Statistics

Problem Statement for "NCool"

Problem Statement

You are given a convex polygon and you must count the number of N-cool points. A point is N-cool if it is a lattice point covered by the polygon and also an endpoint of some N-cool segment. A line segment is N-cool if it contains at least N lattice points that are covered by the polygon. A point is considered covered by the polygon if it is inside or on the boundary of the polygon. Endpoints of a segment are considered to be inside of it. A lattice point is a point with integer coordinates.

Consider the example in the picture below. Here N is equal to 6, and there are 21 6-cool points, marked green. Also two 6-cool segments, which are colored red, are shown.

You are given int[]s x and y describing the vertices of the polygon (in no particular order). The coordinates of each vertex are specified by corresponding elements of x and y. Return the number of N-cool points.

Definition

Class:
NCool
Method:
nCoolPoints
Parameters:
int[], int[], int
Returns:
int
Method signature:
int nCoolPoints(int[] x, int[] y, int n)
(be sure your method is public)

Notes

  • A polygon is convex if it contains all the line segments connecting any pair of its points.

Constraints

  • x and y will each contain between 3 and 50 elements, inclusive.
  • x and y will contain the same number of elements.
  • All elements of x and y will be between 0 and 10000, inclusive.
  • The number of lattice points inside or on the boundary of the specified polygon will not be greater than 500000.
  • N will be between 2 and 500000, inclusive.
  • The polygon specified by x and y will be convex and will have nonzero area.

Examples

  1. {0, 1, 2, 7, 7}

    {3, 1, 6, 1, 5}

    6

    Returns: 21

    This is the example from the problem statement.

  2. {0, 1, 0}

    {0, 0, 1}

    2

    Returns: 3

    These three points form a triangle, whose sides are 2-cool segments, so all three vertices are 2-cool.

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

    {0, 1, 2, 2, 1, 0, 0, 0, 2}

    3

    Returns: 6

    One point can be mentioned in the input two or more times.

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

    {1, 0, 2, 0, 2, 0, 2, 0, 2, 1}

    5

    Returns: 4

    There can be 3 points of the polygon, lying on the same line.

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

    {1, 0, 2, 0, 2, 0, 2, 0, 2, 1}

    4

    Returns: 10

  6. {0, 0, 1, 1, 2, 2}

    {0, 1, 0, 2, 1, 2}

    3

    Returns: 6

  7. {0, 0, 1, 2}

    {0, 1, 2, 2}

    3

    Returns: 2

  8. {1, 1, 500, 500}

    {1, 1000, 1, 1000}

    1000

    Returns: 1000

  9. {1, 1, 500, 500}

    {1, 1000, 1, 1000}

    501

    Returns: 500000

  10. {1, 1, 500, 500}

    {1, 1000, 1, 1000}

    2

    Returns: 500000

  11. {1753, 2893, 250, 8566, 5384, 162, 9536, 8739, 2893, 8566, 2893, 5384, 162, 250, 2893, 8566, 162, 9536, 9536, 250, 1753, 1753, 250, 8566, 1753, 1753, 162, 162, 8739, 5384, 162, 8566, 5384, 8739, 1753, 9536, 8739, 9536, 1753, 1753, 2893, 2893, 5384, 8739, 5384, 9536, 250, 2893, 5384, 1753}

    {9, 0, 2, 9, 0, 7, 7, 2, 0, 9, 0, 0, 7, 2, 0, 9, 7, 7, 7, 2, 9, 9, 2, 9, 9, 9, 7, 7, 2, 0, 7, 9, 0, 2, 9, 7, 2, 7, 9, 9, 0, 0, 0, 2, 0, 7, 2, 0, 0, 9}

    566

    Returns: 76481

  12. {9997, 9993, 74, 100, 400, 9898, 9978, 9653, 17, 9976, 9898, 9997, 9993, 400, 9898, 9993, 9976, 100, 9993, 9898, 9993, 100, 9993, 400, 9898, 9997, 9898, 100, 9976, 9653, 9976, 9898, 9976, 9653, 100, 9978, 400, 400, 9653, 9976, 17, 400, 9993, 74, 17, 9653, 100, 9997, 74, 9653}

