Statistics

Problem Statement for "PointErasing"

Problem Statement

You are given a int[] y of length N. The values in y describe N points in the plane: for each x = 0, 1, ..., N - 1 there is a point at coordinates (x, y[x]).

Krolik is going to perform the following operation repeatedly:
  1. Choose two of the remaining (i.e. not yet erased) points, say A and B, with different y-coordinates.
  2. Consider the rectangle with sides parallel to coordinate axes and points A and B in two opposite corners.
  3. Erase all points strictly inside the rectangle.
In each iteration, Krolik must choose A and B in such a way that at least one point is erased. If no more operations can be performed, Krolik will count the number of remaining points and write it into a notebook. Return a int[] containing all possible values of the number Krolik can write down, in ascending order.

Definition

Class:
PointErasing
Method:
getOutcomes
Parameters:
int[]
Returns:
int[]
Method signature:
int[] getOutcomes(int[] y)
(be sure your method is public)

Notes

  • A point is strictly inside a rectangle if it is inside the rectangle and does not lie on the border of the rectangle.

Constraints

  • y will contain between 1 and 50 elements, inclusive.
  • Each element of y will be between 0 and 1,000,000,000, inclusive.

Examples

  1. { 1, 2, 1, 1, 0, 4, 3 }

    Returns: {4, 6 }

    Krolik will end with 4 points if Krolik takes the following steps: Choose (1, 2) and (4, 0) to erase (2, 1) and (3, 1). Choose (0, 1) and (5, 4) to erase (1, 2). If Krolik first chooses (0, 1) and (5, 4) to erase (1, 2), 6 points remain and there are no valid moves left.  

  2. { 0, 0, 4, 4, 8, 8, 4, 4 }

    Returns: {6 }

  3. { 522 }

    Returns: {1 }

  4. { 19, 19, 19, 19, 19, 19 }

    Returns: {6 }

  5. { 0, 1, 2, 3, 4 }

    Returns: {2 }

  6. { 7, 8, 8, 7, 6, 7, 9, 3, 5, 0 }

    Returns: {3, 4, 5 }

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

    Returns: {4, 5, 6, 7, 9 }

  8. { 5, 5, 4, 4, 5, 8, 5, 5, 5, 5, 5, 9, 2, 0, 9, 4, 5, 5, 3, 4, 4, 4, 4, 7, 4 }

    Returns: {6, 7, 8, 10, 11, 12, 13, 15, 16, 17 }

  9. {1,3,1,4,0,3,1,3}

    Returns: {4, 5, 6 }

  10. {5, 5, 4, 4, 5, 8, 5, 5, 5, 5, 5, 9, 2, 0, 9, 4, 5, 5, 3, 4, 4, 4, 4, 7, 4, 5, 5, 4, 4, 5, 8, 5, 5, 5, 5, 5, 9, 2, 0, 9, 4, 5, 5, 3, 4, 4, 4, 4, 7, 4}

    Returns: {9, 10, 11, 13, 14, 15, 16, 18, 19, 20 }

    just two copies of #7 glued together

  11. { 0 }

    Returns: {1 }

  12. { 1000000000 }

    Returns: {1 }

  13. { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: {50 }

  14. { 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000 }

    Returns: {50 }

  15. { 714663, 714663 }

    Returns: {2 }

  16. { 1, 244218 }

    Returns: {2 }

  17. { 40613540, 16168720 }

    Returns: {2 }

  18. { 5965, 5965, 5965 }

    Returns: {3 }

  19. { 868037, 868037, 48227842 }

    Returns: {3 }

  20. { 227, 1452, 227 }

    Returns: {3 }

  21. { 43403, 179910169, 179910169 }

    Returns: {3 }

  22. { 59797769, 1, 1 }

    Returns: {3 }

  23. { 5991928, 52, 5991928 }

    Returns: {3 }

  24. { 141127197, 141127197, 318 }

    Returns: {3 }

  25. { 14649, 921833, 30562662 }

    Returns: {2 }

  26. { 3, 400364, 251 }

    Returns: {3 }

  27. { 428093, 1061, 723662 }

    Returns: {3 }

  28. { 254, 675461, 12 }

    Returns: {3 }

  29. { 326462, 39, 75 }

    Returns: {3 }

  30. { 42137453, 16365, 166 }

    Returns: {2 }

  31. { 915177142, 0, 42, 3, 91490203, 36, 669, 190, 2235271, 4, 5, 2235271, 20, 2235271, 222, 187, 437075, 2235271, 2235271, 2235271, 2235271, 2235271, 73193, 42, 2235271, 35216, 42, 2235271, 53, 2235271, 2235271, 16078734, 669, 241, 53, 2235271, 2235271, 1491990, 2235271, 2235271, 2235271, 2235271, 96, 2235271, 300256808, 2235271, 248957910, 10051, 2235271, 1844 }

