Statistics

Problem Statement for "TwoTowers"

Problem Statement

The figure below shows a tower of rectangles that consists of three rectangles: a 5x3 rectangle A, a 4x4 rectangle B, and a 1x9 rectangle C. 


    AAA
    AAA
    AAA
    AAA
    AAA
    BBBB
    BBBB
    BBBB
    BBBB
   CCCCCCCCC

In such a tower there are only two rules:

  1. The rectangles must form a single sequence from top to bottom, each rectangle standing on the next one (except for the bottom one that stands on the ground).
  2. The bottom side of each rectangle must completely stand on the top side of the rectangle immediately below it. (The touching sides may be exactly equal.)

Note that the second rule implies that as we go from the top to the bottom, the width of the tower never decreases.


Alice and Bob have a collection of N rectangles. You are given their description: the int[]s A and B, each containing N elements. For each valid index i, one of their rectangles has the dimensions A[i] times B[i].

When building the tower, the rectangles can be rotated by multiples of 90 degrees. E.g., a 5x3 rectangle can be also used as a 3x5 rectangle. The rectangles can be used in any order.


Alice used all N rectangles to build the tallest possible tower. Then, Bob took apart Alice's tower and instead he used all N rectangles to build the shortest possible tower. Return the difference between the heights of those two towers.

Definition

Class:
TwoTowers
Method:
maxDifference
Parameters:
int[], int[]
Returns:
int
Method signature:
int maxDifference(int[] A, int[] B)
(be sure your method is public)

Notes

  • For any collection of rectangles there is always at least one way to rotate them and reorder them into a valid tower, so the return value is always well-defined.

Constraints

  • A will have between 1 and 50 elements, inclusive.
  • Each element of A will be between 1 and 10^6, inclusive.
  • B will have the same number of elements as A.
  • Each element of B will be between 1 and 10^6, inclusive.

Examples

  1. {3}

    {5}

    Returns: 2

    A single 3x5 rectangle. Alice will place it as follows: AAA AAA AAA AAA AAA while Bob will place it as follows: AAAAA AAAAA AAAAA Thus, Alice's tower has height 5, Bob's tower has height 3, and the difference is 5-3 = 2.

  2. {5, 4, 1}

    {3, 4, 9}

    Returns: 10

    These are the three rectangles from the first figure in the problem statement. That particular tower (of height 10) is neither the tallest nor the shortest tower possible: Alice can build a tower of height 18 and Bob can build a tower of height 8.(Note that each of them needs to rotate and reorder the rectangles in a different way. For example, Bob's tower must have the 4x4 square on the top.)

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

    {1, 2, 3, 4, 5}

    Returns: 0

    Here the rotations do not matter (all rectangles are actually squares) and their order is forced: both Alice and Bob must place them from the smallest one on the top to the largest one on the bottom. Thus, they will both build the same tower and the height difference is zero.

  4. {1}

    {1}

    Returns: 0

  5. {1, 2, 3}

    {3, 2, 1}

    Returns: 4

  6. {2, 7, 9, 8}

    {2, 7, 9, 8}

    Returns: 0

  7. {6, 5, 9, 7, 7, 10}

    {6, 5, 9, 7, 7, 10}

    Returns: 0

  8. {7, 1, 2, 1, 5, 8, 9, 1, 6, 10}

    {7, 1, 2, 1, 5, 8, 9, 1, 6, 10}

    Returns: 0

  9. {4, 4, 9, 9, 6, 8, 4, 1, 9, 6, 6, 10, 6}

    {4, 4, 9, 9, 6, 8, 4, 1, 9, 6, 6, 10, 6}

    Returns: 0

  10. {4, 1, 3, 6, 2, 6, 10, 7, 9, 9, 5, 2, 4, 6, 4, 8, 2, 7, 10, 6, 5, 4, 9, 5, 6, 9, 10, 1, 8, 5, 10, 7, 5, 9, 4, 10, 2, 4, 7, 8, 5, 10, 9, 3, 8, 1, 3, 9}

    {4, 1, 3, 6, 2, 6, 10, 7, 9, 9, 5, 2, 4, 6, 4, 8, 2, 7, 10, 6, 5, 4, 9, 5, 6, 9, 10, 1, 8, 5, 10, 7, 5, 9, 4, 10, 2, 4, 7, 8, 5, 10, 9, 3, 8, 1, 3, 9}

    Returns: 0

  11. {2, 5, 9, 10, 9, 8, 7, 6, 1, 10, 5, 10, 9, 8, 6, 1, 10, 4, 4, 6, 7, 3, 3, 8, 4, 3, 2, 3, 10, 6, 9, 7, 2, 5, 8, 1, 2, 7, 2, 6, 1, 5, 1, 3, 3, 9, 8}

    {2, 5, 9, 10, 9, 8, 7, 6, 1, 10, 5, 10, 9, 8, 6, 1, 10, 4, 4, 6, 7, 3, 3, 8, 4, 3, 2, 3, 10, 6, 9, 7, 2, 5, 8, 1, 2, 7, 2, 6, 1, 5, 1, 3, 3, 9, 8}

    Returns: 0

  12. {8, 9, 8, 10, 10, 1, 2, 3, 3, 9, 6, 1, 10, 4, 1, 7, 2, 1, 2, 5, 1, 9, 5, 4, 10, 9, 3, 9, 10, 5, 10, 10, 2, 10, 8, 6, 9, 1, 2, 7, 7, 6, 5, 10, 8, 10, 3, 2}

    {8, 9, 8, 10, 10, 1, 2, 3, 3, 9, 6, 1, 10, 4, 1, 7, 2, 1, 2, 5, 1, 9, 5, 4, 10, 9, 3, 9, 10, 5, 10, 10, 2, 10, 8, 6, 9, 1, 2, 7, 7, 6, 5, 10, 8, 10, 3, 2}

    Returns: 0

  13. {8, 8, 1, 7, 10, 9, 2, 5, 8, 9, 2, 4, 6, 6, 3, 8, 1, 10, 2, 8, 8, 5, 9, 1, 9, 4, 5, 1, 5, 9, 8, 7, 2, 2, 9, 10, 10, 8, 9, 6, 10, 5, 7, 4, 2, 2, 9}