    {2, 4, 1, 9, 0, 8, 0, 9, 6, 6, 8, 2, 4, 0, 8, 4, 6, 9, 4, 8, 4, 9, 4, 0, 8, 2, 8, 9, 6, 9, 6, 8, 6, 9, 9, 0, 0, 0, 9, 6, 6, 0, 4, 1, 6, 9, 9, 2, 1, 9}

    566

    Returns: 98515

  13. {9997, 2, 21, 9987, 9996, 1, 9996, 2, 1, 9996, 21, 9997, 2, 9996, 9997, 1, 21, 21, 9996, 2, 9997, 9996, 2, 2, 1, 9997, 2, 2, 2, 2, 1, 1, 9997, 9996, 9987, 9996, 9987, 2, 9997, 9997, 9996, 9997, 9996, 9987, 1, 1, 2, 1, 1, 1}

    {1, 4, 0, 0, 9, 9, 9, 4, 9, 9, 0, 1, 4, 9, 1, 9, 0, 0, 9, 4, 1, 9, 4, 4, 9, 1, 4, 4, 4, 4, 9, 9, 1, 9, 0, 9, 0, 4, 1, 1, 9, 1, 9, 0, 9, 9, 4, 9, 9, 9}

    566

    Returns: 99894

  14. {9633, 701, 9606, 5405, 270, 93, 123, 8819, 9651, 701, 5405, 8819, 9651, 270, 5405, 270, 93, 9606, 701, 5405, 93, 8819, 5405, 93, 123, 9651, 8819, 5405, 9606, 270, 9606, 5405, 9651, 5405, 5405, 701, 5405, 123, 9633, 93, 93, 5405, 270, 9606, 8819, 93, 270, 9606, 8819, 270}

    {4, 9, 9, 0, 0, 8, 3, 2, 8, 9, 0, 2, 8, 0, 0, 0, 8, 9, 9, 0, 8, 2, 0, 8, 3, 8, 2, 0, 9, 0, 9, 0, 8, 0, 0, 9, 0, 3, 4, 8, 8, 0, 0, 9, 2, 8, 0, 9, 2, 0}

    610

    Returns: 86375

  15. {9837, 179, 4, 145, 9984, 9990, 9858, 9981, 9588, 408, 9588, 9981, 179, 9984, 408, 9981, 9858, 9837, 145, 9984, 145, 9588, 9990, 9990, 9984, 179, 179, 9981, 4, 145, 9588, 9858, 9984, 9981, 9984, 145, 179, 9837, 9858, 4, 9858, 9858, 179, 9981, 179, 9837, 9990, 408, 9837, 9837}

    {8, 8, 4, 0, 7, 6, 0, 4, 9, 9, 9, 4, 8, 7, 9, 4, 0, 8, 0, 7, 0, 9, 6, 6, 7, 8, 8, 4, 4, 0, 9, 0, 7, 4, 7, 0, 8, 8, 0, 4, 0, 0, 8, 4, 8, 8, 6, 9, 8, 8}

    610

    Returns: 97753

  16. {19, 1, 9988, 9996, 1, 9997, 9992, 9992, 9997, 1, 1, 9992, 9988, 19, 1, 9996, 9996, 9992, 9988, 19, 9992, 1, 9996, 9996, 9996, 1, 19, 1, 1, 19, 9992, 19, 9992, 9988, 9988, 9988, 9997, 9992, 9992, 1, 9996, 1, 1, 9996, 9988, 9997, 9992, 9997, 9988, 19}

    {0, 9, 9, 6, 2, 2, 0, 0, 2, 2, 2, 0, 9, 0, 2, 6, 6, 0, 9, 0, 0, 9, 6, 6, 6, 9, 0, 2, 2, 0, 0, 0, 0, 9, 9, 9, 2, 0, 0, 2, 6, 2, 9, 6, 9, 2, 0, 2, 9, 0}