    Returns: {3 }

  32. { 4443497, 10082, 10082, 2, 10082, 5864, 10082, 1166468, 13129326, 10082, 2137, 10082, 10082, 10082, 10082, 10082, 3537418, 10082, 10082, 344058861, 10082, 10082, 5864, 499, 991488525, 0, 4443497, 17202, 4443497, 4443497, 1166468, 4443497, 4443497, 11, 4443497, 4443497, 115042432, 4443497, 31153810, 539, 1, 4443497, 4443497, 165, 4443497, 5864, 4443497, 4443497, 4443497, 10082 }

    Returns: {4 }

  33. { 2760, 9, 3625974, 20491, 3625974, 3625974, 3625974, 3625974, 3625974, 3625974, 4463246, 3625974, 5526, 3625974, 685570201, 3625974, 3625974, 3625974, 3625974, 3625974, 598208, 3625974, 3625974, 3625974, 627289, 3625974, 3625974, 2501, 26, 17790, 3625974, 3625974, 3625974, 3625974, 78, 3625974, 344609, 3625974, 775172, 6923365, 3625974, 3625974, 3625974, 473522996, 3625974, 104650, 9, 7, 987376920, 0 }

    Returns: {3 }

  34. { 1294, 7574788, 7574788, 7574788, 7574788, 1146, 7574788, 70511226, 5721, 296, 845980809, 0, 845980809, 7574788, 66355904, 0, 376373, 845980809, 8, 0, 1294, 488223832, 7574788, 0, 845980809, 33165, 37, 18294079, 1294, 37, 33165, 296, 1294, 37, 1294, 18294079, 1294, 1294, 70511226, 1695, 1294, 1294, 1294, 482800038, 7574788 }

    Returns: {10 }

  35. { 2667, 5149981, 1213883, 3022052, 356, 166030, 3022052, 3022052, 3022052, 3022052, 21, 3022052, 3022052, 3022052, 3022052, 186, 3022052, 3022052, 285922179, 3022052, 805467778, 0, 2667, 3022052, 805467778, 805467778, 805467778, 805467778, 2667, 2667, 2781883, 8531928, 37938198, 0, 0, 148119, 2667, 2667, 389, 2667, 37938198, 2667, 2667, 2667, 3022052 }

    Returns: {10 }

  36. { 0, 0, 883049, 2330406, 1260434, 0, 333862280, 0, 2330406, 624, 0, 0, 0, 961417543, 2845, 0, 504964650, 3, 134444, 0, 961417543, 961417543, 961417543, 4344040, 624, 4969578, 624, 0, 624, 961417543, 149, 961417543, 0, 0, 961417543, 961417543, 961417543, 624, 961417543, 961417543, 0, 961417543, 9, 186, 961417543, 0, 624, 0, 961417543, 961417543 }

    Returns: {30 }

  37. { 863379710, 0, 3653, 5554639, 5554639, 5554639, 6452201, 6654726, 3653, 3653, 5554639, 5554639, 5554639, 5554639, 5554639, 3653, 3653, 5544376, 3653, 5554639, 5554639, 5554639, 5554639, 5554639, 351, 3653, 4913868, 5554639, 5554639, 148187711, 42256103, 109416455, 3653, 5554639, 5554639, 3653, 5554639, 3653, 5554639, 5554639, 3653, 5554639, 494452, 5554639, 5554639, 3653, 3653, 65939043, 23, 5554639 }

    Returns: {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26 }

  38. { 3424334, 3424334, 3424334, 3780, 7072591, 3780, 3424334, 3646374, 13745, 3424334, 3424334, 3780, 3780, 3780, 3780, 3424334, 3424334, 3424334, 3780, 3424334, 3424334, 3424334, 3780, 3780, 0, 985902359, 3780, 207, 3780, 3424334, 3424334, 3424334, 3780, 6, 3424334, 3780, 3424334, 12, 3424334, 3424334, 94537, 3780, 3780, 3780, 3424334, 3424334, 9206, 218029, 2001, 3780 }

    Returns: {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 }

  39. { 681, 17361200, 681, 2, 681, 15, 681, 2, 17361200, 270, 34, 681, 17361200, 681, 681, 17361200, 11, 126026, 17361200, 89, 681, 52, 18, 23, 17361200, 1131084, 17361200, 681, 15554832, 716543369, 681, 17361200, 17361200, 124, 30, 121, 681, 256757, 681, 17361200, 2, 681, 681, 681, 17361200, 20920, 21, 681, 753449372, 0 }