    {8, 8, 1, 7, 10, 9, 2, 5, 8, 9, 2, 4, 6, 6, 3, 8, 1, 10, 2, 8, 8, 5, 9, 1, 9, 4, 5, 1, 5, 9, 8, 7, 2, 2, 9, 10, 10, 8, 9, 6, 10, 5, 7, 4, 2, 2, 9}

    Returns: 0

  14. {52, 43, 69, 47}

    {52, 43, 69, 47}

    Returns: 0

  15. {12, 80}

    {12, 80}

    Returns: 0

  16. {55, 47, 7, 45, 75, 8, 51, 82, 35, 33, 27, 38, 27, 60, 85}

    {55, 47, 7, 45, 75, 8, 51, 82, 35, 33, 27, 38, 27, 60, 85}

    Returns: 0

  17. {57, 100, 57, 41, 87, 8, 20, 75, 62, 1, 4, 55}

    {57, 100, 57, 41, 87, 8, 20, 75, 62, 1, 4, 55}

    Returns: 0

  18. {67, 57, 79, 33, 38, 14, 39, 16, 22, 55, 44, 64, 55, 31, 65, 73, 66, 34, 41, 72, 3, 78, 87, 49, 77, 76, 90, 77, 89, 80, 60, 79, 72, 23, 88, 90, 49, 6, 24, 79, 24, 80, 10, 63, 53, 8, 29, 60, 23, 77}

    {67, 57, 79, 33, 38, 14, 39, 16, 22, 55, 44, 64, 55, 31, 65, 73, 66, 34, 41, 72, 3, 78, 87, 49, 77, 76, 90, 77, 89, 80, 60, 79, 72, 23, 88, 90, 49, 6, 24, 79, 24, 80, 10, 63, 53, 8, 29, 60, 23, 77}

    Returns: 0

  19. {1, 80, 18, 96, 10, 72, 50, 1, 50, 64, 95, 59, 81, 48, 94, 16, 66, 52, 14, 12, 54, 53, 71, 14, 80, 23, 86, 64, 61, 57, 77, 12, 51, 68, 65, 42, 56, 96, 26, 41, 51, 10, 17, 92, 63, 43, 84, 84, 14, 33}

    {1, 80, 18, 96, 10, 72, 50, 1, 50, 64, 95, 59, 81, 48, 94, 16, 66, 52, 14, 12, 54, 53, 71, 14, 80, 23, 86, 64, 61, 57, 77, 12, 51, 68, 65, 42, 56, 96, 26, 41, 51, 10, 17, 92, 63, 43, 84, 84, 14, 33}

    Returns: 0

  20. {12, 46, 4, 51, 80, 11, 77, 29, 67, 83, 27, 65, 33, 92, 98, 40, 65, 78, 15, 72, 8, 37, 93, 23, 63, 90, 31, 52, 79, 61, 1, 76, 52, 78, 31, 81, 71, 48, 14, 44, 9, 21, 76, 14, 31, 24, 11, 19, 66, 22}

    {12, 46, 4, 51, 80, 11, 77, 29, 67, 83, 27, 65, 33, 92, 98, 40, 65, 78, 15, 72, 8, 37, 93, 23, 63, 90, 31, 52, 79, 61, 1, 76, 52, 78, 31, 81, 71, 48, 14, 44, 9, 21, 76, 14, 31, 24, 11, 19, 66, 22}

    Returns: 0

  21. {10, 12, 17, 76, 51, 45, 16, 54, 38, 71, 82, 29, 87, 45, 99, 12, 83, 41, 14, 5, 26, 72, 18, 43, 12, 41, 99, 92, 85, 55, 65, 70, 74, 97, 99, 88, 46, 67, 67, 55, 82, 57, 56, 87, 53, 94, 63, 3}

    {10, 12, 17, 76, 51, 45, 16, 54, 38, 71, 82, 29, 87, 45, 99, 12, 83, 41, 14, 5, 26, 72, 18, 43, 12, 41, 99, 92, 85, 55, 65, 70, 74, 97, 99, 88, 46, 67, 67, 55, 82, 57, 56, 87, 53, 94, 63, 3}

    Returns: 0

  22. {342292, 51456, 628798}

    {342292, 51456, 628798}

    Returns: 0

  23. {945022, 106024, 460424, 810917, 611113}

    {945022, 106024, 460424, 810917, 611113}

    Returns: 0

  24. {100971, 887741, 350922, 458391, 774665, 955520, 61879, 349915, 826046, 791281}

    {100971, 887741, 350922, 458391, 774665, 955520, 61879, 349915, 826046, 791281}

    Returns: 0

  25. {958306, 852730, 701373, 428631, 491577, 777453, 958899, 970773, 543114, 498062, 726412}

    {958306, 852730, 701373, 428631, 491577, 777453, 958899, 970773, 543114, 498062, 726412}

    Returns: 0

  26. {977767, 967077, 240585, 208256, 657826, 27662, 566149, 517551, 341011, 964867, 148906, 708201, 171778, 811705, 303117, 76118, 49244, 782849, 878399, 948686, 634003, 313211, 46363, 673114, 647376, 894104, 701839, 6609, 268627, 361410, 947162, 201563, 582496, 225506, 387318, 945884, 388692, 140101, 212230, 469133, 646128, 36217, 835134, 777725, 853426, 316261, 631909}

    {977767, 967077, 240585, 208256, 657826, 27662, 566149, 517551, 341011, 964867, 148906, 708201, 171778, 811705, 303117, 76118, 49244, 782849, 878399, 948686, 634003, 313211, 46363, 673114, 647376, 894104, 701839, 6609, 268627, 361410, 947162, 201563, 582496, 225506, 387318, 945884, 388692, 140101, 212230, 469133, 646128, 36217, 835134, 777725, 853426, 316261, 631909}

    Returns: 0

  27. {442265, 116178, 443158, 884564, 438632, 364385, 793549, 521960, 269300, 47601, 759227, 592391, 756801, 722938, 956188, 514635, 240885, 283717, 425229, 61316, 915071, 25168, 412212, 200006, 802817, 437577, 384657, 545471, 93025, 361918, 757666, 909518, 654972, 929150, 658080, 355471, 462643, 908050, 877012, 71072, 923964, 68635, 496149, 279767, 67483, 170144, 214672, 238479, 974010}

    {442265, 116178, 443158, 884564, 438632, 364385, 793549, 521960, 269300, 47601, 759227, 592391, 756801, 722938, 956188, 514635, 240885, 283717, 425229, 61316, 915071, 25168, 412212, 200006, 802817, 437577, 384657, 545471, 93025, 361918, 757666, 909518, 654972, 929150, 658080, 355471, 462643, 908050, 877012, 71072, 923964, 68635, 496149, 279767, 67483, 170144, 214672, 238479, 974010}

    Returns: 0

  28. {495601, 831855, 207045, 311127, 6228, 119734, 633879, 591833, 854132, 12440, 263304, 559313, 223346, 558161, 390773, 493891, 960975, 224667, 348572, 419918, 955573, 40198, 705702, 677872, 614965, 434866, 341260, 850336, 843438, 563715, 361471, 938608, 7846, 114597, 21556, 326078, 830213, 50949, 638555, 229297, 862916, 861088, 885507, 549704, 906441, 641638, 3524, 36610, 914224, 581599}

    {495601, 831855, 207045, 311127, 6228, 119734, 633879, 591833, 854132, 12440, 263304, 559313, 223346, 558161, 390773, 493891, 960975, 224667, 348572, 419918, 955573, 40198, 705702, 677872, 614965, 434866, 341260, 850336, 843438, 563715, 361471, 938608, 7846, 114597, 21556, 326078, 830213, 50949, 638555, 229297, 862916, 861088, 885507, 549704, 906441, 641638, 3524, 36610, 914224, 581599}

    Returns: 0

  29. {402073, 936446, 800140, 486579, 200246, 94134, 290724, 986755, 707911, 975552, 666705, 930247, 414639, 534999, 364762, 39647, 929736, 68438, 318812, 630653, 749013, 326306, 54559, 639850, 961336, 463208, 485922, 426528, 763912, 755323, 348772, 754435, 94301, 265510, 894370, 934935, 993607, 440845, 391643, 983866, 102996, 742713, 395725, 395808, 184991, 310056, 31240}

    {402073, 936446, 800140, 486579, 200246, 94134, 290724, 986755, 707911, 975552, 666705, 930247, 414639, 534999, 364762, 39647, 929736, 68438, 318812, 630653, 749013, 326306, 54559, 639850, 961336, 463208, 485922, 426528, 763912, 755323, 348772, 754435, 94301, 265510, 894370, 934935, 993607, 440845, 391643, 983866, 102996, 742713, 395725, 395808, 184991, 310056, 31240}

    Returns: 0

  30. {10, 10}

    {10, 10}

    Returns: 0

  31. {3, 2, 1, 10}

    {1, 3, 10, 2}

    Returns: 20

  32. {2, 3, 5, 10, 8, 8, 8, 10, 5, 7, 8}

    {5, 3, 8, 10, 2, 8, 5, 10, 7, 8, 8}

    Returns: 18

  33. {7, 2, 2, 10, 1, 6, 6, 10, 3, 1, 5, 6, 3}

    {3, 5, 1, 2, 1, 7, 2, 6, 3, 6, 10, 10, 6}

    Returns: 42

  34. {5, 4, 8, 9, 6, 3, 9, 6, 2, 3, 3, 10, 4, 9, 10, 9, 6, 9, 4, 4, 1, 6, 7, 3, 8, 10, 3, 4, 7, 1, 8, 6, 9, 9, 2, 5, 2, 3, 9, 10, 4, 5, 10, 7, 2, 5, 9, 6}

    {5, 4, 8, 9, 6, 3, 9, 6, 2, 3, 3, 10, 4, 9, 4, 9, 9, 9, 10, 4, 1, 6, 7, 8, 3, 10, 3, 4, 7, 1, 8, 6, 9, 9, 5, 5, 2, 3, 6, 10, 4, 2, 10, 2, 7, 5, 9, 6}

    Returns: 44

  35. {10, 1, 10, 4, 5, 8, 6, 2, 3, 10, 3, 5, 6, 5, 2, 5, 4, 1, 5, 10, 4, 4, 8, 8, 2, 7, 1, 10, 3, 2, 7, 5, 4, 7, 4, 2, 4, 4, 9, 2, 9, 7, 5, 6, 6, 2, 2, 6, 8}

    {10, 1, 10, 2, 5, 4, 6, 7, 3, 10, 3, 5, 6, 5, 4, 5, 4, 1, 5, 10, 4, 5, 8, 8, 2, 7, 1, 10, 3, 2, 6, 5, 4, 7, 8, 2, 8, 4, 9, 2, 9, 2, 4, 6, 7, 2, 2, 6, 4}

    Returns: 34

  36. {5, 7, 5, 10, 1, 2, 5, 8, 9, 4, 9, 9, 8, 5, 6, 7, 9, 4, 10, 6, 10, 4, 10, 3, 4, 4, 1, 1, 10, 9, 10, 5, 10, 5, 4, 6, 10, 10, 9, 6, 9, 3, 6, 6, 3, 3, 8, 2, 1}

    {5, 7, 5, 10, 1, 2, 6, 8, 9, 4, 9, 9, 8, 10, 6, 7, 9, 4, 9, 6, 10, 4, 10, 3, 4, 4, 1, 1, 10, 3, 10, 9, 10, 5, 4, 6, 10, 10, 9, 5, 5, 3, 6, 6, 5, 3, 8, 2, 1}

    Returns: 24

  37. {2, 5, 10, 7, 6, 8, 5, 3, 4, 3, 6, 4, 5, 1, 4, 10, 8, 1, 6, 1, 5, 5, 9, 7, 9, 4, 8, 8, 1, 2, 3, 7, 8, 3, 4, 1, 7, 8, 9, 9, 2, 9, 1, 9, 8, 9, 8, 10, 3, 3}

    {2, 5, 10, 7, 6, 8, 5, 3, 4, 3, 6, 4, 5, 1, 4, 10, 2, 10, 6, 1, 5, 5, 9, 7, 9, 4, 8, 8, 1, 8, 3, 8, 7, 3, 4, 9, 7, 8, 9, 9, 2, 9, 1, 1, 8, 9, 8, 1, 3, 3}