    610

    Returns: 99911

  17. {1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0}

    {9952, 9794, 12, 209, 209, 9952, 209, 12, 209, 9952, 209, 209, 12, 9794, 209, 12, 9794, 9794, 12, 12, 209, 9794, 209, 209, 209, 9952, 9952, 12, 9794, 209, 9952, 9794, 9794, 9794, 9794, 9952, 9794, 9952, 12, 9794, 9794, 9794, 9952, 209, 209, 9952, 9794, 9952, 9794, 209}

    2

    Returns: 19527

  18. {0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0}

    {20, 5, 9995, 9984, 20, 9984, 5, 9995, 9995, 9995, 5, 9995, 20, 20, 9984, 9984, 9984, 9995, 5, 20, 20, 5, 5, 9984, 9984, 5, 9995, 20, 9995, 20, 5, 9984, 9995, 9995, 9984, 9995, 9995, 20, 20, 20, 9984, 5, 9995, 9984, 5, 5, 9995, 20, 20, 20}

    3

    Returns: 19956

  19. {1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0}

    {0, 2, 9999, 10000, 10000, 2, 9999, 9999, 9999, 10000, 2, 9999, 9999, 9999, 10000, 9999, 10000, 10000, 10000, 10000, 10000, 0, 0, 10000, 10000, 9999, 2, 9999, 9999, 0, 0, 10000, 9999, 10000, 2, 2, 0, 10000, 0, 9999, 9999, 2, 0, 0, 10000, 0, 9999, 10000, 10000, 2}

    10

    Returns: 19999

  20. {183, 905, 859, 976, 211, 694, 502, 21, 12, 985}

    {93, 87, 90, 19, 1, 0, 95, 7, 79, 40}

    2

    Returns: 82544

  21. {999, 3, 998, 0}

    {0, 1, 1, 0}

    100

    Returns: 1996

  22. {999, 0, 999, 0}

    {0, 1, 1, 0}

    10

    Returns: 2000

  23. {566, 566, 575, 1266, 1266, 1234, 585, 567, 570, 577, 1265, 1251, 602, 1214, 1265}

    {1257, 580, 1266, 621, 1251, 566, 567, 572, 1262, 568, 575, 568, 566, 1266, 1265}

    10000

    Returns: 0

  24. {1306, 672, 850, 967, 1188, 1293, 1037, 632, 814, 678, 1293, 1037, 967, 1188, 814, 1293, 672, 672, 1188, 850, 632, 850, 678, 814, 632, 678, 850, 1293, 1306, 814, 1037, 672, 1293, 1188, 967, 1037, 850, 1306, 1037, 678, 814, 672}

    {1307, 651, 1309, 633, 636, 913, 629, 730, 1301, 1095, 913, 629, 633, 636, 1301, 913, 651, 651, 636, 1309, 730, 1309, 1095, 1301, 730, 1095, 1309, 913, 1307, 1301, 629, 651, 913, 636, 633, 629, 1309, 1307, 629, 1095, 1301, 651}

    2

    Returns: 395900

  25. {1228, 589, 1065, 819, 752, 586, 1165, 628, 953, 1163, 576, 819, 576, 752, 752, 819, 576, 1228, 1163, 1165, 1065, 589}

    {1124, 1271, 1258, 629, 1273, 665, 759, 653, 1271, 750, 825, 629, 825, 1273, 1273, 629, 825, 1124, 750, 759, 1258, 1271}

    410980

    Returns: 0

  26. {1299, 623, 633, 1190, 611, 1308, 610, 740, 614, 620, 918, 1310, 1294, 610, 1309, 1309, 692, 974, 625, 613, 637, 692, 974, 1310, 1309, 623, 974, 1309, 974, 637, 1294, 1294, 1294, 918, 1190, 1309, 1309, 692, 623, 633}