    Returns: {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 }

  40. { 1563121, 1563121, 1824, 1563121, 1563121, 1563121, 1824, 1563121, 1563121, 1563121, 0, 18, 1112, 1824, 1824, 0, 1563121, 0, 1384, 1563121, 866993821, 866993821, 297, 866993821, 0, 1563121, 1563121, 342017, 1563121, 1563121, 1824, 560573275, 1563121, 585521622, 1824, 1824, 1824, 1563121, 1563121, 40182101, 1563121, 4, 2532, 1563121, 1824 }

    Returns: {10, 11, 13, 14, 16, 17, 19, 20 }

  41. { 998535, 998535, 1490, 1490, 998535, 1490, 998535, 1490, 1490, 1490, 1490, 7845645, 998535, 998535, 998535, 994, 1490, 998535, 998535, 998535, 0, 998535, 127207733, 0, 907028433, 1490, 48, 1490, 998535, 907028433, 123734, 1490, 0, 998535, 907028433, 35311759, 1490, 998535, 1490, 998535, 124, 19132, 1195, 1490, 1490 }

    Returns: {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

  42. { 950808464, 0, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 705, 705, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 9157, 5088982, 5088982, 705, 5088982, 5088982, 5088982, 5088982, 1133715, 53416, 5088982, 5088982, 5088982, 211, 705, 5088982, 5088982, 5088982, 5088982, 5088982, 5088982, 705, 5088982, 5088982 }

    Returns: {4, 10, 13, 17, 19, 26, 41 }

  43. { 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 2572262, 313240104, 101639520, 313240104, 1010, 2572262, 1130731, 2572262, 2572262, 0, 515661381, 26, 1010, 16558, 1010, 2572262, 1010, 7578, 1010, 1010, 1010, 1010, 1010, 1010, 1763557, 1010, 1010, 1010, 2572262, 1010, 1010, 1010, 1010, 1010, 1010 }

    Returns: {24, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39 }

  44. { 2988283, 2988283, 2988283, 2988283, 60710666, 1091, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 1091, 2988283, 8116597, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 2988283, 0, 582510503 }

    Returns: {6, 7, 18, 19, 33, 34, 45, 46 }

  45. { 3651, 3651, 3651, 3651, 2135457, 3651, 3651, 3651, 3651, 3651, 657961611, 3651, 188650, 657961611, 0, 17, 0, 31932746, 657961611, 3651, 3651, 126281, 0, 2135457, 657961611, 3651, 2135457, 2135457, 2135457, 2135457, 2135457, 3651, 2135457, 2135457, 2135457, 2135457, 2135457, 2135457, 2135457, 2135457, 2135457, 40, 2135457, 2135457, 2135457 }

    Returns: {14, 19, 23, 28, 33 }

  46. { 5991945, 5991945, 239844318, 47092, 5991945, 5991945, 5991945, 5991945, 5290, 15632, 5991945, 5991945, 5991945, 5991945, 5991945, 5991945, 5290, 5991945, 5991945, 5290, 0, 5290, 91, 0, 105, 17604, 0, 0, 1059, 981216148, 0, 0, 0, 5520, 981216148, 5290, 5290, 5290, 5290, 5290, 5290, 5290, 5290, 5290, 5290 }

    Returns: {21, 23, 25, 27, 29, 31, 33 }

  47. { 982545851, 0, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702, 5340702 }

    Returns: {50 }

  48. { 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 1997290, 0, 774620716, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299, 2299 }

    Returns: {50 }

  49. { 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 436, 888617302, 0 }

    Returns: {50 }

  50. { 2211324, 2211324, 2211324, 2211324, 2211324, 2211324, 2211324, 2211324, 2211324, 2211324, 0, 2211324, 919728917, 460, 0, 919728917, 0, 8161567, 0, 919728917, 0, 0, 394162902, 2211324, 919728917, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892, 892 }

    Returns: {40 }

  51. { 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 2362, 0, 744261754, 0, 744261754, 2362, 2362, 0, 744261754, 7985492, 744261754, 744261754, 744261754, 0, 2362, 744261754, 7985492, 7985492, 7985492, 7985492, 7985492, 7985492, 7985492, 7985492, 7985492, 7985492 }

    Returns: {41 }

  52. { 4567, 372, 298, 372, 3369192, 224873, 27557, 3674, 107239, 13055, 224873, 419, 40, 40, 426, 13055, 907156902, 28, 13206220, 2986940, 349089308, 207785, 4186688, 119, 0, 968520409, 7818812, 862414, 142, 70777037, 195, 3369192, 880, 11828846, 7, 298, 161, 294265924, 461, 20778, 146247292, 56726, 127587, 37, 10, 18282006, 304292, 119, 4186688, 4567 }

