n= 5000 k= 10 p= 0.5
#sigma: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
#sample size array: [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]
learned_dic: {1: 0, 2: 1, 3: 2, 4: 4, 5: 1, 6: 3, 7: 6, 8: 6, 9: 7, 10: 8, 27: 60, 30: 71, 34: 57, 35: 54, 38: 51, 39: 48, 41: 68, 45: 62, 46: 51, 53: 49, 109: 54, 116: 44, 143: 57, 156: 67, 161: 59, 163: 52, 169: 57, 188: 50, 190: 62, 213: 60, 218: 62, 230: 76, 247: 60, 248: 68, 251: 58, 272: 52, 275: 52, 276: 55, 294: 55, 301: 63, 306: 57, 308: 58, 311: 59, 317: 57, 321: 51, 326: 55, 375: 63, 385: 66, 386: 62, 403: 56, 405: 56, 409: 48, 410: 58, 431: 65, 432: 57, 433: 53, 447: 58, 452: 59, 477: 64, 478: 53, 482: 59, 483: 54, 485: 45, 490: 60, 497: 62, 509: 63, 533: 49, 536: 54, 557: 50, 566: 51, 571: 62, 574: 72, 575: 44, 591: 68, 593: 56, 595: 40, 596: 62, 599: 57, 608: 58, 622: 60, 639: 66, 641: 68, 655: 57, 658: 59, 663: 58, 667: 58, 669: 52, 690: 61, 691: 54, 692: 63, 693: 49, 703: 47, 720: 65, 729: 58, 731: 56, 741: 57, 747: 56, 753: 66, 762: 51, 778: 52, 788: 64, 798: 56, 799: 47, 807: 59, 811: 54, 812: 64, 828: 57, 855: 58, 864: 60, 870: 59, 873: 58, 897: 57, 900: 64, 902: 57, 909: 61, 914: 45, 916: 64, 918: 60, 920: 49, 942: 59, 967: 61, 991: 54, 993: 75, 998: 60, 1003: 73, 1011: 61, 1018: 62, 1023: 64, 1027: 54, 1029: 51, 1031: 63, 1036: 66, 1040: 67, 1049: 53, 1051: 68, 1052: 71, 1069: 55, 1075: 55, 1085: 56, 1088: 69, 1090: 62, 1092: 64, 1115: 63, 1120: 68, 1123: 53, 1124: 61, 1125: 59, 1127: 66, 1131: 60, 1151: 61, 1157: 72, 1161: 59, 1162: 46, 1164: 50, 1165: 64, 1166: 57, 1168: 50, 1172: 52, 1196: 60, 1200: 67, 1203: 57, 1208: 56, 1222: 61, 1238: 63, 1247: 55, 1248: 69, 1254: 55, 1257: 59, 1269: 54, 1284: 61, 1287: 50, 1310: 51, 1318: 52, 1319: 57, 1327: 49, 1332: 46, 1345: 54, 1351: 57, 1358: 59, 1364: 68, 1374: 61, 1388: 60, 1392: 52, 1397: 52, 1399: 55, 1404: 48, 1428: 56, 1435: 61, 1436: 59, 1440: 68, 1443: 56, 1446: 62, 1464: 62, 1508: 52, 1513: 50, 1519: 48, 1534: 58, 1547: 69, 1550: 51, 1553: 44, 1562: 60, 1566: 59, 1567: 57, 1573: 58, 1577: 66, 1578: 59, 1581: 56, 1584: 55, 1587: 66, 1602: 41, 1616: 54, 1621: 58, 1623: 66, 1630: 52, 1632: 55, 1634: 64, 1670: 58, 1675: 53, 1679: 51, 1692: 58, 1695: 54, 1712: 61, 1719: 45, 1726: 70, 1732: 56, 1744: 56, 1746: 64, 