    {567, 580, 1254, 1266, 1172, 1247, 839, 568, 621, 1250, 1266, 926, 1265, 927, 613, 1186, 1264, 567, 575, 640, 569, 1264, 567, 926, 613, 580, 567, 613, 567, 569, 1265, 1265, 1265, 1266, 1266, 1186, 613, 1264, 580, 1254}

    566

    Returns: 300228

  27. {701, 701, 693, 1, 700, 17, 1, 700, 700, 701, 701, 701, 701, 701, 1, 700, 1, 700, 1, 1, 17, 1, 700, 700, 693, 701, 701, 700, 17, 17, 700, 1, 700, 17, 700, 17, 1, 1, 1, 693, 700, 1, 693, 701, 700, 701, 701, 693, 701, 1}

    {7, 699, 1, 700, 701, 701, 1, 2, 2, 699, 7, 7, 699, 699, 1, 2, 700, 2, 700, 1, 701, 700, 2, 2, 1, 7, 7, 701, 701, 701, 2, 700, 701, 701, 2, 701, 700, 1, 1, 1, 2, 1, 1, 699, 2, 7, 7, 1, 7, 700}

    610

    Returns: 224081

  28. {810, 9697, 693, 3893, 7575, 8298, 1992, 599, 6405, 3077, 810, 1992, 3893, 1992, 1992, 8298, 7575, 693, 599, 810, 9697, 3893, 3893, 3077, 9697, 810, 3077, 8298, 810, 599}

    {3, 43, 6, 48, 3, 6, 45, 22, 1, 48, 3, 45, 48, 45, 45, 6, 3, 6, 22, 3, 43, 48, 48, 48, 43, 3, 48, 6, 3, 22}

    5

    Returns: 347883

  29. {9, 9980, 9915, 8, 9991, 13, 23, 17, 9979, 8, 13, 23, 9980, 9915, 9991, 8, 23, 9980, 9980, 9979, 8, 8, 8, 8, 9991, 8, 13, 23, 9980, 9, 9980, 8, 9915, 8, 8, 9979, 9991, 9979, 13, 9980}

    {28, 46, 49, 21, 32, 49, 0, 4, 0, 13, 49, 0, 46, 49, 32, 21, 0, 46, 46, 0, 13, 21, 21, 13, 32, 21, 49, 0, 46, 28, 46, 21, 49, 21, 13, 0, 32, 0, 49, 46}

    50

    Returns: 498556

  30. {2, 9999, 9996, 9998, 1, 0, 9999, 0, 4, 0, 4, 9996, 0, 0, 9999, 9996, 4, 9999, 0, 0, 9996, 0, 9999, 9996, 2, 9999, 9999, 4, 9998, 0, 9996, 0, 9998, 4, 0, 9998, 9999, 2, 9999, 0, 0, 9998, 0, 9998, 9999, 9996, 0, 0, 9999, 9999}

    {0, 46, 0, 49, 1, 48, 2, 7, 49, 7, 49, 0, 7, 48, 2, 0, 49, 2, 7, 48, 0, 7, 2, 0, 0, 2, 2, 49, 49, 7, 0, 48, 49, 49, 7, 49, 2, 0, 2, 48, 48, 49, 48, 49, 2, 0, 48, 48, 2, 46}

    500

    Returns: 499980

  31. {1753, 2893, 250, 8566, 5384, 162, 9536, 8739, 2893, 8566, 2893, 5384, 162, 250, 2893, 8566, 162, 9536, 9536, 250, 1753, 1753, 250, 8566, 1753, 1753, 162, 162, 8739, 5384, 162, 8566, 5384, 8739, 1753, 9536, 8739, 9536, 1753, 1753, 2893, 2893, 5384, 8739, 5384, 9536, 250, 2893, 5384, 1753}

    {9, 0, 2, 9, 0, 7, 7, 2, 0, 9, 0, 0, 7, 2, 0, 9, 7, 7, 7, 2, 9, 9, 2, 9, 9, 9, 7, 7, 2, 0, 7, 9, 0, 2, 9, 7, 2, 7, 9, 9, 0, 0, 0, 2, 0, 7, 2, 0, 0, 9}

    9145

    Returns: 568

  32. {9997, 9993, 74, 100, 400, 9898, 9978, 9653, 17, 9976, 9898, 9997, 9993, 400, 9898, 9993, 9976, 100, 9993, 9898, 9993, 100, 9993, 400, 9898, 9997, 9898, 100, 9976, 9653, 9976, 9898, 9976, 9653, 100, 9978, 400, 400, 9653, 9976, 17, 400, 9993, 74, 17, 9653, 100, 9997, 74, 9653}

    {2, 4, 1, 9, 0, 8, 0, 9, 6, 6, 8, 2, 4, 0, 8, 4, 6, 9, 4, 8, 4, 9, 4, 0, 8, 2, 8, 9, 6, 9, 6, 8, 6, 9, 9, 0, 0, 0, 9, 6, 6, 0, 4, 1, 6, 9, 9, 2, 1, 9}

    9897

    Returns: 574

  33. {9997, 2, 21, 9987, 9996, 1, 9996, 2, 1, 9996, 21, 9997, 2, 9996, 9997, 1, 21, 21, 9996, 2, 9997, 9996, 2, 2, 1, 9997, 2, 2, 2, 2, 1, 1, 9997, 9996, 9987, 9996, 9987, 2, 9997, 9997, 9996, 9997, 9996, 9987, 1, 1, 2, 1, 1, 1}

    {1, 4, 0, 0, 9, 9, 9, 4, 9, 9, 0, 1, 4, 9, 1, 9, 0, 0, 9, 4, 1, 9, 4, 4, 9, 1, 4, 4, 4, 4, 9, 9, 1, 9, 0, 9, 0, 4, 1, 1, 9, 1, 9, 0, 9, 9, 4, 9, 9, 9}

    9962

    Returns: 568

  34. {9633, 701, 9606, 5405, 270, 93, 123, 8819, 9651, 701, 5405, 8819, 9651, 270, 5405, 270, 93, 9606, 701, 5405, 93, 8819, 5405, 93, 123, 9651, 8819, 5405, 9606, 270, 9606, 5405, 9651, 5405, 5405, 701, 5405, 123, 9633, 93, 93, 5405, 270, 9606, 8819, 93, 270, 9606, 8819, 270}

    {4, 9, 9, 0, 0, 8, 3, 2, 8, 9, 0, 2, 8, 0, 0, 0, 8, 9, 9, 0, 8, 2, 0, 8, 3, 8, 2, 0, 9, 0, 9, 0, 8, 0, 0, 9, 0, 3, 4, 8, 8, 0, 0, 9, 2, 8, 0, 9, 2, 0}

    9478

    Returns: 608

  35. {9837, 179, 4, 145, 9984, 9990, 9858, 9981, 9588, 408, 9588, 9981, 179, 9984, 408, 9981, 9858, 9837, 145, 9984, 145, 9588, 9990, 9990, 9984, 179, 179, 9981, 4, 145, 9588, 9858, 9984, 9981, 9984, 145, 179, 9837, 9858, 4, 9858, 9858, 179, 9981, 179, 9837, 9990, 408, 9837, 9837}

    {8, 8, 4, 0, 7, 6, 0, 4, 9, 9, 9, 4, 8, 7, 9, 4, 0, 8, 0, 7, 0, 9, 6, 6, 7, 8, 8, 4, 4, 0, 9, 0, 7, 4, 7, 0, 8, 8, 0, 4, 0, 0, 8, 4, 8, 8, 6, 9, 8, 8}

    9857

    Returns: 604

  36. {19, 1, 9988, 9996, 1, 9997, 9992, 9992, 9997, 1, 1, 9992, 9988, 19, 1, 9996, 9996, 9992, 9988, 19, 9992, 1, 9996, 9996, 9996, 1, 19, 1, 1, 19, 9992, 19, 9992, 9988, 9988, 9988, 9997, 9992, 9992, 1, 9996, 1, 1, 9996, 9988, 9997, 9992, 9997, 9988, 19}

    {0, 9, 9, 6, 2, 2, 0, 0, 2, 2, 2, 0, 9, 0, 2, 6, 6, 0, 9, 0, 0, 9, 6, 6, 6, 9, 0, 2, 2, 0, 0, 0, 0, 9, 9, 9, 2, 0, 0, 2, 6, 2, 9, 6, 9, 2, 0, 2, 9, 0}

    9962

    Returns: 602

  37. {1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0}

    {9952, 9794, 12, 209, 209, 9952, 209, 12, 209, 9952, 209, 209, 12, 9794, 209, 12, 9794, 9794, 12, 12, 209, 9794, 209, 209, 209, 9952, 9952, 12, 9794, 209, 9952, 9794, 9794, 9794, 9794, 9952, 9794, 9952, 12, 9794, 9794, 9794, 9952, 209, 209, 9952, 9794, 9952, 9794, 209}

    9941

    Returns: 2

  38. {0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0}

    {20, 5, 9995, 9984, 20, 9984, 5, 9995, 9995, 9995, 5, 9995, 20, 20, 9984, 9984, 9984, 9995, 5, 20, 20, 5, 5, 9984, 9984, 5, 9995, 20, 9995, 20, 5, 9984, 9995, 9995, 9984, 9995, 9995, 20, 20, 20, 9984, 5, 9995, 9984, 5, 5, 9995, 20, 20, 20}

    9991

    Returns: 2

  39. {1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0}

    {0, 2, 9999, 10000, 10000, 2, 9999, 9999, 9999, 10000, 2, 9999, 9999, 9999, 10000, 9999, 10000, 10000, 10000, 10000, 10000, 0, 0, 10000, 10000, 9999, 2, 9999, 9999, 0, 0, 10000, 9999, 10000, 2, 2, 0, 10000, 0, 9999, 9999, 2, 0, 0, 10000, 0, 9999, 10000, 10000, 2}

    9998

    Returns: 10

  40. {183, 905, 859, 976, 211, 694, 502, 21, 12, 985}

    {93, 87, 90, 19, 1, 0, 95, 7, 79, 40}

    970

    Returns: 0

  41. {999, 3, 998, 0}

    {0, 1, 1, 0}

    1001

    Returns: 0

  42. {999, 0, 999, 0}

    {0, 1, 1, 0}

    1001

    Returns: 0

  43. {566, 566, 575, 1266, 1266, 1234, 585, 567, 570, 577, 1265, 1251, 602, 1214, 1265}

    {1257, 580, 1266, 621, 1251, 566, 567, 572, 1262, 568, 575, 568, 566, 1266, 1265}

    702

    Returns: 0

  44. {1306, 672, 850, 967, 1188, 1293, 1037, 632, 814, 678, 1293, 1037, 967, 1188, 814, 1293, 672, 672, 1188, 850, 632, 850, 678, 814, 632, 678, 850, 1293, 1306, 814, 1037, 672, 1293, 1188, 967, 1037, 850, 1306, 1037, 678, 814, 672}

    {1307, 651, 1309, 633, 636, 913, 629, 730, 1301, 1095, 913, 629, 633, 636, 1301, 913, 651, 651, 636, 1309, 730, 1309, 1095, 1301, 730, 1095, 1309, 913, 1307, 1301, 629, 651, 913, 636, 633, 629, 1309, 1307, 629, 1095, 1301, 651}

    681

    Returns: 0

  45. {1228, 589, 1065, 819, 752, 586, 1165, 628, 953, 1163, 576, 819, 576, 752, 752, 819, 576, 1228, 1163, 1165, 1065, 589}

    {1124, 1271, 1258, 629, 1273, 665, 759, 653, 1271, 750, 825, 629, 825, 1273, 1273, 629, 825, 1124, 750, 759, 1258, 1271}

    559

    Returns: 100916

  46. {1299, 623, 633, 1190, 611, 1308, 610, 740, 614, 620, 918, 1310, 1294, 610, 1309, 1309, 692, 974, 625, 613, 637, 692, 974, 1310, 1309, 623, 974, 1309, 974, 637, 1294, 1294, 1294, 918, 1190, 1309, 1309, 692, 623, 633}

    {567, 580, 1254, 1266, 1172, 1247, 839, 568, 621, 1250, 1266, 926, 1265, 927, 613, 1186, 1264, 567, 575, 640, 569, 1264, 567, 926, 613, 580, 567, 613, 567, 569, 1265, 1265, 1265, 1266, 1266, 1186, 613, 1264, 580, 1254}

    497

    Returns: 400274

  47. {701, 701, 693, 1, 700, 17, 1, 700, 700, 701, 701, 701, 701, 701, 1, 700, 1, 700, 1, 1, 17, 1, 700, 700, 693, 701, 701, 700, 17, 17, 700, 1, 700, 17, 700, 17, 1, 1, 1, 693, 700, 1, 693, 701, 700, 701, 701, 693, 701, 1}

    {7, 699, 1, 700, 701, 701, 1, 2, 2, 699, 7, 7, 699, 699, 1, 2, 700, 2, 700, 1, 701, 700, 2, 2, 1, 7, 7, 701, 701, 701, 2, 700, 701, 701, 2, 701, 700, 1, 1, 1, 2, 1, 1, 699, 2, 7, 7, 1, 7, 700}

    404

    Returns: 480345

  48. {810, 9697, 693, 3893, 7575, 8298, 1992, 599, 6405, 3077, 810, 1992, 3893, 1992, 1992, 8298, 7575, 693, 599, 810, 9697, 3893, 3893, 3077, 9697, 810, 3077, 8298, 810, 599}

    {3, 43, 6, 48, 3, 6, 45, 22, 1, 48, 3, 45, 48, 45, 45, 6, 3, 6, 22, 3, 43, 48, 48, 48, 43, 3, 48, 6, 3, 22}

    8305

    Returns: 0

  49. {9, 9980, 9915, 8, 9991, 13, 23, 17, 9979, 8, 13, 23, 9980, 9915, 9991, 8, 23, 9980, 9980, 9979, 8, 8, 8, 8, 9991, 8, 13, 23, 9980, 9, 9980, 8, 9915, 8, 8, 9979, 9991, 9979, 13, 9980}

    {28, 46, 49, 21, 32, 49, 0, 4, 0, 13, 49, 0, 46, 49, 32, 21, 0, 46, 46, 0, 13, 21, 21, 13, 32, 21, 49, 0, 46, 28, 46, 21, 49, 21, 13, 0, 32, 0, 49, 46}

    9979

    Returns: 66

  50. {2, 9999, 9996, 9998, 1, 0, 9999, 0, 4, 0, 4, 9996, 0, 0, 9999, 9996, 4, 9999, 0, 0, 9996, 0, 9999, 9996, 2, 9999, 9999, 4, 9998, 0, 9996, 0, 9998, 4, 0, 9998, 9999, 2, 9999, 0, 0, 9998, 0, 9998, 9999, 9996, 0, 0, 9999, 9999}

    {0, 46, 0, 49, 1, 48, 2, 7, 49, 7, 49, 0, 7, 48, 2, 0, 49, 2, 7, 48, 0, 7, 2, 0, 0, 2, 2, 49, 49, 7, 0, 48, 49, 49, 7, 49, 2, 0, 2, 48, 48, 49, 48, 49, 2, 0, 48, 48, 2, 46}

    9995

    Returns: 560

  51. {0, 1, 2, 3, 2 }

    {5, 2, 0, 0, 2 }

    2

    Returns: 7

  52. {0, 2, 9992, 9990 }

    {0, 0, 6660, 6660 }

    1000

    Returns: 16653

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