    Returns: {4 }

  53. { 52641, 4731, 126424, 2095, 7358, 5, 17, 33, 101003894, 1039372, 0, 937409232, 0, 123981211, 1085203, 0, 937409232, 0, 937409232, 52641, 937409232, 52641, 52641, 52641, 937409232, 60681767, 3, 3, 22849411, 28, 7, 35804663, 154502, 5, 10800860, 7358, 126424, 4996990, 181906, 130126198, 8, 154502, 101003894, 79, 52641 }

    Returns: {11 }

  54. { 73431, 2297261, 14156112, 7316911, 2295, 817614, 23825, 22573, 22573, 407612, 739842446, 28695125, 871, 56178811, 102521, 14156112, 9, 755708, 350933469, 358, 879835991, 6, 879835991, 0, 0, 0, 879835991, 879835991, 73431, 755708, 73431, 0, 0, 73431, 0, 7316911, 756131, 15066167, 42, 34294528, 358, 1077471, 5361, 4704754, 73431 }

    Returns: {12 }

  55. { 46433, 77083624, 46433, 169, 7463689, 546, 54711133, 2641353, 46433, 12947, 65, 876788105, 46433, 46433, 94, 46433, 15, 46433, 46433, 46433, 46433, 376834608, 7463689, 860548, 935530965, 0, 46433, 286846, 8576143, 600510, 46433, 3688470, 7823746, 2641353, 6599739, 46433, 6517192, 10231138, 46433, 46433, 46433, 1594129, 11899254, 77083624, 876788105, 186, 1343, 46433, 46433, 46433 }

    Returns: {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 }

  56. { 307801, 17422969, 774455072, 258938, 307801, 29550, 53567, 14, 88183235, 5, 957147507, 307801, 957147507, 307801, 307801, 307801, 307801, 0, 957147507, 11, 957147507, 4, 0, 307801, 0, 307801, 225027, 79447, 797767028, 18, 28694, 955783404, 79356541, 307801, 307801, 141276, 307801, 307801, 307801, 307801, 186667052, 307801, 868690305, 5407255, 307801 }

    Returns: {9, 10, 11, 12, 13, 14, 15, 16, 17, 18 }

  57. { 196703, 45352403, 24943423, 3250, 100, 147438577, 28234, 11, 196703, 196703, 196703, 61582219, 6224, 372, 319213638, 196703, 20, 196703, 19733, 147438577, 958997621, 958997621, 1, 958997621, 0, 0, 0, 0, 196703, 196703, 0, 196703, 196703, 0, 958997621, 1179, 196703, 196703, 196703, 61582219, 242061570, 1333385, 123, 196703, 196703 }

    Returns: {13, 14, 15, 16, 17, 18, 19, 20, 21 }

  58. { 80040, 80040, 173, 19076, 80040, 80040, 80040, 80040, 80040, 47812, 1929, 15043, 80040, 80040, 80040, 80040, 80040, 80040, 9837, 4, 29902, 1240, 80040, 80040, 991956857, 0, 80040, 247844, 80040, 80040, 80040, 125156, 80040, 44107, 296, 80040, 80040, 80040, 80040, 80040, 80040, 80040, 80040, 80040, 80040, 80040, 80040, 797, 80040, 80040 }

    Returns: {6, 7, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 }

  59. { 36239, 159483283, 36239, 71317, 143872298, 36239, 258310, 36239, 36239, 36239, 0, 0, 884392, 651, 889436585, 36239, 7266471, 0, 1036, 1036, 8980, 36239, 0, 889436585, 889436585, 36239, 185740304, 22052, 36239, 36239, 33753014, 262, 36239, 36239, 36239, 36239, 20, 36239, 36239, 36239, 36239, 36239, 36239, 36239, 36239 }

    Returns: {16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 }

  60. { 39220, 39220, 39220, 9, 39220, 39220, 39220, 39220, 39220, 39220, 39220, 39220, 39220, 39220, 39220, 39220, 1683, 39220, 39220, 39220, 826466742, 826466742, 826466742, 39220, 826466742, 25776, 1076, 253, 826466742, 0, 826466742, 826466742, 826466742, 826466742, 0, 39220, 39220, 1683, 51, 39220, 3109981, 39220, 39220, 39220, 39220 }

    Returns: {18, 19, 20, 21, 30, 31, 32, 33, 34, 35, 36 }

  61. { 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 0, 644563977, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976, 126976 }