1748: 62, 1752: 65, 1757: 57, 1765: 55, 1775: 50, 1786: 60, 1788: 53, 1789: 61, 1793: 60, 1847: 50, 1852: 61, 1865: 65, 1866: 53, 1869: 55, 1871: 54, 1875: 51, 1881: 46, 1883: 56, 1886: 58, 1888: 57, 1893: 63, 1899: 65, 1903: 58, 1908: 64, 1911: 56, 1924: 60, 1931: 55, 1945: 52, 1946: 59, 1952: 66, 1960: 57, 1965: 48, 1975: 68, 1981: 62, 1983: 57, 1984: 60, 1990: 55, 1991: 70, 2008: 61, 2009: 63, 2014: 66, 2023: 50, 2029: 56, 2049: 57, 2062: 52, 2067: 72, 2070: 52, 2071: 54, 2079: 69, 2080: 57, 2081: 55, 2083: 66, 2102: 49, 2104: 57, 2108: 48, 2114: 48, 2115: 55, 2135: 56, 2147: 64, 2148: 49, 2149: 50, 2153: 58, 2157: 66, 2158: 52, 2159: 66, 2169: 50, 2185: 65, 2187: 63, 2201: 59, 2205: 55, 2214: 52, 2218: 56, 2239: 61, 2257: 62, 2262: 42, 2263: 58, 2267: 53, 2278: 71, 2291: 56, 2308: 54, 2313: 60, 2321: 61, 2326: 70, 2333: 47, 2338: 68, 2341: 53, 2344: 70, 2349: 59, 2350: 60, 2360: 68, 2364: 57, 2386: 70, 2419: 66, 2424: 60, 2443: 66, 2463: 63, 2470: 52, 2473: 58, 2475: 47, 2476: 58, 2485: 55, 2489: 44, 2490: 57, 2494: 55, 2502: 60, 2512: 59, 2514: 66, 2517: 52, 2527: 55, 2532: 74, 2537: 59, 2540: 56, 2573: 45, 2576: 58, 2580: 47, 2583: 54, 2590: 58, 2632: 46, 2639: 67, 2645: 55, 2648: 56, 2653: 65, 2657: 62, 2660: 58, 2664: 57, 2688: 58, 2690: 67, 2694: 58, 2700: 63, 2701: 58, 2707: 66, 2722: 53, 2732: 58, 2735: 59, 2746: 64, 2756: 61, 2757: 68, 2758: 68, 2762: 57, 2765: 53, 2778: 56, 2781: 58, 2783: 61, 2787: 65, 2790: 64, 2793: 53, 2797: 64, 2808: 47, 2820: 57, 2824: 53, 2834: 57, 2837: 56, 2845: 67, 2861: 55, 2863: 66, 2888: 52, 2892: 51, 2903: 56, 2913: 58, 2945: 54, 2947: 50, 2967: 56, 2972: 43, 2983: 54, 2990: 46, 2996: 49, 3001: 55, 3003: 48, 3005: 47, 3007: 56, 3010: 49, 3021: 55, 3051: 47, 3054: 50, 3056: 51, 3060: 54, 3063: 70, 3064: 49, 3072: 67, 3082: 59, 3083: 46, 3088: 51, 3117: 58, 3124: 56, 3128: 57, 3131: 53, 3146: 58, 3147: 56, 3150: 68, 3159: 56, 3166: 63, 3170: 54, 3172: 55, 3178: 58, 3183: 59, 3185: 53, 3189: 52, 3199: 56, 3202: 64, 3204: 70, 3206: 52, 3211: 46, 3212: 66, 3214: 54, 3215: 49, 3218: 60, 3226: 55, 3233: 50, 3253: 59, 3254: 68, 3255: 46, 3260: 60, 3266: 56, 3274: 59, 3288: 56, 3291: 51, 3296: 55, 3311: 70, 3330: 62, 3337: 68, 3342: 55, 3352: 56, 3353: 51, 3356: 66, 3359: 59, 3364: 66, 3366: 73, 3381: 71, 