Statistics

Problem Statement for "DieDesign"

Problem Statement

Yves and Zola are playing dice.

Yves has one N-sided die. You are given the int[] pips with N elements. Each element of pips is the number of pips (small dots) on one side of his die.

Zola has a blank N-sided die and a permanent marker she can use to draw pips onto her die. She can distribute the pips arbitrarily, but to keep it fair, the total number of pips she draws must be exactly equal to the total number of pips on Yves's die.

Once Zola finishes her die, they will both roll their die and higher score wins. As the way the dice were chosen gives an advantage to Zola, Yves wins ties.

Design Zola's die. Maximize the probability that she wins. Return a int[] with N elements describing Zola's die. If there are multiple optimal solutions, you may return any of them.

Definition

Class:
DieDesign
Method:
design
Parameters:
int[]
Returns:
int[]
Method signature:
int[] design(int[] pips)
(be sure your method is public)

Notes

  • The limit of 5000 pips per side only applies to Yves's die. Zola may place more than 5000 pips on some sides of her die, if she wants to.

Constraints

  • pips will have between 1 and 30 elements, inclusive.
  • Each element of pips will be between 0 and 5000, inclusive.

Examples

  1. {1,2,3,4,5,6}

    Returns: {0, 0, 0, 7, 7, 7 }

    Sometimes this game happens to be perfectly fair. With the die we designed for Zola she will win 50 percent of all games.

  2. {0,0,0,2}

    Returns: {0, 0, 1, 1 }

    Having the two pips on different faces is much better for Zola than having the same die as Yves.

  3. {1,1,13,1}

    Returns: {4, 4, 4, 4 }

    Sometimes Zola's die will turn out to be the better one of the pair.

  4. {1,2,4,8,16,32,64,128,256,512,1024,2048,4096,4963,4964,4965,4966,4967,4968,4969,4970,4971,4972,4973,4974,4975,4976,4977,4978,4979}

    Returns: {231, 257, 257, 257, 257, 257, 257, 257, 257, 257, 257, 257, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980, 4980 }

  5. {1,3,9,27,81,243,729,2187}

    Returns: {600, 244, 244, 244, 244, 244, 730, 730 }

  6. {1,2,4,8,16,32,64,128,256,512,1024,2048,4096}

    Returns: {1011, 513, 513, 513, 513, 513, 513, 513, 513, 513, 513, 1025, 1025 }

  7. {1,2,3,4,5,90,100}

    Returns: {74, 6, 6, 6, 6, 6, 101 }

  8. {1,2,3,4,5,100}

    Returns: {85, 6, 6, 6, 6, 6 }

  9. {250,500,750,1000,1250,1500,1750,2000,2250,2500,2750,3000,3250,3500,3750,4000,4250,4500,4750,5000}

    Returns: {239, 0, 0, 0, 0, 0, 0, 0, 0, 2251, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  10. {876, 1252, 2146, 2782, 2964, 3160, 4177, 4293, 4470, 4994}

    Returns: {79, 0, 0, 3161, 4471, 4471, 4471, 4471, 4995, 4995 }

  11. {666, 4927, 1836, 4225, 1726, 4159, 2110, 2511, 4096, 4960, 931, 4605, 511, 2350, 1452, 3999, 1976, 3312, 3883, 57, 4825, 3273, 4989, 1927}

    Returns: {184, 58, 58, 58, 58, 58, 58, 58, 667, 667, 2512, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990 }

  12. {4623, 97, 2057, 4369, 1744, 4360, 3052, 3858, 1755, 2723, 3280, 314, 4804, 3397, 2666, 4404, 2823, 61, 895, 168, 2547, 398, 4988, 1791}

    Returns: {467, 399, 399, 399, 399, 399, 399, 399, 399, 399, 399, 399, 3398, 3398, 4805, 4805, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989 }

  13. {1448, 4179, 70, 4220, 4819, 2517, 4701, 2437, 3356, 4717, 4782, 3068, 2708, 2001, 2307, 1752, 2759, 3304, 3046, 1733, 1120, 2907, 4209, 237, 3803, 1213, 4472, 2882}

    Returns: {208, 71, 71, 71, 71, 71, 238, 238, 238, 238, 238, 3357, 3357, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820, 4820 }