    Returns: {50 }

  62. { 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 967628564, 185138, 0, 967628564, 0, 3510, 0, 595173, 13319, 967628564, 13319, 0, 13319, 248412427, 967628564, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319, 13319 }

    Returns: {38 }

  63. { 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 970030225, 47558, 608, 0, 970030225, 0, 71, 47558, 0, 16020372, 0, 275, 2705233, 271508, 0, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558, 47558 }

    Returns: {37 }

  64. { 83997, 184486104, 83997, 3784, 83997, 83997, 1, 1, 1, 1, 1, 1, 391809264, 391809264, 391809264, 391809264, 391809264, 3784, 3784, 3784, 3784, 83997, 3784, 3784, 3784, 3784, 3784, 3784, 3784, 3784, 7, 3784, 3784, 3784, 3784, 3784, 3784, 3784, 3784, 3784, 3784 }

    Returns: {22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37 }

  65. { 44216, 44216, 44216, 1049, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 44216, 0, 39361041, 39361041, 1049, 1049, 1049, 1049, 1049, 1049, 1049, 1049, 1049, 1049, 1049, 1049, 44216, 1049, 1049, 1049, 1049, 1049, 2, 1049, 1049, 1049, 1049 }

    Returns: {10, 15, 22, 27, 29, 34, 41, 46 }

  66. { 428093, 428093, 428093, 428093, 428093, 1061, 428093, 428093, 428093, 428093, 675461, 428093, 1061, 428093, 428093, 428093, 428093, 428093, 428093, 428093, 428093, 3, 3, 3, 723662, 1061, 1061, 428093, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 12, 1061 }

    Returns: {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 }

  67. { 27748, 27748, 27748, 27748, 25470, 27748, 27748, 27748, 27748, 1885155, 27748, 25470, 27748, 27748, 27748, 27748, 27748, 27748, 27748, 27748, 13, 13, 13, 35232310, 35232310, 35232310, 35232310, 25470, 25470, 27748, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 25470, 27748, 25470, 25470, 25470 }

    Returns: {14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45 }

  68. { 10685, 10685, 6815, 10685, 10685, 2659168, 10685, 10685, 10685, 10685, 10685, 10685, 10685, 10685, 6815, 10685, 1, 1, 1, 1, 384041977, 384041977, 384041977, 6815, 6815, 6815, 6815, 10685, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 6815, 4050, 6815 }

    Returns: {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 }

  69. { 22995, 22995, 6641, 22995, 22995, 6641, 22995, 22995, 22995, 22995, 22995, 22995, 22995, 22995, 45050, 22995, 121550348, 121550348, 121550348, 121550348, 149, 149, 149, 149, 149, 45050, 45050, 45050, 45050, 22995, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 45050, 22995, 45050, 45050, 45050 }

    Returns: {14, 15, 16, 17, 24, 25, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 44, 45 }

  70. { 496217, 496217, 510, 496217, 496217, 496217, 496217, 496217, 496217, 496217, 496217, 613117, 496217, 496217, 510, 496217, 496217, 496217, 496217, 0, 0, 57298872, 57298872, 57298872, 510, 496217, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 93, 510, 510, 510, 510, 510 }

    Returns: {12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43 }

  71. { 2432846, 2432846, 2432846, 11298160, 2432846, 2432846, 2432846, 2432846, 2432846, 2432846, 2432846, 2432846, 11298160, 2432846, 2432846, 11298160, 2432846, 2432846, 2432846, 2432846, 897057813, 897057813, 897057813, 897057813, 897057813, 11299, 11298160, 2432846, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 11298160, 355707062, 11298160, 11298160, 11298160, 11298160 }

    Returns: {13, 14, 21, 22, 23, 24, 27, 28, 29, 30, 37, 38, 39, 40, 43, 44 }

  72. { 2657, 2657, 2820, 2657, 2657, 2657, 2657, 2657, 2657, 2657, 2657, 2657, 2097, 2657, 22, 437666049, 437666049, 2097, 2097, 2097, 2657, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 2097, 73, 2097 }

    Returns: {6, 7, 9, 10, 15, 16, 18, 19, 33, 34, 36, 37, 42, 43, 45, 46 }

  73. { 5902801, 5902801, 1201162, 5902801, 5902801, 5902801, 5902801, 5902801, 5902801, 5902801, 5902801, 5902801, 281923884, 5902801, 951962733, 627, 281923884, 281923884, 281923884, 5902801, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 281923884, 5902801, 281923884, 281923884 }

    Returns: {6, 7, 15, 16, 33, 34, 36, 37, 42, 43, 45, 46 }

  74. { 1222, 1920034, 1222, 1222, 1222, 44, 1222, 3, 319717563, 319717563, 44, 44, 44, 44, 44, 44, 44, 44, 44, 1222, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 18, 44 }