3391: 51, 3393: 47, 3399: 57, 3403: 49, 3410: 64, 3425: 51, 3427: 50, 3436: 54, 3449: 55, 3460: 53, 3461: 61, 3463: 65, 3471: 57, 3479: 57, 3486: 54, 3500: 73, 3501: 67, 3509: 57, 3523: 54, 3531: 63, 3534: 57, 3539: 57, 3541: 45, 3547: 52, 3566: 50, 3588: 56, 3589: 59, 3595: 51, 3603: 47, 3606: 66, 3618: 67, 3619: 61, 3620: 58, 3625: 59, 3636: 57, 3657: 53, 3668: 47, 3683: 51, 3693: 54, 3695: 60, 3708: 51, 3711: 69, 3714: 56, 3715: 61, 3719: 52, 3726: 58, 3738: 36, 3739: 53, 3741: 45, 3746: 58, 3748: 50, 3757: 66, 3762: 62, 3764: 37, 3772: 54, 3777: 48, 3778: 67, 3783: 51, 3786: 69, 3790: 47, 3799: 70, 3802: 61, 3810: 60, 3814: 71, 3831: 53, 3833: 58, 3837: 66, 3846: 57, 3852: 68, 3855: 57, 3861: 63, 3863: 63, 3868: 61, 3876: 55, 3883: 58, 3891: 63, 3926: 59, 3933: 55, 3936: 46, 3944: 65, 3950: 59, 3955: 53, 3957: 65, 3973: 59, 3992: 52, 3994: 52, 3997: 47, 4002: 57, 4007: 48, 4018: 61, 4020: 70, 4025: 60, 4032: 55, 4036: 47, 4051: 62, 4058: 52, 4060: 58, 4064: 49, 4069: 51, 4072: 51, 4073: 44, 4076: 61, 4079: 52, 4085: 56, 4088: 52, 4094: 59, 4096: 57, 4097: 46, 4098: 58, 4110: 52, 4121: 54, 4126: 59, 4132: 56, 4159: 53, 4176: 55, 4189: 56, 4197: 65, 4204: 57, 4206: 65, 4230: 50, 4239: 54, 4246: 54, 4260: 54, 4264: 63, 4277: 53, 4317: 55, 4326: 57, 4328: 58, 4333: 56, 4339: 58, 4349: 61, 4352: 65, 4370: 59, 4374: 59, 4378: 49, 4401: 59, 4405: 67, 4407: 55, 4418: 64, 4435: 55, 4442: 73, 4464: 49, 4478: 63, 4481: 54, 4483: 64, 4484: 53, 4491: 53, 4506: 58, 4514: 68, 4522: 55, 4525: 56, 4534: 48, 4537: 60, 4548: 56, 4557: 66, 4592: 60, 4593: 57, 4598: 60, 4599: 52, 4600: 55, 4601: 55, 4609: 55, 4617: 68, 4639: 55, 4641: 68, 4655: 51, 4659: 57, 4666: 55, 4669: 55, 4671: 49, 4680: 55, 4689: 80, 4690: 60, 4693: 54, 4700: 46, 4704: 59, 4705: 49, 4716: 50, 4725: 67, 4727: 53, 4728: 70, 4730: 46, 4736: 73, 4742: 58, 4749: 54, 4763: 52, 4770: 61, 4777: 51, 4784: 49, 4785: 52, 4789: 49, 4790: 52, 4805: 51, 4808: 63, 4810: 60, 4813: 68, 4829: 55, 4832: 51, 4833: 62, 4842: 59, 4858: 63, 4869: 56, 4876: 52, 4884: 54, 4905: 67, 4910: 56, 4915: 57, 4918: 59, 4925: 50, 4939: 52, 4949: 56, 4950: 49, 4956: 60, 4957: 61, 4972: 62, 4976: 52}