    Returns: 48

  38. {68, 15, 29, 98}

    {68, 98, 29, 15}

    Returns: 166

  39. {96, 22, 11}

    {96, 22, 11}

    Returns: 0

  40. {12, 58, 36, 13, 39, 26, 76, 97, 97, 64, 80}

    {64, 58, 76, 12, 80, 26, 36, 39, 13, 97, 97}

    Returns: 366

  41. {48, 82, 32, 52, 65, 23, 23, 23, 78, 7}

    {78, 23, 32, 82, 23, 7, 65, 52, 48, 23}

    Returns: 294

  42. {38, 59, 23, 23, 71, 39, 59, 38, 38, 79, 95, 7, 40, 5, 85, 9, 79, 77, 52, 73, 65, 55, 19, 49, 50, 85, 70, 29, 68, 72, 53, 89, 57, 70, 24, 33, 52, 42, 43, 16, 49, 56, 18, 12, 95, 56, 32, 31}

    {38, 55, 23, 23, 71, 39, 59, 38, 38, 79, 95, 7, 24, 5, 85, 9, 40, 77, 52, 56, 65, 59, 19, 49, 50, 79, 70, 29, 68, 72, 53, 89, 57, 70, 85, 33, 52, 42, 43, 16, 49, 56, 18, 12, 95, 73, 32, 31}

    Returns: 164

  43. {87, 7, 32, 23, 79, 46, 45, 11, 88, 64, 34, 36, 99, 77, 48, 27, 7, 34, 63, 30, 86, 14, 68, 40, 24, 51, 36, 95, 76, 92, 26, 68, 36, 98, 21, 21, 41, 20, 36, 62, 13, 37, 89, 34, 20, 51, 87}

    {87, 7, 45, 23, 79, 63, 32, 11, 88, 98, 34, 48, 99, 77, 36, 27, 7, 34, 92, 30, 86, 14, 68, 40, 24, 51, 36, 95, 76, 46, 26, 68, 36, 64, 21, 34, 41, 20, 36, 62, 13, 37, 89, 21, 20, 51, 87}

    Returns: 236

  44. {27, 14, 26, 64, 50, 39, 92, 33, 2, 43, 47, 54, 13, 12, 43, 34, 69, 30, 75, 93, 89, 18, 32, 87, 64, 71, 90, 81, 26, 99, 5, 95, 22, 4, 73, 41, 30, 88, 47, 30, 32, 63, 48, 26, 55, 24, 60, 77}

    {34, 26, 43, 64, 95, 39, 92, 33, 2, 43, 47, 54, 60, 12, 81, 27, 69, 30, 75, 93, 89, 18, 32, 87, 64, 13, 99, 14, 26, 90, 5, 50, 30, 4, 73, 41, 30, 88, 47, 22, 32, 63, 48, 26, 55, 24, 71, 77}

    Returns: 388

  45. {67, 2, 71, 38, 62, 41, 40, 79, 90, 86, 67, 91, 89, 96, 81, 65, 49, 80, 29, 87, 7, 28, 28, 98, 63, 76, 57, 64, 52, 70, 52, 18, 54, 46, 2, 90, 68, 44, 70, 96, 14, 98, 79, 47, 66, 50, 34, 20, 7, 28}

    {67, 2, 71, 38, 62, 41, 40, 79, 90, 86, 67, 98, 89, 96, 49, 65, 66, 80, 29, 87, 7, 28, 28, 96, 63, 76, 57, 64, 52, 70, 52, 18, 54, 46, 2, 90, 81, 44, 70, 91, 14, 98, 79, 47, 68, 50, 34, 20, 7, 28}

    Returns: 78

  46. {580634, 851778, 908210, 971347, 139774, 247291}

    {908210, 247291, 971347, 580634, 139774, 851778}

    Returns: 1990400

  47. {65913, 653895, 767530, 558194, 161450, 985368}

    {65913, 653895, 161450, 767530, 558194, 985368}

    Returns: 1212160

  48. {559408, 280619, 487518, 550020, 643105, 489667, 922464, 157872, 381150, 141500, 703658, 900004}

    {922464, 559408, 141500, 157872, 643105, 489667, 280619, 550020, 703658, 487518, 381150, 900004}

    Returns: 3405038

  49. {734616, 385582, 60868, 584836, 779724, 190589, 921569, 576640, 249947, 504914, 812399, 502740, 447650, 59806, 736576}

    {734616, 385582, 576640, 584836, 779724, 504914, 59806, 60868, 249947, 190589, 812399, 921569, 502740, 447650, 736576}

    Returns: 3383720

  50. {180155, 921126, 207736, 843456, 348679, 1964, 620763, 548757, 771651, 209709, 575068, 890535, 469581, 171528, 305766, 547064, 673246, 455602, 686482, 495294, 581315, 457236, 905075, 719917, 22505, 174907, 610792, 449019, 418246, 998633, 33841, 584622, 51816, 63529, 635330, 723357, 106795, 217630, 505520, 197437, 837534, 578300, 936220, 33612, 827823, 559562, 940586, 807055}

    {180155, 457236, 207736, 843456, 348679, 1964, 455602, 905075, 771651, 209709, 575068, 890535, 469581, 171528, 305766, 547064, 33841, 620763, 686482, 495294, 581315, 921126, 548757, 719917, 22505, 174907, 610792, 449019, 418246, 998633, 673246, 584622, 51816, 63529, 635330, 723357, 106795, 217630, 505520, 197437, 837534, 578300, 807055, 33612, 827823, 559562, 940586, 936220}

    Returns: 3507878

  51. {9489, 291981, 599204, 482469, 918754, 964526, 467673, 194652, 129259, 981652, 271290, 386575, 488475, 56524, 515902, 725889, 34364, 446547, 672693, 85889, 722420, 939765, 797178, 733093, 220248, 388711, 205699, 241662, 759216, 613787, 150164, 215939, 519536, 539016, 780880, 111848, 304720, 807908, 635353, 668742, 774975, 718684, 566641, 796666, 902647, 104269, 831858, 881766, 513812, 203600}

    {9489, 291981, 599204, 482469, 918754, 964526, 467673, 194652, 129259, 939765, 271290, 386575, 488475, 56524, 515902, 725889, 881766, 733093, 672693, 85889, 722420, 34364, 797178, 446547, 220248, 388711, 205699, 241662, 759216, 613787, 150164, 215939, 513812, 539016, 780880, 111848, 304720, 807908, 635353, 668742, 774975, 718684, 566641, 796666, 902647, 104269, 831858, 981652, 519536, 203600}