    Returns: {5, 6, 8, 9, 14, 15, 17, 18, 32, 33, 35, 36, 41, 42, 44, 45 }

  75. { 49636065, 409325, 49636065, 49636065, 49636065, 409325, 49636065, 14, 199317474, 199317474, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 49636065, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 409325, 709, 409325, 409325 }

    Returns: {6, 9, 10, 15, 18, 19, 33, 36, 37, 42, 45, 46 }

  76. { 405356, 32612926, 405356, 405356, 405356, 405356, 405356, 405356, 405356, 405356, 405356, 40042, 405356, 405356, 405356, 8, 101926943, 101926943, 101926943, 40042, 405356, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40042, 40, 40042 }

    Returns: {6, 7, 9, 10, 15, 16, 18, 19, 33, 34, 36, 37, 42, 43, 45, 46 }

  77. { 1791242, 1791242, 7084, 1791242, 1791242, 1791242, 1791242, 1791242, 1791242, 1791242, 1791242, 1791242, 4500078, 1791242, 1791242, 1791242, 47288148, 2, 4500078, 1791242, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 4500078, 30841084, 4500078, 4500078 }

    Returns: {6, 7, 9, 10, 15, 16, 18, 19, 33, 34, 36, 37, 42, 43, 45, 46 }

  78. { 10902, 17594, 10902, 10902, 10902, 10902, 17594, 10902, 10902, 10902, 10902, 8144, 10902, 10902, 10902, 10902, 8144, 10902, 10902, 10902, 8144, 10902, 10902, 10902, 19, 19, 19, 6342639, 8144, 8144, 8144, 10902, 8144, 8144, 8144, 8144, 8144, 10902, 8144, 8144, 8144, 8144, 10902, 8144, 8144, 8144, 8144, 10902, 8144, 8144 }

    Returns: {7, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 41 }

  79. { 23506, 6106, 23506, 23506, 23506, 358848, 23506, 23506, 23506, 358848, 23506, 23506, 23506, 23506, 23506, 6106, 23506, 23506, 23506, 23506, 6106, 23506, 23506, 23506, 23506, 17, 53232473, 53232473, 6106, 6106, 6106, 23506, 6106, 6106, 6106, 6106, 6106, 2462, 6106, 6106, 6106, 23506, 6106, 6106, 6106, 2462, 6106, 6106 }

    Returns: {6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 39 }

  80. { 114693, 7712684, 114693, 114693, 114693, 114693, 114693, 120, 114693, 114693, 114693, 114693, 7712684, 114693, 114693, 114693, 114693, 7712684, 114693, 114693, 114693, 114693, 120, 114693, 114693, 114693, 69, 8791666, 120, 120, 120, 114693, 120, 120, 120, 120, 120, 91, 120, 120, 120, 120, 114693, 120, 120, 120, 120, 120, 91, 120 }

    Returns: {4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41 }

  81. { 36315, 37582, 36315, 36315, 36315, 37582, 36315, 36315, 36315, 36315, 37582, 36315, 36315, 36315, 36315, 36315, 37582, 36315, 36315, 36315, 36315, 12622, 36315, 36315, 36315, 36315, 36315, 3, 624005, 12622, 12622, 12622, 12622, 36315, 12622, 12622, 12622, 36315, 12622, 12622, 12622, 36315, 12622, 12622, 12622, 12622, 12622, 36315, 12622 }

    Returns: {4, 7, 9, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 40 }

  82. { 98608, 134223, 98608, 98608, 98608, 98608, 2490, 98608, 98608, 98608, 134223, 98608, 98608, 98608, 98608, 98608, 134223, 98608, 98608, 98608, 98608, 2490, 98608, 98608, 98608, 98608, 218, 113146373, 2490, 2490, 2490, 2490, 2490, 98608, 2490, 2490, 2490, 1075, 2490, 2490, 2490, 2490, 2490, 1075, 2490, 2490, 2490, 2490, 1075, 2490 }

    Returns: {4, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41 }

  83. { 70277, 1578, 70277, 70277, 70277, 70277, 70277, 209499, 70277, 70277, 70277, 70277, 1578, 70277, 70277, 70277, 209499, 70277, 70277, 70277, 70277, 70277, 209499, 70277, 70277, 70277, 70277, 696122298, 226, 209499, 209499, 209499, 209499, 70277, 209499, 209499, 209499, 209499, 209499, 356068, 209499, 209499, 209499, 70277, 209499, 209499, 209499, 209499, 70277, 209499 }