learned_list: [1, 2, 5, 3, 6, 4, 7, 8, 9, 10, 3738, 3764, 595, 1602, 2262, 2972, 116, 575, 1553, 2489, 4073, 485, 914, 1719, 2573, 3541, 3741, 1162, 1332, 1881, 2632, 2990, 3083, 3211, 3255, 3936, 4097, 4700, 4730, 703, 799, 2333, 2475, 2580, 2808, 3005, 3051, 3393, 3603, 3668, 3790, 3997, 4036, 39, 409, 1404, 1519, 1965, 2108, 2114, 3003, 3777, 4007, 4534, 53, 533, 693, 920, 1327, 2102, 2148, 2996, 3010, 3064, 3215, 3403, 4064, 4378, 4464, 4671, 4705, 4784, 4789, 4950, 188, 557, 1164, 1168, 1287, 1513, 1775, 1847, 2023, 2149, 2169, 2947, 3054, 3233, 3427, 3566, 3748, 4230, 4716, 4925, 38, 46, 321, 566, 762, 1029, 1310, 1550, 1679, 1875, 2892, 3056, 3088, 3291, 3353, 3391, 3425, 3595, 3683, 3708, 3783, 4069, 4072, 4655, 4777, 4805, 4832, 163, 272, 275, 669, 778, 1172, 1318, 1392, 1397, 1508, 1630, 1945, 2062, 2070, 2158, 2214, 2470, 2517, 2888, 3189, 3206, 3547, 3719, 3992, 3994, 4058, 4079, 4088, 4110, 4599, 4763, 4785, 4790, 4876, 4939, 4976, 433, 478, 1049, 1123, 1675, 1788, 1866, 2267, 2341, 2722, 2765, 2793, 2824, 3131, 3185, 3460, 3657, 3739, 3831, 3955, 4159, 4277, 4484, 4491, 4727, 35, 109, 483, 536, 691, 811, 991, 1027, 1269, 1345, 1616, 1695, 1871, 2071, 2308, 2583, 2945, 2983, 3060, 3170, 3214, 3436, 3486, 3523, 3693, 3772, 4121, 4239, 4246, 4260, 4481, 4693, 4749, 4884, 276, 294, 326, 1069, 1075, 1247, 1254, 1399, 1584, 1632, 1765, 1869, 1931, 1990, 2081, 2115, 2205, 2485, 2494, 2527, 2645, 2861, 3001, 3021, 3172, 3226, 3296, 3342, 3449, 3876, 3933, 4032, 4176, 4317, 4407, 4435, 4522, 4600, 4601, 4609, 4639, 4666, 4669, 4680, 4829, 403, 405, 593, 731, 747, 798, 1085, 1208, 1428, 1443, 1581, 1732, 1744, 1883, 1911, 2029, 2135, 2218, 2291, 2540, 2648, 2778, 2837, 2903, 2967, 3007, 3124, 3147, 3159, 3199, 3266, 3288, 3352, 3588, 3714, 4085, 4132, 4189, 4333, 4525, 4548, 4869, 4910, 4949, 34, 143, 169, 306, 317, 432, 599, 655, 741, 828, 897, 902, 1166, 1203, 1319, 1351, 1567, 1757, 1888, 1960, 1983, 2049, 2080, 2104, 2364, 2490, 2664, 2762, 2820, 2834, 3128, 3399, 3471, 3479, 3509, 3534, 3539, 3636, 3846, 3855, 4002, 4096, 4204, 4326, 4593, 4659, 4915, 251, 308, 410, 447, 608, 663, 667, 729, 855, 873, 1534, 1573, 1621, 1670, 1692, 1886, 1903, 2153, 2263, 2473, 2476, 2576, 2590, 2660, 2688, 2694, 2701, 2732, 2781, 2913, 3117, 3146, 3178, 3620, 3726, 3746, 3833, 3883, 4060, 4098, 4328, 4339, 4506, 4742, 161, 311, 452, 482, 658, 807, 870, 942, 1125, 