  14. {1089, 582, 749, 4894, 4443, 4167, 1505, 2159, 4258, 356, 1850, 2721, 4886, 4956, 3014, 1181, 2891, 4853, 3775, 4789, 3572, 4218, 539, 4287, 2804, 4195, 3501, 968, 3367, 1728}

    Returns: {164, 0, 0, 0, 0, 0, 0, 0, 0, 750, 750, 1182, 1182, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957, 4957 }

  15. {2745, 2476, 1205, 2432, 3387, 4543, 1231, 4791, 2605, 3596, 4305, 2097, 2041, 1862, 2186, 1856, 2904, 4485, 3708, 4362, 4349, 4919, 2226, 2823, 4829, 4177, 2804, 2300, 4542, 3762}

    Returns: {5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2905, 4544, 4544, 4830, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920, 4920 }

  16. {3702, 4485, 3495, 2079, 2968, 4455, 3913, 3138, 3907, 2667, 3705, 3371, 2181, 3373, 1213, 2909, 4427, 2422, 2544, 3607, 4840, 3317, 3712, 1055, 2683, 4436, 3433, 3315, 3003, 1274}

    Returns: {28, 0, 0, 0, 0, 0, 0, 0, 3713, 3914, 3914, 3914, 3914, 4456, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486, 4486 }

  17. {2970, 2231, 4492, 3956, 3271, 1038, 1645, 3415, 4263, 4126, 2823, 1298, 1736, 2188, 3119, 1709, 3669, 4088, 1344, 1386, 3913, 2695, 3177, 4498, 2341, 1787}

    Returns: {13, 0, 0, 0, 0, 0, 0, 0, 0, 1788, 4127, 4264, 4499, 4499, 4499, 4499, 4499, 4499, 4499, 4499, 4499, 4499, 4499, 4499, 4499, 4499 }

  18. {2333, 2943, 4567, 4071, 3787, 4649, 2835, 4203, 3872, 3006, 2972, 2138, 2278, 4768, 2763, 3301, 2019, 2053, 3621, 3076, 2447, 2817, 3456, 2637, 2472, 2791, 3016, 3406, 4858}

    Returns: {44, 0, 0, 0, 0, 0, 0, 0, 0, 3873, 3873, 4072, 4204, 4204, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859, 4859 }

  19. {2075, 4255, 3238, 3974, 2131, 3978, 3977, 1696, 3241, 4969, 3977, 931, 2072, 1809, 1695, 4255, 1808, 2130, 2073, 3977, 2131, 3109, 2132, 2131, 3239, 3238, 4256}

    Returns: {16, 0, 0, 0, 0, 0, 0, 0, 2133, 3979, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257, 4257 }

  20. {14, 62, 256, 1023, 4, 2048, 10, 31, 1023, 62, 10, 2046, 15, 1026, 3, 2050, 4, 126, 1022, 15, 513, 1025, 18, 8, 0, 512}

    Returns: {234, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 257, 514, 1027, 1027, 1027, 1027, 1027, 1027, 1027, 1027, 1027, 1027 }

  21. {2046, 510, 33, 1022, 5, 66, 514, 258, 2, 31, 1022, 1022, 2, 1022, 2047, 10, 2049, 32, 5, 128, 3, 17, 3, 2048, 1023, 14, 5, 1025}

    Returns: {174, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 259, 259, 515, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1026 }

  22. {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31 }

  23. {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,40}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 }

  24. {1,1,1,2,2,3,4,4,4,4,5,6,6,7,7,7,8,8,9,9,9,9,10,10,11,12,14,15,15,15}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11 }

  25. {1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9 }

  26. {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 }

  27. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  28. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

  29. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,17,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

  30. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

  31. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

  32. {47}

    Returns: {47 }

  33. {47,47}

    Returns: {46, 48 }

  34. {47,48}

    Returns: {46, 49 }

  35. {47,49}

    Returns: {46, 50 }

  36. {0,49}

    Returns: {48, 1 }

  37. {5000,5000,5000}

    Returns: {4998, 5001, 5001 }

  38. {5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000,5000}

    Returns: {4971, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  39. {512,3524,4535,3716,4675,2813,2108,4197,3166,3214,335,3428,193,839,5,2161,3944,4478,74,2585,4649,3503,1884,1947,4286,4210,2941}

    Returns: {228, 194, 336, 336, 336, 336, 336, 336, 336, 336, 336, 336, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676, 4676 }

  40. {1982,272,4595,3065,2895,4923,2800,4569,4711,1605,1954,289,1028,2735,802,2972,4737,3142,4164,4424,2071,795,1859,2743,1790,3858,902,3413}

    Returns: {294, 290, 290, 903, 1029, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143 }

  41. {2892,2345,1957,4548,2142,2924,4363,4631,328,3964,2557,4609,3239,2131,4254,1809,4967,933,1696,3111,3976,2073,4944,4571,1222,3636,124,1395,4480}

    Returns: {326, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 4632, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968, 4968 }

  42. {678,611,2177,4188,4479,3903,3568,2994,271,4979,2170,4985,4234,3865,2580,182,4726,1990,1731,2834,3535,1507,1447,3848,1627,1047,806,1119,4666,2818}

    Returns: {2363, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 2178, 4986, 4986, 4986, 4986, 4986 }

  43. {3214,885,2186,3636,3,1002,3392,550,3024,169,2164,341,1150,1484,4191,4022,1647,4052,4327,3715,4617,4647,81,604,1434,1233,4451,2771,382}

    Returns: {1556, 1485, 1485, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 1648, 4648, 4648, 4648, 4648, 4648, 4648 }

  44. {1921,501,3102,1008,181,725,2479,441,4488,2520,1958,4381,1238,4505,4749,2237,4676,661,4611,4024,2807,4559,427,938,3387,3421,2897,2480,4622}

    Returns: {1058, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1239, 2521, 4750, 4750, 4750, 4750, 4750, 4750, 4750, 4750, 4750, 4750, 4750, 4750 }

  45. {4896,1144,520,4160,959,3778,3717,146,3560,4619,4277,542,2356,4015,4115,934,2008,2885,2712,1367,3789,185,4814,804,3763,3772,2267,4463}

    Returns: {998, 960, 960, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 4897, 4897, 4897, 4897, 4897, 4897, 4897, 4897, 4897, 4897, 4897, 4897 }

  46. {194,4589,1550,2351,334,2156,4442,3954,3143,560,893,4266,4833,4906,3910,4400,2965,4738,2553,3375,1678,749,841,4197,2498,3318,2725,4415,2950,891}

    Returns: {1003, 894, 894, 894, 894, 894, 894, 894, 894, 894, 894, 894, 894, 894, 894, 2157, 4907, 4907, 4907, 4907, 4907, 4907, 4907, 4907, 4907, 4907, 4907, 4907, 4907, 4907 }

  47. {3490,2953,411,2865,4774,462,3210,2194,2083,1725,2373,1713,3809,2453,3647,3608,2600,448,1272,4753,3929,5,225,3463,3747}

    Returns: {571, 463, 463, 463, 463, 463, 463, 463, 463, 463, 2454, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930 }

  48. {3587,2111,2408,839,2482,1014,1390,3465,2757,4075,3489,1921,4123,4671,4204,2155,2564,4544,188,4988,3107,4871,4827,4872,3783,4573,1470,3088,350}

    Returns: {106, 0, 0, 189, 351, 351, 351, 351, 351, 351, 351, 351, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989 }

  49. {1486,638,3972,3367,493,1838,3782,1441,4898,3259,36,1139,596,4589,3187,6,3148,4090,3728,3057,1003,4188,3280,836,704,3443}

    Returns: {1058, 1140, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 1487, 4189, 4189, 4189, 4189, 4189, 4189, 4189, 4189, 4189 }

  50. {4509,854,1432,4084,3897,3598,4885,767,3239,4296,4142,2682,3543,1610,2591,3253,611,1085,3994,2728,858,2068,3976,759,2925,243,3232,666}

    Returns: {989, 859, 859, 859, 859, 859, 859, 859, 859, 859, 859, 859, 859, 859, 4297, 4297, 4297, 4297, 4297, 4297, 4297, 4297, 4297, 4297, 4297, 4297, 4297, 4510 }

  51. {1836,4225,1726,4159,2110,2511,4096,4960,931,4605,511,2350,1452,3999,1976,3312,3883,57,4825,3273,4989,1927,4541,3064,874,2767,526,1286,4832}

    Returns: {193, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 932, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990, 4990 }

  52. {1957,1500,655,1160,4218,1377,1355,632,759,1031,4825,3225,2853,997,3396,2415,4499,1798,2841,738,2573,834,293,1653,4580}

    Returns: {2112, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 1958, 2854, 2854, 3226 }

  53. {2705,744,2615,3514,4146,4472,4690,2884,4270,4255,3485,3597,3572,3384,4019,185,1595,2674,401,4912,3510,828,3597,4774,1016,788}

    Returns: {935, 829, 829, 1017, 1017, 1017, 1017, 1017, 1017, 1017, 1017, 1017, 1017, 4913, 4913, 4913, 4913, 4913, 4913, 4913, 4913, 4913, 4913, 4913, 4913, 4913 }

  54. {3581,483,2733,1535,3348,3840,4243,3891,4230,979,1879,1626,216,4423,4043,2664,1163,1342,2368,594,384,4953,2446,362,51,2098,2823}

    Returns: {648, 595, 595, 595, 595, 595, 595, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 2824, 4424 }

  55. {4550,1761,3025,3036,1094,1658,3665,282,2470,4936,2454,3455,907,3462,3426,2846,4077,2103,371,4628,4020,1881,2216,3322,479,196}

    Returns: {626, 480, 480, 480, 480, 480, 480, 480, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463, 3463 }

  56. {1562,3418,3005,4261,726,2827,2777,3614,555,536,3876,2185,527,1329,1677,1863,3457,3871,1617,2430,48,935,4952,4623,97,2057,4369,1744}

    Returns: {2289, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2186, 2431, 3877, 3877 }

  57. {3052,3858,1755,2723,3280,314,4804,3397,2666,4404,2823,61,895,168,2547,398,4988,1791,4294,27,286,4543,4818,403,3141,3801,1564,735,2271}

    Returns: {481, 404, 404, 404, 404, 404, 404, 404, 404, 404, 404, 404, 404, 404, 404, 404, 3398, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989, 4989 }

  58. {3239,4179,2849,309,534,2490,4926,2549,426,4998,3618,3796,3332,2724,736,2074,3444,3059,804,3091,3092,1445,2422,244,249,4711,4725,1567,1032,4596}

    Returns: {971, 805, 805, 805, 805, 805, 805, 805, 805, 805, 805, 3445, 3445, 3445, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619, 3619 }

  59. {706,62,3464,3503,3410,3465,4737,1045,1261,3077,4414,3768,2151,1208,615,324,4832,1978,4815,1050,577,143,1122,1004,4247,1042}

    Returns: {1473, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 1262, 4833, 4833, 4833, 4833, 4833, 4833, 4833 }

  60. {2393,4669,4937,3426,4484,3998,4759,192,1371,4897,4439,4737,1194,1894,960,1241,2335,3967,4014,3773,4956,2533,3356,3684,4960,1503,104,3505,3992}

    Returns: {277, 193, 193, 193, 193, 193, 193, 193, 193, 193, 961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961, 4961 }

  61. {3342,2813,3071,4552,2473,2517,3231,3084,291,4311,2201,1160,3828,3214,830,881,4856,278,3012,2786,4683,1208,8,2133,2877,1310,325,3377}

    Returns: {426, 326, 326, 326, 326, 326, 326, 326, 1311, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3829 }

  62. {2649,1208,2176,2098,2709,3348,913,1683,1446,1888,2311,2012,3773,4323,2792,1278,4324,2956,913,1199,1455,4625,1863,4422,4681,4321,2624,4438}

    Returns: {6, 0, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2793, 2957, 2957, 2957, 2957, 2957, 2957, 2957, 2957, 2957, 2957, 2957 }

  63. {2041,334,2994,3116,1408,4015,4987,1394,1583,3298,439,3841,2677,4493,4419,611,2120,780,1134,4221,4747,1706,2242,4892,3190,909}

    Returns: {2435, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 2243, 3299, 3299, 3299, 3299, 3299, 3299, 4988 }

  64. {4529,2930,979,3078,3049,4366,1843,2383,2055,4985,2628,4666,313,1699,2426,3654,2664,935,1198,4849,1499,2133,2810,2244,775,2413,1703}

    Returns: {88, 0, 0, 0, 980, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079, 3079 }

  65. {2216,1778,1624,4033,4056,634,3127,190,4856,1228,871,3435,2465,1804,3391,1554,705,1754,1830,4489,731,4551,3434,2531,2583}

    Returns: {1986, 1831, 1831, 1831, 1831, 1831, 2217, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584, 2584 }

  66. {972,746,2574,3724,1735,962,709,4389,2790,4642,3966,1793,486,2612,2526,3104,2169,4848,486,621,2097,3745,4129,1804,4201,4186,3975}

    Returns: {1024, 973, 973, 973, 973, 973, 973, 973, 973, 973, 973, 973, 973, 973, 4202, 4202, 4202, 4202, 4390, 4390, 4390, 4390, 4390, 4390, 4390, 4390, 4390 }

  67. {2609,3575,4229,2038,4996,2691,4672,1718,4682,1453,1551,1960,340,240,4981,4174,4961,2134,4989,2414,1626,2812,4849,4953,4581,2758,4131}

    Returns: {145, 0, 0, 0, 0, 0, 0, 341, 341, 341, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997, 4997 }

  68. {2685,3053,1513,1287,4042,618,288,3202,3802,3686,2410,769,4033,2215,2734,2312,1777,3501,618,2092,3133,2650,3765,2391,1319,1982}

    Returns: {45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2735, 2735, 3803, 4043, 4043, 4043, 4043, 4043, 4043, 4043, 4043, 4043, 4043, 4043, 4043, 4043 }

  69. {2970,1886,2531,297,1774,4707,3880,201,2912,75,2329,2243,4529,3406,4338,1933,3720,3721,433,677,1066,3296,3631,1533,2030,376}

    Returns: {654, 434, 434, 434, 434, 434, 434, 434, 434, 678, 678, 678, 3881, 3881, 3881, 3881, 3881, 3881, 3881, 3881, 3881, 3881, 3881, 3881, 3881, 3881 }

  70. {3704,4359,4291,816,4570,217,4460,3672,4427,3977,4824,1320,1298,1952,2257,2609,1586,4565,4039,4166,2250,3766,2092,2760,4301,954,1809,2082}

    Returns: {191, 0, 0, 0, 0, 0, 0, 218, 218, 218, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571, 4571 }

  71. {267,1129,2003,3669,694,2655,4486,1769,2650,770,2131,4247,1286,2277,2956,1142,1348,644,1509,457,4170,1470,4946,4550,841,2343}

    Returns: {1571, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 2344, 2344, 2344, 2344, 2656, 2656, 2656, 2656, 2656, 2656, 2656, 2656, 2656, 2656, 2656, 2656 }

  72. {2626,1519,708,3683,2259,808,2444,1600,4855,4054,1179,1116,1993,4410,1969,4985,2559,2104,3722,215,2531,1544,208,3528,1427}

    Returns: {36, 0, 216, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627, 2627 }

  73. {3988,1545,3674,105,3027,2026,3288,4155,1466,1444,1466,4939,411,1762,2581,4996,3298,2456,2192,760,2480,1884,356,4592,3860,2507,1932}

    Returns: {58, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582, 2582 }

  74. {3739,1467,1448,4540,2480,3769,2368,2387,424,2512,310,561,4909,3274,4647,4146,3481,1199,3100,3150,4446,1836,4342,4589,3387,3645,4421}

    Returns: {12, 0, 0, 0, 0, 0, 0, 425, 562, 562, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648, 4648 }

  75. {2068,3281,2624,2745,1021,3097,3566,1151,735,3552,2044,1930,28,2105,4440,207,2761,3249,4353,2481,1622,2077,554,414,1989,1430}

    Returns: {2218, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2106, 2762 }

  76. {2888,2836,684,4089,2137,2298,4894,3014,1674,392,2133,3991,1906,895,4326,2503,1512,3250,2303,4847,1651,4325,2295,1314,1322,2622,1255,2279,3949}

    Returns: {23, 0, 0, 0, 2304, 2304, 2623, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015, 3015 }

  77. {2340,2141,1237,3203,1796,1817,1459,706,2376,4233,1193,3810,2418,258,873,4545,1809,1698,870,1613,4091,3139,2477,2091,99}

    Returns: {54, 0, 100, 100, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478, 2478 }

  78. {2952,3440,792,720,2699,2130,4368,1898,4759,1128,2014,4073,4512,1643,279,1373,194,4664,2570,1864,3004,1876,2004,4002,3035,1652,3478}

    Returns: {2224, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 2131, 3036, 3036, 3036, 3036, 3036, 3036, 3036, 3036, 3036, 3479 }

  79. {3797,4878,1822,291,3331,3818,1899,3469,148,3463,4199,540,4019,1584,3201,1536,16,1962,4032,4258,96,4509,2421,3926,2574,2510}

    Returns: {498, 292, 292, 292, 292, 292, 292, 541, 541, 541, 541, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259, 4259 }

  80. {4252,4135,3076,1822,441,1781,1790,4024,4816,3612,4082,3276,4454,3294,1146,3429,2926,105,4293,2782,4470,876,4994,2964,4177,3160,2146,1252,432}

    Returns: {117, 106, 106, 106, 442, 442, 442, 442, 442, 442, 442, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471, 4471 }

  81. {432,4612,2144,2118,1443,3066,3060,1892,4673,4741,4536,1091,1931,869,1100,2944,420,1188,1430,3195,2216,4278,514,4360,1261,1973}

    Returns: {2275, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 2217, 3067, 3196, 3196, 3196 }

  82. {3723,4246,2151,771,2872,2101,77,4531,2286,4370,2192,3808,4297,3825,1233,2977,1105,1703,161,804,443,3149,4045,1687,4332,4717,1292}

    Returns: {2329, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 2287, 4532, 4718, 4718 }

  83. {3012,475,4569,1488,4504,1952,3944,3927,3497,467,4072,1919,4199,4718,2659,4176,1802,3181,3736,1111,1391,1407,1622,2724,15,4849,4287,1638,4492,3668}

    Returns: {133, 16, 16, 16, 16, 16, 16, 16, 16, 16, 476, 476, 1953, 4719, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850, 4850 }

  84. {2388,4273,3559,3869,4541,3572,175,1366,4771,3507,3267,264,4567,404,496,4963,834,1700,3949,1542,4517,262,4371,984,135,2717}

    Returns: {668, 497, 497, 497, 497, 497, 497, 497, 497, 497, 497, 497, 497, 985, 4772, 4964, 4964, 4964, 4964, 4964, 4964, 4964, 4964, 4964, 4964, 4964 }

  85. {3928,2279,807,958,2939,3959,74,2281,4681,3769,3653,1520,1009,2119,3020,3816,441,4030,268,3488,671,1720,3036,1607,1887,4795,1173}

    Returns: {1098, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 2282, 4031, 4031 }

  86. {4058,4211,873,2380,4963,4426,814,4014,1590,309,1230,4146,2117,1213,2297,3055,1203,2725,4356,3033,1041,1174,3508,3331,4675,2601}

    Returns: {1338, 1231, 1231, 1231, 1231, 1231, 1231, 1231, 1231, 1231, 1231, 1231, 1231, 1231, 3056, 4427, 4427, 4427, 4427, 4427, 4427, 4427, 4427, 4427, 4427, 4676 }

  87. {1472,4955,3072,155,856,3477,1366,532,825,1063,845,626,1785,234,1482,3167,790,524,4574,3944,142,1005,1415,2734,1072,1077,2283,1836,1136,421}

    Returns: {1610, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1483, 1837, 1837, 1837, 1837, 1837, 1837, 1837, 1837, 1837, 1837, 1837, 1837 }

  88. {1300,3433,4536,239,594,1999,4127,3495,4164,4906,518,2901,1988,2922,2182,1542,362,2503,364,1452,484,4288,2549,2521,3579,2787,385,3011}

    Returns: {726, 595, 595, 595, 595, 595, 595, 595, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012 }

  89. {1349, 4345, 4746, 3134, 3243, 4103, 4841, 1595, 2287, 1025, 818, 1655, 4967, 554, 3793, 1695, 1680, 4358, 3337, 1664, 4764, 2600, 2764, 2373, 76, 422, 888, 2084, 1540, 1963 }

    Returns: {2534, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2374, 2765, 3338, 3338, 3338 }

  90. {1807, 249, 73, 3658, 3930, 1272, 2544, 878, 2923, 2709, 4440, 3165, 4492, 3042, 2987, 2503, 2327, 1729, 3840, 2612, 4303, 3169, 2709, 2157, 4560, 933, 3099, 278, 1816, 335 }

    Returns: {137, 74, 74, 336, 336, 336, 336, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170 }

  91. {4999, 4998, 4997, 4989, 4939, 4899, 4989, 4997, 4998, 4999, 4899, 4939, 4979, 4989, 4991, 4998, 4991, 4999, 4997, 4969, 4998, 4997, 4995, 4999, 4989, 4997, 4999, 4999, 4999, 4999 }

    Returns: {4526, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000 }

  92. {2, 5, 8, 5, 12, 45, 67, 32, 89, 35, 12, 98, 65, 23, 766, 34, 122, 6, 123, 1424, 125, 125, 127, 231, 232, 233, 234, 235 }

    Returns: {195, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 236, 236, 236, 236, 236, 236, 236, 236 }

  93. {1, 1, 1, 1, 4, 4, 4, 12 }

    Returns: {2, 2, 2, 2, 5, 5, 5, 5 }

  94. {5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000 }

    Returns: {4991, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  95. {2, 3, 3, 4, 8, 8, 9, 9 }

    Returns: {1, 0, 0, 5, 10, 10, 10, 10 }

  96. {1, 2, 6, 8, 9, 123, 125, 127, 128, 3451, 232, 677, 678, 677, 679, 123, 125, 127, 128, 111, 1111, 1112, 1113, 1114, 1115 }

    Returns: {136, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 1116, 1116, 1116, 1116, 1116, 1116, 1116, 1116, 1116, 1116 }

  97. {67, 34, 0, 69, 24, 78, 58, 62, 64, 5, 45, 81 }

    Returns: {1, 6, 6, 6, 6, 70, 82, 82, 82, 82, 82, 82 }

  98. {5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000 }

    Returns: {4971, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  99. {100, 0, 0, 0, 1, 1, 1, 2, 2, 2, 5, 5, 5, 2, 1, 6 }

    Returns: {28, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 }

  100. {1, 2, 9, 10 }

    Returns: {5, 3, 3, 11 }

  101. {1, 2, 2, 10 }

    Returns: {6, 3, 3, 3 }

  102. {5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985, 4984, 4983, 4982, 4981, 4980, 4979, 4978, 4977, 4976, 4975, 4974, 4973, 4972, 4971 }

    Returns: {4536, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  103. {5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

    Returns: {4971, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  104. {3921, 2313, 5000, 4981, 4321, 4322, 4851, 5000, 5000, 5000, 5000, 5000, 5000, 4567, 3817, 2561, 3999, 2999, 1999, 999, 3999, 3812, 4821, 381, 3000, 4000, 1999, 2001, 1000, 4999 }

    Returns: {258, 0, 0, 0, 0, 0, 0, 382, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  105. {5000, 4999, 4998, 4997, 4996, 5000, 4999, 4998, 4997, 4996, 5000, 4999, 4998, 4997, 4996, 5000, 5000, 4999, 4998, 4997, 4996, 5000, 4999, 4998, 4997, 4996, 5000, 4999, 4998, 4997 }

    Returns: {4915, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

  106. {0, 0, 0, 7, 7, 7 }

    Returns: {2, 1, 1, 1, 8, 8 }

  107. {3989, 4117, 2984, 4343, 4419, 2813, 4865, 4383, 3088, 4648, 2875, 3006, 4758, 3466, 4703, 2643, 2831, 2986, 3524, 4068, 2530, 3390, 4814, 4426, 3870, 4049, 3258, 4574, 2512, 4270 }

    Returns: {284, 0, 0, 0, 0, 0, 0, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866, 4866 }

  108. {5000, 4999, 4996, 4991, 4984, 4975, 4964, 4951, 4936, 4919, 4900, 4879, 4856, 4831, 4804, 4775, 4744, 4711, 4676, 4639, 4600, 4559, 4516, 4471, 4424, 4375, 4324, 4271, 4216, 4159 }

    Returns: {1417, 0, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001 }

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