    Returns: {4, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41 }

  84. { 195761, 52696, 195761, 195761, 195761, 445245, 195761, 195761, 195761, 445245, 195761, 195761, 195761, 445245, 195761, 195761, 195761, 195761, 195761, 52696, 195761, 195761, 195761, 195761, 195761, 277, 1609210, 52696, 52696, 52696, 195761, 52696, 52696, 52696, 52696, 369, 52696, 52696, 52696, 52696, 52696, 195761, 52696, 52696, 52696, 52696, 52696, 369, 52696, 52696 }

    Returns: {5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41 }

  85. { 33375, 4666, 33375, 33375, 33375, 33375, 33375, 33375, 555192, 33375, 33375, 33375, 33375, 33375, 555192, 33375, 33375, 33375, 33375, 4666, 33375, 33375, 33375, 33375, 33375, 33375, 278, 1771115, 4666, 4666, 4666, 4666, 4666, 4666, 33375, 4666, 4666, 4666, 4666, 4666, 4666, 33375, 4666, 4666, 4666, 4666, 4666, 33375, 4666 }

    Returns: {4, 8, 9, 10, 13, 14, 15, 16, 18, 19, 20, 21, 24, 25, 26, 27, 30, 31, 32, 33, 36, 38, 42 }

  86. { 9863, 9863, 198, 9863, 9863, 9863, 9863, 9863, 378283, 9863, 9863, 9863, 9863, 9863, 9863, 198, 9863, 9863, 9863, 9863, 9863, 9863, 198, 9863, 9863, 9863, 9863, 9863, 5, 7168927, 198, 198, 198, 198, 198, 9863, 198, 198, 198, 198, 198, 198, 16, 198, 198, 198, 198, 198, 16, 198 }

    Returns: {5, 10, 11, 15, 16, 17, 20, 21, 22, 25, 26, 27, 28, 31, 32, 33, 37, 38, 43 }

  87. { 78, 53, 78, 78, 78, 78, 78, 78, 53, 78, 78, 78, 78, 78, 53, 78, 78, 78, 78, 78, 53, 78, 78, 78, 78, 78, 78, 0, 0, 167983, 167983, 53, 53, 53, 53, 78, 53, 53, 53, 53, 78, 53, 53, 53, 53, 53, 53, 24, 53, 53 }

    Returns: {7, 11, 13, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 37, 39, 43 }

  88. { 2483090, 2556733, 2483090, 2483090, 2483090, 2483090, 2483090, 2556733, 2483090, 2483090, 2483090, 2483090, 2483090, 2483090, 2556733, 2483090, 2483090, 2483090, 2483090, 34649, 2483090, 2483090, 2483090, 2483090, 2483090, 2483090, 7, 7, 522092517, 522092517, 522092517, 34649, 34649, 34649, 34649, 34649, 2483090, 34649, 34649, 34649, 34649, 34649, 34649, 2483090, 34649, 34649, 34649, 34649, 2483090, 34649 }

    Returns: {7, 11, 12, 13, 16, 17, 18, 22, 23, 24, 26, 27, 28, 32, 33, 34, 37, 38, 39, 43 }

  89. { 169, 169, 169, 64786188, 169, 169, 169, 169, 169, 64786188, 169, 169, 169, 169, 169, 115, 169, 169, 169, 169, 115, 169, 169, 169, 169, 169, 0, 540837749, 115, 115, 115, 115, 169, 115, 115, 115, 115, 169, 115, 115, 115, 115, 7, 115, 115, 115, 115 }

    Returns: {9, 13, 14, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 35, 36, 40 }

  90. { 9938753, 16086361, 9938753, 9938753, 9938753, 9938753, 153573, 9938753, 9938753, 9938753, 9938753, 153573, 9938753, 9938753, 9938753, 9938753, 9938753, 9938753, 153573, 9938753, 9938753, 9938753, 9938753, 9938753, 9938753, 9, 9, 9, 135441860, 153573, 153573, 153573, 153573, 153573, 9938753, 153573, 153573, 153573, 153573, 9938753, 153573, 153573, 153573, 153573, 153573, 2422, 153573, 153573, 153573, 153573 }

    Returns: {9, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 43 }

  91. { 4144170, 4144170, 4144170, 4144170, 84997749, 4144170, 4144170, 4144170, 4144170, 4144170, 69387, 4144170, 4144170, 4144170, 4144170, 4144170, 69387, 4144170, 4144170, 4144170, 4144170, 4144170, 84997749, 4144170, 4144170, 4144170, 4144170, 112980624, 112980624, 112980624, 11974, 84997749, 84997749, 84997749, 84997749, 4144170, 84997749, 84997749, 84997749, 84997749, 84997749, 4144170, 84997749, 84997749, 84997749, 84997749, 84997749, 98905143, 84997749, 84997749 }