1161, 1257, 1358, 1436, 1566, 1578, 1946, 2201, 2349, 2512, 2537, 2735, 3082, 3183, 3253, 3274, 3359, 3589, 3625, 3926, 3950, 3973, 4094, 4126, 4370, 4374, 4401, 4704, 4842, 4918, 27, 213, 247, 490, 622, 864, 918, 998, 1131, 1196, 1388, 1562, 1786, 1793, 1924, 1984, 2313, 2350, 2424, 2502, 3218, 3260, 3695, 3810, 4025, 4537, 4592, 4598, 4690, 4810, 4956, 690, 909, 967, 1011, 1124, 1151, 1222, 1284, 1374, 1435, 1712, 1789, 1852, 2008, 2239, 2321, 2756, 2783, 3461, 3619, 3715, 3802, 3868, 4018, 4076, 4349, 4770, 4957, 45, 190, 218, 386, 497, 571, 596, 1018, 1090, 1446, 1464, 1748, 1981, 2257, 2657, 3330, 3762, 4051, 4833, 4972, 301, 375, 509, 692, 1031, 1115, 1238, 1893, 2009, 2187, 2463, 2700, 3166, 3531, 3861, 3863, 3891, 4264, 4478, 4808, 4858, 477, 788, 812, 900, 916, 1023, 1092, 1165, 1634, 1746, 1908, 2147, 2746, 2790, 2797, 3202, 3410, 4418, 4483, 431, 720, 1752, 1865, 1899, 2185, 2653, 2787, 3463, 3944, 3957, 4197, 4206, 4352, 385, 639, 753, 1036, 1127, 1577, 1587, 1623, 1952, 2014, 2083, 2157, 2159, 2419, 2443, 2514, 2707, 2863, 3212, 3356, 3364, 3606, 3757, 3837, 4557, 156, 1040, 1200, 2639, 2690, 2845, 3072, 3501, 3618, 3778, 4405, 4725, 4905, 41, 248, 591, 641, 1051, 1120, 1364, 1440, 1975, 2338, 2360, 2757, 2758, 3150, 3254, 3337, 3852, 4514, 4617, 4641, 4813, 1088, 1248, 1547, 2079, 3711, 3786, 1726, 1991, 2326, 2344, 2386, 3063, 3204, 3311, 3799, 4020, 4728, 30, 1052, 2278, 3381, 3814, 574, 1157, 2067, 1003, 3366, 3500, 4442, 4736, 2532, 993, 230, 4689]
learned_dic: {1: 0, 2: 1, 3: 3, 4: 2, 5: 4, 6: 4, 7: 4, 8: 7, 9: 8, 10: 8, 15: 51, 18: 65, 27: 59, 28: 48, 42: 68, 44: 59, 47: 60, 58: 52, 64: 55, 73: 70, 82: 54, 93: 54, 94: 52, 99: 59, 101: 63, 102: 64, 105: 47, 119: 67, 128: 39, 129: 62, 135: 58, 136: 57, 142: 47, 144: 51, 185: 50, 193: 57, 199: 58, 201: 43, 207: 50, 219: 54, 222: 55, 227: 46, 231: 49, 250: 49, 269: 52, 272: 56, 301: 52, 309: 58, 313: 45, 323: 55, 324: 63, 330: 49, 346: 62, 347: 53, 361: 60, 363: 60, 365: 47, 373: 62, 392: 66, 399: 64, 401: 41, 427: 54, 428: 55, 445: 57, 456: 55, 457: 64, 461: 53, 465: 67, 470: 49, 477: 67, 498: 66, 501: 47, 508: 57, 522: 64, 550: 52, 557: 56, 585: 69, 587: 60, 594: 64, 595: 62, 616: 52, 620: 48, 649: 67, 654: 49, 660: 62, 665: 56, 666: 49, 667: 63, 681: 50, 692: 59, 708: 58, 712: 47, 721: 54, 737: 55, 750: 57, 760: 58, 768: 53, 769: 62, 789: 56, 792: 56, 807: 51, 814: 51, 816: 56, 839: 49, 848: 60, 852: 64, 859: 63, 861: 59, 863: 57, 878: 47, 891: 42, 895: 48, 897: 66, 920: 60, 926: 58, 939: 50, 944: 51, 956: 54, 977: 47, 983: 51, 987: 45, 992: 54, 994: 51, 1008: 45, 1013: 60, 1017: 58, 1024: 67, 1026: 54, 1027: 53, 1054: 59, 1058: 49, 1078: 59, 1094: 52, 1097: 53, 1102: 50, 1124: 66, 1125: 61, 1131: 50, 1132: 51, 1153: 70, 1155: 58, 1158: 45, 1160: 53, 1162: 58, 1163: 56, 1164: 62, 1173: 47, 1193: 60, 1197: 58, 1203: 52, 1207: 49, 1217: 51, 1218: 54, 1227: 67, 1261: 61, 1283: 65, 1297: 49, 1301: 59, 1304: 61, 1312: 60, 1319: 50, 1324: 60, 1326: 58, 1336: 59, 1339: 52, 1357: 64, 1386: 52, 1392: 65, 1395: 62, 1396: 59, 1410: 60, 1420: 53, 1425: 69, 1427: 51, 1435: 61, 1442: 47, 1469: 52, 1488: 48, 1489: 59, 1494: 41, 1496: 51, 1497: 49, 1499: 53, 1513: 51, 1515: 71, 1522: 60, 1528: 57, 1534: 52, 1535: 62, 1541: 68, 1550: 51, 1553: 58, 1555: 61, 1557: 48, 1570: 51, 1581: 44, 1602: 66, 1608: 61, 1612: 52, 1615: 71, 1617: 57, 1619: 58, 1622: 55, 1630: 70, 1639: 56, 1642: 59, 1652: 44, 1657: 71, 1660: 60, 1663: 39, 1665: 49, 1679: 68, 1691: 59, 1692: 56, 1695: 54, 1706: 60, 1708: 63, 1717: 59, 1719: 56, 1727: 58, 1740: 52, 1746: 58, 1761: 55, 1797: 62, 1799: 53, 1811: 56, 1819: 51, 1829: 55, 1832: 43, 1846: 51, 1847: 51, 1874: 46, 1876: 56, 1878: 56, 1887: 53, 1890: 53, 1896: 49, 1903: 68, 1908: 65, 1966: 54, 1969: 46, 1970: 52, 1973: 51, 1981: 49, 1987: 63, 1994: 56, 1995: 63, 2003: 61, 2004: 46, 2005: 67, 2011: 53, 2022: 61, 2026: 60, 2034: 49, 2041: 61, 2042: 58, 2051: 60, 2055: 62, 2068: 52, 2070: 58, 2071: 54, 2072: 57, 2076: 60, 2095: 66, 2100: 54, 2101: 48, 2104: 53, 2106: 57, 2110: 56, 2118: 53, 2141: 57, 2147: 60, 2149: 52, 2155: 56, 2156: 62, 2165: 71, 2172: 50, 2183: 60, 2185: 59, 2194: 59, 2198: 64, 2207: 53, 2210: 51, 2216: 60, 2218: 56, 2229: 55, 2235: 56, 2237: 53, 2264: 65, 2281: 65, 2316: 49, 2317: 59, 2318: 61, 2336: 66, 2339: 60, 2340: 54, 2341: 60, 2345: 57, 2358: 47, 2370: 59, 2371: 61, 2376: 39, 2378: 77, 2396: 57, 2404: 61, 2410: 52, 2413: 59, 2416: 53, 2427: 53, 2446: 69, 2452: 52, 2470: 45, 2474: 52, 2483: 59, 2487: 54, 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learned_list: 