    Returns: 2479116

  52. {942585, 133255, 948455, 150346, 449052, 426490, 598523, 848585, 333042, 711142, 188543, 634296, 856242, 814930, 393317, 19868, 956491, 109690, 445104, 781409, 174904, 715643, 963856, 899655, 68169, 105691, 136153, 108273, 831256, 80158, 842171, 901978, 228547, 30050, 189697, 861505, 405500, 101194, 67169, 853914, 585543, 504918, 784823, 926148, 18300, 128663, 181238, 349976, 702418}

    {942585, 861505, 948455, 68169, 19868, 426490, 598523, 848585, 393317, 711142, 136153, 634296, 856242, 814930, 109690, 449052, 956491, 18300, 445104, 781409, 174904, 715643, 963856, 899655, 150346, 105691, 188543, 228547, 831256, 80158, 842171, 901978, 585543, 30050, 189697, 133255, 405500, 101194, 67169, 853914, 108273, 504918, 784823, 333042, 926148, 128663, 181238, 349976, 702418}

    Returns: 5474788

  53. {816075, 977481, 371360, 254589, 374017, 279327, 959540, 997795, 197463, 46371, 320430, 946061, 46707, 185872, 952440, 62028, 548884, 326398, 322709, 458162, 752237, 968911, 356769, 923534, 962842, 49392, 385436, 780284, 822602, 680935, 630515, 263872, 668164, 992489, 191952, 545541, 819630, 831220, 658129, 171475, 199769, 649287, 25285, 558380, 787570, 828751, 488286}

    {630515, 977481, 371360, 649287, 968911, 548884, 959540, 997795, 197463, 46371, 320430, 946061, 46707, 185872, 952440, 62028, 385436, 326398, 322709, 458162, 752237, 171475, 356769, 923534, 962842, 49392, 279327, 780284, 822602, 680935, 816075, 263872, 668164, 992489, 191952, 545541, 819630, 831220, 658129, 374017, 199769, 254589, 25285, 558380, 787570, 828751, 488286}

    Returns: 3294502

  54. {4, 5, 6, 2}

    {10, 3, 10, 8}

    Returns: 18

  55. {10, 6, 4, 5, 5}

    {8, 4, 8, 3, 10}

    Returns: 15

  56. {7, 4, 1, 6, 1, 4, 2, 2, 5, 4, 8, 8, 3}

    {10, 2, 1, 10, 6, 5, 10, 1, 5, 6, 6, 6, 3}

    Returns: 30

  57. {5, 2, 8, 9, 9, 8, 6, 10, 7, 3}

    {5, 2, 8, 7, 10, 5, 4, 4, 1, 3}

    Returns: 20

  58. {5, 7, 8, 4, 4, 1, 5, 10, 10, 4, 9, 1, 6, 5, 3, 7, 2, 2, 4, 9, 3, 10, 3, 10, 2, 7, 6, 5, 1, 9, 9, 5, 3, 9, 1, 9, 10, 5, 10, 5, 7, 10, 10, 6, 6, 4, 5}

    {4, 6, 7, 6, 4, 3, 6, 9, 1, 8, 3, 9, 6, 7, 2, 2, 2, 9, 7, 9, 3, 3, 3, 8, 2, 4, 6, 7, 4, 8, 2, 9, 8, 4, 1, 1, 6, 9, 4, 7, 1, 3, 9, 7, 6, 4, 2}

    Returns: 135

  59. {4, 7, 5, 10, 8, 7, 7, 8, 1, 3, 3, 4, 6, 10, 9, 6, 3, 1, 1, 3, 3, 3, 1, 1, 6, 4, 1, 9, 3, 1, 6, 5, 5, 7, 3, 8, 8, 3, 3, 9, 7, 1, 3, 3, 8, 3, 7, 6}

    {1, 1, 10, 8, 4, 5, 3, 5, 9, 5, 10, 7, 3, 6, 2, 10, 6, 9, 4, 4, 10, 8, 8, 3, 4, 5, 1, 2, 7, 1, 6, 10, 1, 8, 1, 2, 5, 6, 4, 6, 1, 6, 4, 4, 4, 3, 6, 4}

    Returns: 165

  60. {1, 2, 3, 10, 9, 10, 7, 6, 6, 8, 8, 8, 8, 10, 3, 1, 7, 10, 9, 9, 8, 6, 6, 7, 3, 9, 9, 9, 4, 8, 7, 1, 6, 5, 10, 4, 8, 4, 4, 2, 8, 7, 10, 4, 8, 1, 6, 4, 4, 6}

    {10, 9, 4, 1, 7, 1, 9, 10, 6, 9, 9, 6, 6, 9, 8, 10, 1, 10, 10, 3, 2, 4, 2, 5, 10, 5, 7, 10, 1, 2, 9, 9, 6, 7, 5, 6, 5, 3, 8, 9, 3, 10, 10, 9, 3, 5, 5, 1, 10, 7}

    Returns: 181

  61. {9, 10, 7, 10, 10, 8, 9, 10, 1, 5, 5, 8, 5, 9, 7, 3, 4, 7, 7, 8, 1, 5, 8, 2, 9, 5, 6, 9, 9, 4, 2, 10, 2, 1, 3, 5, 6, 7, 2, 4, 10, 10, 5, 4, 6, 2, 9, 4, 8}

    {3, 2, 8, 1, 4, 2, 6, 1, 8, 2, 9, 2, 8, 4, 3, 2, 3, 2, 4, 4, 3, 10, 4, 7, 9, 8, 7, 1, 9, 3, 4, 9, 10, 1, 6, 2, 5, 9, 8, 8, 7, 4, 8, 4, 5, 10, 9, 3, 7}

    Returns: 176

  62. {74, 80, 23, 93}

    {75, 21, 40, 4}

    Returns: 166

  63. {98, 69}

    {70, 83}

    Returns: 42

  64. {25, 26, 76, 11, 83, 56, 72, 29, 71, 1, 66, 20, 32, 91, 60}

    {56, 12, 66, 98, 99, 100, 68, 7, 80, 78, 22, 85, 94, 50, 37}

    Returns: 549

  65. {39, 52, 64, 12, 39, 37, 40, 64, 77, 73, 16, 96}

    {41, 67, 43, 44, 58, 26, 6, 79, 1, 4, 94, 64}

    Returns: 404

  66. {85, 71, 37, 55, 43, 82, 17, 83, 9, 88, 14, 48, 28, 36, 63, 94, 37, 77, 48, 93, 41, 27, 25, 28, 24, 21, 27, 62, 48, 77, 39, 21, 52, 86, 41, 76, 50, 15, 16, 54, 93, 1, 4, 26, 50, 22, 87, 91, 87, 87}

    {85, 62, 16, 5, 31, 85, 3, 27, 10, 55, 53, 89, 26, 29, 75, 18, 61, 72, 58, 100, 10, 21, 40, 11, 85, 56, 88, 75, 52, 37, 67, 23, 19, 88, 28, 46, 67, 48, 33, 10, 18, 70, 86, 11, 32, 78, 40, 47, 59, 93}

    Returns: 1364

  67. {83, 65, 57, 78, 56, 13, 21, 91, 96, 71, 6, 19, 61, 77, 40, 79, 88, 53, 60, 65, 53, 85, 67, 65, 54, 65, 30, 65, 35, 23, 55, 78, 15, 16, 93, 99, 97, 41, 49, 25, 29, 52, 89, 6, 20, 9, 99, 78}

    {24, 48, 46, 84, 56, 37, 92, 78, 8, 58, 56, 92, 3, 92, 93, 99, 71, 5, 3, 90, 7, 78, 16, 6, 14, 70, 15, 69, 32, 2, 70, 19, 39, 65, 62, 1, 11, 65, 77, 70, 80, 74, 34, 100, 61, 24, 28, 28}

    Returns: 1827

  68. {90, 99, 11, 86, 77, 75, 64, 15, 3, 60, 88, 57, 4, 6, 64, 59, 27, 96, 99, 16, 75, 52, 42, 55, 47, 95, 100, 21, 38, 54, 99, 86, 62, 73, 32, 38, 59, 43, 50, 68, 40, 56, 79, 97, 43, 57, 1, 20, 94}

    {32, 79, 46, 29, 16, 40, 11, 97, 89, 62, 42, 13, 42, 1, 51, 26, 99, 68, 35, 70, 32, 18, 95, 82, 5, 8, 40, 17, 78, 64, 67, 39, 13, 64, 56, 25, 94, 54, 15, 47, 81, 51, 60, 24, 36, 100, 37, 5, 76}

    Returns: 1819

  69. {32, 5, 38, 44, 4, 63, 73, 50, 89, 86, 36, 83, 54, 78, 23, 86, 15, 76, 1, 50, 84, 69, 98, 72, 48, 94, 12, 72, 85, 89, 26, 73, 57, 66, 70, 99, 68, 91, 95, 86, 20, 32, 78, 46, 70, 62, 82, 100, 52}

    {48, 55, 37, 51, 22, 24, 27, 64, 46, 70, 80, 33, 54, 98, 46, 49, 34, 22, 51, 7, 77, 98, 6, 50, 69, 57, 42, 5, 36, 92, 86, 100, 50, 50, 29, 50, 29, 48, 4, 16, 38, 16, 69, 79, 91, 15, 92, 53, 81}

    Returns: 1620

  70. {270029, 387270, 400388, 381474, 54657}

    {983454, 360178, 847912, 811328, 975654}

    Returns: 2538892

  71. {176715, 684068, 525482, 170722, 438374}

    {742416, 738659, 808539, 28755, 264643}

    Returns: 1219047

  72. {362905, 723554, 61525, 749544, 591773, 763049, 509390, 246744, 887942, 645949, 106314, 902732}

    {327093, 703042, 587695, 792792, 75159, 448701, 510092, 577573, 553290, 966872, 398398, 370426}

    Returns: 3268200

  73. {863356, 203105, 666306, 602420, 483371, 216810, 398368, 503968, 358028, 944434, 259680, 407713, 292973, 573707}

    {751473, 415938, 398201, 104157, 387159, 2337, 739610, 7854, 245516, 288083, 46033, 847019, 120369, 469946}

    Returns: 3937306

  74. {486887, 764487, 250696, 450652, 838876, 934659, 893283, 874352, 873851, 594816, 7991, 294813, 465776, 409278, 341146, 926524, 164610, 983659, 998631, 380489, 337738, 883195, 390470, 866749, 791505, 982169, 368359, 245702, 349245, 936148, 763927, 746146, 271106, 428148, 33574, 848707, 761723, 200769, 300131, 773646, 819590, 865308, 577778, 63026, 624356, 995917, 956306, 180495, 413925}

    {84879, 283740, 496263, 115251, 57883, 54373, 157592, 300473, 614007, 840681, 179607, 493669, 547172, 716490, 899679, 404143, 537103, 690243, 718366, 88637, 261871, 936580, 519760, 758822, 330148, 449693, 556988, 596130, 234248, 237144, 308405, 316085, 979729, 124045, 159318, 508926, 709126, 73690, 206320, 540970, 943829, 967541, 957263, 418796, 506090, 554700, 443869, 705222, 221510}

    Returns: 16352447

  75. {264573, 944943, 47490, 401402, 638028, 396778, 295763, 839499, 676250, 540751, 554880, 713404, 690978, 819788, 742531, 906106, 902699, 178790, 15339, 433512, 848733, 328297, 75675, 188706, 786906, 265549, 437273, 895605, 179967, 160291, 735827, 134765, 463689, 198874, 220368, 811867, 828924, 937065, 979505, 587141, 403781, 453164, 883715, 282462, 130569, 926208, 296343, 309156, 682218}

    {486087, 523611, 64150, 29017, 864128, 212809, 4269, 457387, 19373, 108862, 563554, 438524, 786746, 687370, 178188, 464740, 303752, 480508, 934768, 766814, 333642, 434146, 840674, 480154, 465611, 796184, 118576, 637516, 513730, 920221, 577609, 230596, 273882, 62188, 790539, 2200, 603973, 977082, 419625, 60150, 678270, 701359, 536973, 832812, 29931, 699044, 526341, 101025, 797699}

    Returns: 16688380

  76. {632516, 38141, 598024, 486409, 257963, 334828, 489571, 382602, 770970, 469420, 390397, 71957, 697016, 789042, 935864, 922509, 436069, 465537, 567712, 282747, 129331, 735645, 343483, 12031, 515124, 597950, 544405, 556990, 715407, 331598, 575512, 490750, 116607, 700133, 868318, 196908, 462881, 880980, 869659, 996504, 72133, 987687, 259349, 209763, 602743, 666171, 294676, 184922}

    {804493, 519898, 724030, 464215, 226295, 888806, 925221, 947002, 476865, 329485, 285819, 640164, 759535, 540190, 185261, 973047, 855391, 730371, 470112, 386240, 239035, 57963, 540894, 9322, 309489, 192277, 505744, 880518, 194421, 513000, 304828, 535325, 161479, 678469, 764678, 570705, 685805, 670927, 723820, 468556, 980413, 722321, 744796, 386014, 521148, 658207, 800735, 208380}

    Returns: 12576023

  77. {724153, 686999, 253462, 435049, 545990, 110829, 743763, 253788, 331949, 689217, 9059, 50967, 965920, 549628, 951762, 925144, 529701, 339959, 105471, 49553, 926929, 627683, 49770, 474471, 353117, 553918, 522195, 764680, 998817, 386598, 137191, 878053, 127324, 250444, 142604, 53401, 78443, 246208, 265047, 983599, 648300, 136742, 138392, 251954, 119794, 383450, 339967}

    {415355, 431682, 630865, 423732, 422189, 211931, 254994, 420632, 433223, 274976, 731983, 808836, 594465, 146754, 432121, 668690, 183577, 719776, 744482, 510574, 243224, 835757, 979000, 182431, 461420, 737659, 808594, 25647, 828852, 145096, 745991, 681284, 715910, 22113, 37374, 686980, 661224, 54381, 940085, 197762, 328613, 913298, 675087, 724117, 843036, 774447, 185843}

    Returns: 19018290

  78. {2, 4, 6, 7}

    {7, 6, 3, 2}

    Returns: 15

  79. {2, 4, 7, 9}

    {9, 5, 5, 2}

    Returns: 17

  80. {1, 1, 3, 3, 5, 5, 5, 5, 5, 6, 7, 7, 10, 10}

    {8, 9, 7, 8, 5, 6, 6, 6, 6, 3, 2, 3, 2, 2}

    Returns: 56

  81. {1, 2, 2, 3, 3, 6, 8, 8, 9, 9, 10, 10, 10}

    {10, 9, 10, 8, 9, 7, 6, 7, 4, 4, 1, 3, 4}

    Returns: 71

  82. {1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10}

    {9, 10, 10, 10, 10, 7, 7, 8, 8, 8, 8, 9, 9, 9, 6, 6, 6, 6, 5, 5, 6, 6, 5, 5, 5, 5, 4, 4, 4, 3, 3, 4, 4, 4, 1, 2, 2, 2, 2, 3, 3, 1, 1, 1, 1, 1, 1}

    Returns: 248

  83. {1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10}

    {10, 10, 10, 8, 9, 9, 9, 9, 10, 8, 8, 8, 8, 7, 7, 7, 8, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 5, 5, 5, 6, 4, 4, 4, 5, 5, 3, 4, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1}

    Returns: 219

  84. {1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10}

    {10, 10, 10, 10, 9, 9, 9, 10, 8, 9, 9, 9, 8, 7, 8, 8, 8, 8, 8, 6, 7, 7, 6, 6, 6, 6, 4, 4, 5, 5, 5, 5, 5, 6, 6, 2, 2, 2, 3, 3, 3, 3, 4, 4, 1, 1, 1, 1, 1}

    Returns: 242

  85. {1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 10}

    {9, 9, 10, 10, 10, 10, 10, 8, 8, 8, 9, 9, 6, 6, 6, 7, 7, 7, 8, 8, 8, 5, 5, 6, 6, 3, 4, 4, 4, 5, 5, 5, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1}

    Returns: 240

  86. {24, 64, 66, 71, 72, 99}

    {83, 60, 35, 32, 9, 2}

    Returns: 293

  87. {44, 47}

    {88, 37}

    Returns: 54

  88. {2, 4, 5, 11, 14, 22, 32, 54, 56, 60, 63, 64, 68, 80, 92}

    {100, 93, 92, 83, 72, 68, 38, 36, 36, 33, 33, 16, 14, 8, 8}

    Returns: 809

  89. {7, 11, 21, 23, 24, 46, 50, 60, 66, 66, 72, 88, 98}

    {88, 82, 73, 71, 63, 49, 47, 41, 33, 39, 15, 11, 7}

    Returns: 601

  90. {1, 4, 4, 5, 5, 8, 10, 12, 13, 16, 22, 24, 28, 28, 35, 36, 37, 38, 38, 41, 46, 50, 52, 53, 53, 54, 54, 55, 55, 56, 57, 58, 63, 63, 64, 66, 67, 69, 75, 79, 81, 82, 82, 84, 87, 87, 96, 96}

    {99, 96, 98, 90, 94, 90, 86, 71, 71, 70, 70, 68, 67, 68, 65, 62, 61, 54, 61, 52, 44, 36, 33, 30, 31, 28, 29, 26, 26, 26, 25, 24, 22, 24, 22, 22, 21, 21, 21, 19, 17, 17, 17, 15, 7, 14, 3, 6}

    Returns: 2346

  91. {4, 4, 6, 7, 9, 10, 12, 13, 16, 18, 21, 23, 25, 27, 27, 28, 34, 37, 37, 40, 41, 43, 43, 46, 48, 49, 55, 57, 58, 58, 59, 65, 66, 68, 70, 75, 77, 78, 79, 80, 81, 85, 86, 86, 90, 90, 91, 95, 96}

    {99, 100, 98, 96, 95, 93, 91, 90, 90, 85, 83, 82, 80, 79, 79, 78, 77, 75, 76, 73, 68, 67, 67, 66, 63, 61, 60, 55, 45, 53, 43, 39, 36, 31, 30, 25, 22, 21, 18, 16, 14, 13, 7, 12, 5, 6, 4, 3, 1}

    Returns: 2639

  92. {8, 10, 13, 16, 17, 20, 20, 21, 21, 25, 27, 28, 28, 29, 32, 35, 35, 37, 38, 47, 48, 49, 50, 52, 54, 54, 55, 56, 57, 59, 60, 67, 67, 72, 76, 77, 77, 77, 81, 82, 83, 86, 86, 86, 87, 87, 90, 94, 95, 100}

    {100, 99, 97, 95, 94, 90, 90, 85, 88, 84, 79, 75, 75, 74, 74, 70, 70, 67, 66, 66, 65, 64, 62, 61, 49, 60, 47, 44, 43, 43, 43, 36, 37, 34, 34, 29, 31, 32, 28, 28, 27, 16, 19, 22, 7, 15, 7, 6, 4, 2}

    Returns: 2418

  93. {3, 6, 8, 9, 10, 11, 11, 13, 19, 24, 24, 25, 26, 30, 34, 34, 36, 36, 42, 44, 46, 47, 48, 50, 50, 53, 54, 54, 55, 55, 56, 57, 61, 68, 70, 72, 73, 75, 76, 76, 81, 81, 82, 82, 84, 94, 96, 97, 98, 100}

    {99, 99, 89, 88, 88, 80, 85, 78, 72, 71, 71, 69, 66, 64, 60, 63, 57, 59, 55, 50, 50, 49, 48, 39, 47, 38, 34, 37, 31, 33, 29, 29, 28, 28, 28, 28, 27, 27, 21, 26, 13, 15, 11, 11, 11, 10, 9, 8, 7, 4}

    Returns: 2345

  94. {377624, 488795, 738551, 849824, 941184}

    {959496, 463626, 369522, 278649, 13721}

    Returns: 2474708

  95. {68214, 274406, 359090, 503657, 514747, 722213}

    {900577, 892405, 794250, 785369, 691777, 656336}

    Returns: 2410141

  96. {54658, 276342, 302577, 426758, 488711, 503971, 547449, 607052, 607634, 692568, 744304, 745940, 877339, 884521}

    {983151, 954937, 879786, 694306, 667598, 623070, 593382, 592863, 512934, 430872, 395440, 364277, 70174, 14248}

    Returns: 5574314

  97. {196142, 198001, 358260, 553240, 716712, 766458, 767527, 782106, 856357, 917173, 930486, 969964}

    {945329, 863698, 851982, 776396, 725270, 410845, 365187, 350872, 314097, 137250, 116355, 105300}

    Returns: 6330485

  98. {3157, 12525, 35690, 61419, 71776, 95705, 104195, 112750, 193406, 197827, 205839, 211893, 213734, 217437, 226120, 232439, 258325, 270403, 279331, 402960, 478791, 484379, 490465, 552880, 597554, 634899, 644113, 654453, 662561, 693521, 710124, 711927, 712412, 715635, 738584, 747836, 755813, 807183, 850870, 877239, 912101, 914440, 924775, 938477, 954704, 955134, 967963, 979996, 993434}

    {977247, 929052, 878922, 854540, 825173, 782854, 751340, 738525, 648020, 645276, 635092, 602900, 602847, 593250, 588972, 587566, 561942, 557416, 552313, 535384, 521057, 498369, 458928, 453081, 422784, 410385, 406958, 367144, 355125, 323030, 294964, 286625, 264562, 249102, 205943, 186820, 183847, 183323, 164150, 146086, 122226, 118292, 109900, 102481, 84678, 60502, 58052, 55370, 1349}

    Returns: 25521342

  99. {9484, 36621, 52772, 71955, 84321, 145137, 203576, 228956, 229605, 245160, 265655, 283304, 309316, 340680, 350175, 407301, 415568, 426676, 442055, 443603, 448625, 469260, 474037, 534237, 592465, 625901, 644479, 651653, 674881, 676156, 679704, 703345, 768933, 779298, 801760, 801874, 812165, 815829, 817063, 843160, 851066, 865655, 928606, 942715, 942882, 970152, 995147}

    {995166, 987790, 985046, 982537, 973658, 969073, 966484, 959543, 925038, 914451, 910152, 873822, 803159, 800578, 702446, 670335, 666856, 622611, 600870, 596460, 587009, 552192, 547070, 536150, 532063, 517989, 488056, 481464, 414243, 397024, 378891, 377090, 362961, 333150, 326810, 326517, 311164, 307793, 290752, 273977, 261948, 248067, 245395, 176361, 130080, 80906, 15203}

    Returns: 23117402

  100. {40174, 58557, 76948, 78557, 112823, 124323, 142254, 158830, 194325, 213831, 215296, 228723, 248122, 253907, 256407, 262902, 264720, 301468, 302480, 306724, 315194, 315320, 381881, 392777, 399601, 415373, 495403, 523816, 533240, 537258, 577633, 586574, 589995, 601176, 648936, 712524, 715078, 720209, 786684, 802906, 812510, 816342, 857707, 906599, 912424, 920479, 930636, 934209, 941502, 975485}

    {977253, 922997, 909155, 902351, 901090, 875329, 861023, 842910, 841103, 806611, 796409, 792637, 778758, 749629, 710514, 695073, 691341, 657391, 648813, 646984, 627701, 607761, 599176, 595600, 535215, 528342, 503685, 481099, 459760, 458936, 448514, 444634, 410999, 362458, 357392, 347395, 276472, 274360, 246271, 242970, 234435, 205797, 176172, 160394, 154344, 143463, 137632, 115392, 109786, 3219}

    Returns: 24539959

  101. {5603, 18725, 48318, 49352, 69596, 80173, 85277, 128524, 135411, 136949, 187976, 236662, 318755, 323062, 342298, 361129, 400709, 401982, 417065, 424760, 429409, 435310, 473932, 479635, 500985, 503483, 530883, 531283, 558551, 622509, 644799, 650760, 651718, 651925, 707644, 792979, 799367, 812739, 817686, 829689, 849547, 866135, 907079, 913058, 933638, 940245, 943333, 978215}

    {988775, 986451, 982041, 971355, 952339, 880350, 797255, 789174, 786743, 784798, 783868, 778477, 747896, 734921, 722336, 698738, 628832, 606936, 599380, 599148, 594863, 587836, 496958, 496269, 463549, 407514, 394079, 362516, 352039, 318030, 301706, 297348, 257288, 237749, 215760, 212833, 208156, 199359, 150184, 141830, 115208, 102587, 72770, 71996, 49881, 21408, 18811, 15107}

    Returns: 24955669

  102. {2, 2, 2, 2, 2}

    {2, 2, 2, 2, 2}

    Returns: 0

    Here we have five identical 2x2 squares. They can be rotated and reordered arbitrarily, but it will still be a collection of five identical squares. So even though there are 2^5 ways to rotate them and then 5! possible orders, each time you will end up with exactly the same tower: a rectangle of width 2 and height 10.Thus, Alice will build a tower of height 10, Bob will build a tower of height 10, and the difference is 10-10 = 0.

  103. {3 }

    {5 }

    Returns: 2

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