    Returns: {10, 14, 15, 18, 19, 20, 23, 24, 25, 28, 29, 30, 33, 34, 35, 38, 39, 43 }

  92. { 39717, 31, 39717, 39717, 39717, 39717, 1163624, 39717, 39717, 39717, 39717, 39717, 1163624, 39717, 39717, 39717, 39717, 39717, 39717, 1163624, 39717, 39717, 39717, 39717, 39717, 39717, 776751794, 7, 1163624, 1163624, 1163624, 1163624, 1163624, 1163624, 39717, 1163624, 1163624, 1163624, 1163624, 1163624, 1163624, 400318879, 1163624, 1163624, 1163624, 1163624, 39717, 1163624, 1163624, 1163624 }

    Returns: {6, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 39, 43 }

  93. { 633333, 633333, 44730, 633333, 633333, 633333, 633333, 633333, 633333, 44730, 633333, 633333, 633333, 633333, 633333, 633333, 11028696, 633333, 633333, 633333, 633333, 44730, 633333, 633333, 633333, 633333, 9, 197598375, 44730, 44730, 44730, 44730, 44730, 44730, 633333, 44730, 44730, 44730, 44730, 44730, 44730, 20420, 44730, 44730, 44730, 44730, 44730, 633333, 44730 }

    Returns: {5, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 42 }

  94. { 174534, 174534, 1471591, 174534, 174534, 174534, 174534, 174534, 174534, 47479, 174534, 174534, 174534, 174534, 47479, 174534, 174534, 174534, 174534, 47479, 174534, 174534, 174534, 174534, 7, 72315324, 47479, 47479, 47479, 47479, 47479, 47479, 174534, 47479, 47479, 47479, 47479, 47479, 47479, 174534, 47479, 47479, 47479, 47479, 47479, 2125, 47479, 47479, 47479 }

    Returns: {7, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 42 }

  95. { 0, 4, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2 }

    Returns: {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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44 }

  96. {2, 26, 8, 13, 36, 55, 25, 23, 51, 45, 17, 47, 63, 64, 43, 13, 20, 59, 38, 17, 62, 21, 15, 50, 16, 64, 11, 15, 36, 39, 23, 43, 17, 35, 18, 18, 63, 28, 41, 30, 48, 11, 1, 47, 64, 12, 35, 5, 50, 53 }

    Returns: {6 }

  97. {104049400, 104049400, 6862293, 827397890, 529736365, 554435232, 168972506, 10555692, 104049400, 28991180, 80582766, 168972506, 308036332, 737846973, 272073168, 48101890, 422196748, 1025232, 6862293, 467962000, 1025232, 420848452, 57948765, 550704096, 152556148, 220448440, 255452760, 347762541, 305319768, 58108099, 302323670, 502089410, 1025232, 510226857, 150960000, 36818682, 108850365, 550704096, 46168950, 183523151, 580257216, 127118631, 168972506, 550704096, 16045800, 76789944, 296212630, 259661055, 10555692, 483016400 }

    Returns: {7 }

  98. {1, 2, 1, 1, 0, 4, 3, 5, 5, 4, 4, 5, 8, 5, 5, 5, 5, 5, 9, 2, 0, 9, 4, 5, 5, 3, 4, 4, 4, 4, 7, 4 }

    Returns: {6, 7, 8, 9, 10, 11, 12, 13 }

  99. {128959394, 692901014, 436085874, 748533631, 776550280, 289134332, 807385196, 556889023, 95168427, 888844002, 353699825, 809912669, 686611922, 777811292, 912905317, 45033382, 698004710, 51427208, 532780647, 755994994, 808052927, 778205366, 822530700, 168547992, 373798977, 890856879, 469573117, 80335149, 702214256, 7523373, 381141486, 831173649, 700424386, 817227359, 432223632, 329491018, 106361690, 239608827, 886380040, 201530117, 980969181, 92596216, 11442785, 667581102, 870407508, 776864453, 565130835, 420928569, 680808012, 97911481 }

    Returns: {4 }

  100. {1, 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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 }

    Returns: {2 }

  101. {100, 101, 100, 97, 100, 105, 100, 93, 100, 109, 100, 89, 100, 113, 100, 85, 100, 117, 100, 81, 100, 121, 100, 77, 100, 125, 100, 73, 100, 129, 100, 69, 100, 133, 100, 65, 100, 137, 100, 61, 100, 141, 100, 57, 100, 145, 100, 53, 100, 149 }

    Returns: {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 }

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: