Statistics

Problem Statement for "DrawingPointsDivOne"

Problem Statement

This problem statement contains images. It may not display properly outside the applet.

Once upon a time, Little Wojtek had drawn a number of points with integer coordinates onto a sheet of paper. Then he made zero or more steps. Each step looked as follows: Let's call all the points on Wojtek's paper old points. For every four old points that formed the vertices of a 1x1 square, Wojtek would draw a point in the middle of that square. Once he had drawn all such new points, he took an eraser and erased all the old points.


An example is shown in the picture below. On the left is Wojtek's original paper. In the middle is the same paper with the new points filled in. (For clarity, the old points are black and the new ones are red.) On the right is the paper after the old points were erased.


   


He has been playing for a while when he was called downstairs to dinner. He looked at the paper with a surprised face and wondered how many steps he had made.


You are given two int[]s x, y of some equal length n. They describe all of the points that were drawn by Wojtek in the last step of his play. More precisely, you may assume that there are real numbers (not necessarily integers) dy and dx such that the following holds:

  • For each i between 0 and n-1, there is a point at coordinates (dx+x[i], dy+y[i]).
  • There are no other points anywhere on the paper, only those that follow from the previous statement.


Return the maximum number of steps Wojtek could have made. If there is no maximum (that is, if the number of steps can be arbitrarily large), return -1 instead.

Definition

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

Notes

  • Note that the points drawn by Wojtek in the last step of his play could have non-integer coordinates.
  • The paper used by Wojtek could have been arbitrarily large. In other words, ignore the paper size, it does not limit the number of steps in any way.

Constraints

  • x will contain between 1 and 50 elements, inclusive.
  • x and y will contain the same number of elements.
  • Each element of x will be between -70 and 70, inclusive.
  • Each element of y will be between -70 and 70, inclusive.
  • No two points described by x and y will be the same.

Examples

  1. {0, 3}

    {0, 0}

    Returns: 1

    An example scenario: Wojtek draws the initial points at locations (100, 100), (100, 101), (101, 100), (101, 101), (103, 100), (104, 100), (103, 101), (104, 101), (315, 714). In the first and only step, Wojtek draws points at locations (100.5, 100.5) and (103.5, 100.5). These locations correspond to x and y in this test case.

  2. {0,2}

    {0,0}

    Returns: 0

  3. {-70}

    {3}

    Returns: -1

  4. {-41,-40,1,-11,-32,-7,24,-11,49,-15,-22,20,-8,54,54,69,16,-30,36,-6,-30,40,64,20,-66, -37,-33,-18,-35,36,9,61,-43,45,5,60,-8,-58,65,-66,41,12,34,-11,-57,-38,46,63,-55,3}

    {5,-24,-2,-4,23,14,1,70,-26,45,15,48,32,-41,54,-47,-67,-46,-9,-53,54,28,-61,11,53,68, -33,62,37,-8,-17,-17,48,19,-49,56,-41,16,17,-50,28,59,10,50,23,-16,56,31,-70,-44}

    Returns: 9

  5. {39,39}

    {50,26}

    Returns: 22

  6. {49,31,34,60,0,-6,63,29,54,11,-37,-69,30,-25,-29,56,45,43,68,-49,15,-21,-58,1,52,49,-36,-9,8,42,-29,26,14,36,66,-43,65,20,-12,-43,37,46,-12,-69,-31,23,-14}

    {14,23,27,-2,-6,-25,10,-36,35,51,63,-31,70,6,21,15,29,-4,-14,47,57,-68,-31,66,25,-59,43,-35,-38,27,-42,-61,-25,0,-24,-57,25,-32,55,39,42,51,48,28,-31,64,16}

    Returns: 5

  7. {27,-48,22,67,65,25,64,55,52,33,-46,-16}

    {-8,11,-56,69,-43,-39,5,-38,-61,13,-16,10}

    Returns: 21

  8. {28,38,59,32,23,67,20,-68,37,54,-7,56,20,-16,-1,8,46,-7,-25,-69,-59,6,48,52,69,63,14,-48,25,3,-33,-25,4,-8,28,57,-32}

    {31,34,-6,51,-1,-26,-55,-51,56,70,-70,39,56,-27,-26,-56,59,24,-44,38,-8,17,35,62,0,-66,9,-62,64,-7,55,2,55,-15,-45,64,-40}

    Returns: 6

  9. {24,-64,-44,60,-63,-45,-53,4,62,-15,36,-1,-12,-28,-12,40,-65,5,-55,22,-53,-5,62,-68,60,-65,-4,4,-34,-6,-66,-16}

    {56,-62,24,54,-63,-35,44,27,29,-40,19,45,30,28,-3,-47,32,35,40,4,-13,-47,-43,40,10,25,45,-23,70,-38,61,-7}

    Returns: 1

  10. {-19,-67,-28,61,38,-38,-69,58,-57,46,0,18,47,-48,-3,-18,-30,-58,-27,-56,40,-53,-15,16,20,-13,-18,-7,35,27,68,6,-24,-28,2,31,-37,3,53,-46}

    {13,-25,-65,38,-8,-61,-68,8,47,-59,25,-60,-45,-61,49,-46,3,68,-22,-36,62,-55,-29,47,-25,-46,-64,-27,-57,-55,41,56,-25,-31,-18,57,-64,70,64,57}

    Returns: 3

  11. {37,-58,-35,-24,65,59,48,27,19,54,-55,-8,-24,68,-48}

    {-14,42,-30,-39,33,-58,40,-8,-7,29,43,-7,70,-4,-45}

    Returns: 15

  12. {-5,-66,-10,40,-48,-39,-51,-21,62,-59,-55,17,-63,44,-30,-44,20,-42,-13,-57,-7,-41,35,13,38,66,14,69,-45,-13,6,-22}

    {12,38,-34,42,30,16,-59,62,-18,54,25,-68,12,-35,-60,42,16,67,-2,44,36,-21,68,-36,-51,22,53,-8,-51,-35,-56,47}

    Returns: 12

  13. {66,-57,-23,-22,52,0,13,40,-20,48,52,-12,-19,-24,-23,-14,-11,-66,54,-69,-48,-37,-33,69,-62,-25,-52,-31,-68,-60,66,1,-48,-35,-26,-10,67,56,-69,13,50,-66,30,-26,-32,-60,30}

    {-21,-60,-58,18,-12,-29,-33,-7,-50,-67,39,18,-15,-50,-47,-15,62,-37,-2,-14,2,-13,-4,35,-43,-18,29,5,53,-27,-2,-45,-26,-5,41,-66,69,-38,30,-61,42,16,34,27,66,27,-54}

    Returns: 2

  14. {-59,-23,-65,-32,10,51,34,-64,62,59,-45,24,-48,52,-27,-29,26,-39,-23,-66,45,-32,29,-8,36}

    {1,-39,-39,-25,-55,-48,-69,-7,-16,45,52,9,-69,-35,-9,-25,-40,-45,-11,5,-41,69,-37,-56,-17}

    Returns: 1

  15. {-64,-1,64,65,15,-56,11,-13,-15,55,24,44,-22,53,69,24,16,13,-19,0,11,-33,-19,35,21,-40,27,-45,5,-53,-19,7,-62,-59,20,-63,-16,-53,-31,9,-5,44}

    {66,5,8,51,17,70,37,-27,13,63,-37,25,48,45,-24,23,-1,-11,-14,-12,-20,22,-54,-19,69,42,-34,-69,-19,27,68,25,-49,-31,32,9,15,44,-53,34,-63,-41}

    Returns: 7

  16. {34,36,3,-47,-5,-33,-9,29,18,-66,5,-39,33,46,70,-41,42,-61,46,-6,-6,32,-25,51,-32,-54,9,53,35,31,48,23,23,-46,17,-39,11,42,-26,-67,5,51,29,6,14}

    {55,-40,44,19,-1,18,-11,46,14,33,63,21,-57,47,59,8,-65,10,57,-43,9,-34,30,-42,-52,-65,-30,-67,18,-69,-40,53,-10,-21,-49,-57,-7,7,68,-5,-63,-22,-59,7,69}

    Returns: 8

  17. {-62,32,15,-10,-67,-33,-46,50,6,-33,67,-47,-18,16,13,53,65,-54,9,36,-28,-12,30,34,-68,-9,60,14,-62}

    {-32,-42,-26,-25,-59,33,-14,21,-37,39,-37,-41,51,-65,-54,2,36,70,-68,-13,46,0,27,-18,20,2,46,-35,60}

    Returns: 4

  18. {-47,41,20,21,-42,6,54,54,4,23,-12,0,57,-22,66,70,-39,69,30,42,-62,-52,-66,7,60,64,53,-39,46,29,-10,44}

    {-49,-58,51,60,-22,-23,-40,-14,-56,12,-14,27,-56,-21,-16,48,16,-27,41,23,-47,-11,27,-11,20,-16,-18,-38,-33,22,62,4}

    Returns: 0

  19. {-65,-9,70}

    {-28,-15,14}

    Returns: -1

  20. {-59,-32,39,-14,49,69,37,33,51,-21,60,-3,-15,65,-45,28,-14,-69,-13,45}

    {-61,42,-52,-41,30,7,-40,37,8,-11,25,37,-4,35,-28,64,42,-66,64,12}

    Returns: 14

  21. {-5,70,37,11,-12,44,18}

    {30,15,-24,-39,69,-34,40}

    Returns: 31

  22. {-30,58,-4,-2,52,-66,-26,-65,18,-24,27,-10,-44,-42,-43,45,-42,-10,38,22,-60,28,-48,-46}

    {-41,-27,-54,67,-22,64,-53,51,36,-29,16,-43,57,39,27,58,-3,-61,63,35,16,-11,14,57}

    Returns: 0

  23. {35,4,39,34,6,4,-62,8,46,-70,60,11,49,-48,14,-16,-38,-19,42,-34,66,38,-37,40,31,20,-57,-46,32,-30,63,-23,19,0}

    {-41,5,-67,-25,-36,67,-56,15,-62,29,44,-65,-57,2,-28,-40,-56,43,0,67,-3,60,50,-54,-4,-61,37,-41,31,60,-36,-65,64,38}

    Returns: 7

  24. {35,-3,-20,60,13,21,13,33,-1,40,-15,11,28,-28,36,23,36,-42,-54,4,-1,6,7,-56,-14,39,14,54,-48,15,-50,-34,-21,-34,-56}

    {-18,-17,22,59,60,-42,2,-34,-61,-17,-58,-57,-64,-47,-56,-43,29,68,14,-30,-18,-45,3,36,14,-43,22,2,-52,62,65,10,62,-57,15}

    Returns: 10

  25. {-12,-48,61,34,62,7,-59,-10,13,23,4,-16,36,-12,-11}

    {27,66,-23,-3,0,17,-1,-21,-33,50,32,28,17,55,-67}

    Returns: 17

  26. {-63,-37,-58,17,2,-39,8,-43,55,-70,11,-68,55,-36,-14,34,-58,46,-14,48,20,-34,-18,17,-2,-67,-7,10,10,29,18,-45,12,36,5,15,51,-37,38,-44,70,-56,50,55,33,-38}

    {-64,-30,-1,6,16,-48,-28,33,-10,49,-40,24,-32,22,-10,-52,54,20,-29,63,-32,15,-57,-5,13,-68,-63,67,-66,54,4,-49,34,24,4,27,26,-12,-45,-53,-33,27,56,52,-70,-47}

    Returns: 4

  27. {-62,-66,-32,-38,10,18,43,-26,30,-50,-5,-39,-25}

    {1,-2,8,51,37,-15,-40,45,47,-57,-28,2,-69}

    Returns: 34

  28. {-12,67,44,-41,37,16,-37,-24,-35,-19,-24,53,46,-8,14,34,40,11,19,-5,38,-28,52,-5,-17,-8,59,-60,-29,-28,-5,38,-61,-15,-70,26,-8,35,40,-45,67}

    {64,-61,63,54,57,-27,-12,-67,-4,49,41,66,-28,-5,62,-7,6,47,69,27,39,-35,32,-15,-59,-21,-11,56,19,33,6,43,-41,24,-3,-18,65,-37,34,-14,70}

    Returns: 2

  29. {50,-37,-3,55,-41,-53,27,10,5,-35,43,-14,9}

    {-5,-39,-13,-36,-19,-21,9,43,21,-60,27,-25,30}

    Returns: 18

  30. {44,2,29,-44,-32,57,32,-58,69,-9,66,13,-11,2,16,-10,60,-22,40,-30,54,7,39,-68,59,35,-25,69,-48,18,-27,-6,19,32,37,41,-16,49}

    {-39,66,29,36,1,41,39,-68,-31,0,-31,-64,-59,60,44,-36,35,-51,17,32,26,-52,28,54,-21,66,-38,-64,23,53,-68,-57,-70,68,61,-57,-1,62}

    Returns: 1

  31. {-69,-17,-26,-46,31,31,59,18,-68,-1,-49,52,42,-40,-53,-64,-51,9,63,-14,8,63,-17,45,-31,-58,4,-37,-62,-27,39,-20,-51,-34,-23,-21,1,10,-33,59}

    {68,2,51,-47,10,-35,19,-43,-5,57,53,-38,22,-62,-56,37,23,55,-29,-52,1,33,18,49,61,-21,44,-12,10,34,17,35,14,-58,-23,-24,55,34,-16,-26}

    Returns: 6

  32. {-10,32,55,-65}

    {-57,-12,-53,23}

    Returns: 63

  33. {-1,7,25,-29,-70,33,3,-47,-34,-55}

    {-12,34,39,-47,-22,25,56,36,50,61}

    Returns: 20

  34. {-34,65,16,57,-26,-20,-22,-14,40,-54,2,-37,36,-44,-7,3}

    {6,37,-44,68,-43,54,-46,18,-40,-3,49,-7,-34,58,2,30}

    Returns: 18

  35. {-59,45,-39,31,2,-26,8,-69,-21,49,56,53,61,68,-17,27,-48,52,-32,-21,-36,8,-29,-36,70,-41,67,-26,13,19,-64,2,33,44,-24,-34,16,8}

    {-53,-42,54,67,-27,-9,-53,-24,9,27,21,-70,-18,-70,-57,13,-21,41,52,47,-43,-21,-28,61,0,-4,43,38,19,2,65,26,-19,-66,-34,28,-34,42}

    Returns: 7

  36. {54,42,-14,-70,-70,-56,51,61,21,67,13,5,57,-46,-2,-60,-13,28,22,-37,-7,-4,-62,33,63,52,42,32,66,-56,-18,42,21,5,-60,-37,32,-60,-34,-35,-49,-48}

    {-26,-51,11,-42,-57,9,47,-43,-58,51,50,-36,-38,-31,-62,23,-8,44,5,-21,56,-57,-57,24,-40,-43,-19,16,16,12,66,-24,44,-42,-40,16,-40,68,5,-25,51,-8}

    Returns: 1

  37. {54,-69,-26,12,-40,-55,-63,37,33,-47,41,47,-61,-52,5}

    {26,-59,31,-19,-46,34,32,1,-67,-47,31,-17,10,-62,66}

    Returns: 20

  38. {-10,-8,-46,25,41,-26,21,-31,12,-14,-17,-69,-35,65,24,-68,10,24,-37,66,-15,-2,-68,29,-37,15,-20,-69,-15,15,13,-48,-32,7,5,-15,62,-15,7,51,-29,54,-58}

    {-37,-41,63,10,-13,60,-41,19,7,-24,-29,-9,6,-52,61,68,-65,-38,-15,-37,-4,-37,-25,43,-30,54,-25,31,-11,-25,30,-39,31,40,-70,63,22,7,29,11,-4,-43,33}

    Returns: 4

  39. {11,46,-40,39,2,-55,4,-13,-70,33,20,66,-57,32,63,-14,-47,66,-7,19,-30,-26,-36,30,30,14,-47,58,-5}

    {-49,29,-17,7,4,3,-51,-14,54,-55,19,42,-51,-6,-67,-4,15,-56,-59,-20,19,-20,32,-32,24,-58,62,-36,25}

    Returns: 8

  40. {-4,30,46,-5,-34,-14,-65,68,-31,-33,29,-15,-1,64,-27,70,2,-43,-57,30,3,-2,33,41,-54,-65,-43,-57,44,12,-8,28,-22}

    {-4,-55,0,56,-4,-18,-60,-10,-15,-45,5,-16,49,31,38,43,7,32,-54,-57,-59,-28,17,68,60,-54,59,59,-45,-38,-14,7,16}

    Returns: 0

  41. {-49,-3,-60,61,19,-29,-26,49,-8,51,11,-68,13,62,-8,35,-55,9,-39,28,-1,5,32,13,55,31}

    {-10,-8,48,-46,20,-53,37,62,-49,-1,18,49,-3,14,15,-51,-32,-39,-2,45,21,-68,-68,69,-30,70}

    Returns: 17

  42. {-36,-33,-58,16,-21,17,-1,-14,31,-54,50,66,38,66,47,27,31,-59,1,-70,28,19,-6,-41,-68,-45,17,-15,60,18,-63,58,61,16,-40,3,7,19,-56,61,-37,-43,40,11,-7,46,-8,16,38,-19}

    {-23,37,-29,30,-64,54,-54,-3,-35,-14,34,-15,-31,0,53,63,-28,42,43,-38,9,63,-38,-31,5,-8,-48,50,-8,28,-40,-69,-27,52,-10,-34,-34,-21,66,-38,17,-22,18,58,-48,-1,-19,68,44,-17}

    Returns: 2

  43. {65,-68,40,56,2,-12,24,7,-15,12,-58,-1,58,-13,-35,6,56,19,16,54,2,-28,17,10,24,12,36,-54,-25,-31,-16,4,8,-23,13}

    {-34,20,-6,11,67,-1,26,-23,-2,-30,-34,47,-34,3,37,60,-29,6,-58,-23,-15,-6,-58,-60,20,26,59,-14,11,30,-60,60,-50,-31,-24}

    Returns: 0

  44. {-63,8,-45,8,-22,0,-50,-52,57,-41,17,-5,59,48,-40,-54,-37,25,-46,-13,-17,5}

    {70,-45,-55,-11,29,-48,-32,-62,-22,-17,-54,-36,-39,43,-61,53,32,10,6,-6,29,-68}

    Returns: 3

  45. {-24,15,-39,53,-54,-31,9,69,21,-47,34,55,-3,-7,39,-21,-21,-6,10,63,26,-59,-67,-16,-54,22,9,53,-24,-31,62,-36,5,6,36,43,21,61,-19,50,-15,-46,-35,-50,-23,-32}

    {10,-20,22,-15,-62,-19,27,36,-19,18,-47,28,17,-59,-60,-2,12,16,-30,-61,-62,-11,-25,22,-40,-30,-57,49,-64,-24,69,-30,-39,-6,28,5,-26,43,20,-47,48,46,-18,42,68,0}

    Returns: 3

  46. {13,38,40,42,-18,18,-6,-29,-53,66,-24,24,64,-33,-13,3,8,-34,-64,-5,70,-13,21,-69,29,-26,49,28}

    {4,-65,1,47,6,-9,55,-11,20,-37,-61,-4,-55,7,-55,-52,31,-37,-18,-11,-57,-42,-16,59,6,-58,-62,-54}

    Returns: 10

  47. {-49,27,-63,22,-25,-19,-54,-37,10,48,11,7,-21,47,0,-65,-43,0,24,23,29,36,-46,35,29,15,56,-54,-64,37,-62,-16,26,55,-11,0,-7,-35,37}

    {4,47,40,-43,-17,36,-56,9,25,-30,-23,-28,-42,-64,41,37,-61,-60,-8,19,16,67,-59,38,-34,-3,-30,65,-4,-38,52,-15,-27,20,-61,-68,18,-66,32}

    Returns: 6

  48. {-19,21,-42,49,55,-66,-45,-30,-68,-60,66,59,-25}

    {41,-49,-21,61,44,-65,-70,-38,40,-58,-19,-41,4}

    Returns: 19

  49. {52,34,-60,-64,-32,14,-51,36,26,-47,57,-19,-17,-25,-64,19,-33,-64,-12,0,-44,53,-70,2,55,53,3,64,18,-58,4}

    {-3,62,17,-1,-66,51,12,33,65,-40,31,26,66,54,34,-62,38,57,-30,51,-28,-19,66,-47,-46,57,-66,-35,-61,54,-50}

    Returns: 12

  50. {40,-35,29,55,19,38,-65,-21,54,-63,-32,35}

    {70,-26,-47,26,69,57,-68,58,-30,50,52,-37}

    Returns: 19

  51. {59,60,26,-64,-62,-9,-29,53,-23,26,-44,22,47,10,-53,-1,64,28,2}

    {10,62,11,52,30,36,68,-13,70,48,-18,68,-4,69,2,-66,-44,45,18}

    Returns: 21

  52. {46,17,-30,61,-3,55,21,1,-20,-20,-57,21,13,45,-69,4,52,10,-37}

    {-33,3,-19,19,19,-46,-19,26,13,-39,38,21,-14,-49,-65,37,37,-44,-23}

    Returns: 14

  53. {-43,-59,-66,1,1,32,-3}

    {-37,37,-35,-52,34,23,3}

    Returns: 33

  54. {-48,-59,54,63,49,-25,-68,45,-1,10,-5,-5,-4,15,18,16,22,-50,7,48,70,-20,25,-49}

    {18,15,2,-16,-45,-63,51,67,54,36,60,3,35,-11,7,-38,-12,33,30,-58,13,24,40,8}

    Returns: 9

  55. {39,39}

    {50,26}

    Returns: 22

  56. {14,23,27,-2,-6}

    {31,34,60,0,-6}

    Returns: -1

  57. {63,29,54}

    {10,-36,35}

    Returns: 69

  58. {51,63,-31,70}

    {-37,-69,30,-25}

    Returns: 42

  59. {6,21,15,29,-4,-14}

    {-29,56,45,43,68,-49}

    Returns: 12

  60. {15,-21,-58,1,52}

    {57,-68,-31,66,25}

    Returns: 95

  61. {-59,43,-35,-38,27}

    {-36,-9,8,42,-29}

    Returns: 76

  62. {26,14}

    {-61,-25}

    Returns: -1

  63. {0,-24,-57,25,-32}

    {66,-43,65,20,-12}

    Returns: 61

  64. {-43,37,46,-12,-69}

    {39,42,51,48,28}

    Returns: 56

  65. {-31,64,16}

    {23,-14,-23}

    Returns: 93

  66. {-8,11,-56,69,-43}

    {-48,22,67,65,25}

    Returns: 71

  67. {64,55}

    {5,-38}

    Returns: -1

  68. {-61,13,-16,10,31}

    {33,-46,-16,28,38}

    Returns: 69

  69. {59,32,23,67,20}

    {-6,51,-1,-26,-55}

    Returns: 47

  70. {-51,56}

    {37,54}

    Returns: -1

  71. {-7,56,20,-16,-1,8}

    {-70,39,56,-27,-26,-56}

    Returns: 28

  72. {46,-7,-25,-69,-59,6}

    {59,24,-44,38,-8,17}

    Returns: 51

  73. {35,62,0,-66,9}

    {52,69,63,14,-48}

    Returns: 60

  74. {25,3}

    {64,-7}

    Returns: -1

  75. {55,2,55}

    {-25,4,-8}

    Returns: 15

  76. {28,57,-32}

    {-45,64,-40}

    Returns: 107

  77. {24,-64,-44,60,-63}

    {56,-62,24,54,-63}

    Returns: 85

  78. {-35,44}

    {-53,4}

    Returns: -1

  79. {62,-15,36,-1,-12}

    {29,-40,19,45,30}

    Returns: 46

  80. {28,-3,-47}

    {-12,40,-65}

    Returns: 103

  81. {5,-55,22,-53,-5}

    {35,40,4,-13,-47}

    Returns: 58

  82. {-43,40,10,25,45,-23}

    {-68,60,-65,-4,4,-34}

    Returns: 51

  83. {-6,-66,-16,-19,-67,-28}

    {-38,61,-7,13,-25,-65}

    Returns: 49

  84. {38,-8,-61,-68,8,47}

    {38,-38,-69,58,-57,46}

    Returns: 67

  85. {-70,70}

    {0,0}

    Returns: 138

  86. {0,0}

    {70,-70}

    Returns: 138

  87. {0,1}

    {0,1}

    Returns: -1

  88. {39,49,31,34,60,0,-6,63,29,54,11,-37,-69,30,-25,-29,56,45,43,68,-49,15,-21,-58,1,52,-36,-9,8,42,26,14,36,66,-43,65,20,-12,37,46,-31,23,-14,-23,-8,-56,69,-39,5,-38}

    {39,49,31,34,60,0,-6,63,29,54,11,-37,-69,30,-25,-29,56,45,43,68,-49,15,-21,-58,1,52,-36,-9,8,42,26,14,36,66,-43,65,20,-12,37,46,-31,23,-14,-23,-8,-56,69,-39,5,-38}

    Returns: -1

  89. {33,-46,-16,28,38,59,32,23,67,20,-68,37,54,-7,56,-1,8,46,-25,-69,-59,6,48,52,69,63,14,-48,25,3,-33,4,-8,57,-32,-62,24,-63,-35,44,27,29,-40,19,45,30,-3,-47,35,40}

    {33,-46,-16,28,38,59,32,23,67,20,-68,37,54,-7,56,-1,8,46,-25,-69,-59,6,48,52,69,63,14,-48,25,3,-33,4,-8,57,-32,-62,24,-63,-35,44,27,29,-40,19,45,30,-3,-47,35,40}

    Returns: -1

  90. {-53,-5,62,-68,60,-65,-4,4,-34,-6,-66,-16,-19,-67,-28,61,38,-38,-69,58,-57,46,0,18,47,-48,-3,-18,-30,-58,-27,-56,40,-15,16,20,-13,-7,35,27,68,6,-24,2,31,-37,3,53,-46,-11}

    {-53,-5,62,-68,60,-65,-4,4,-34,-6,-66,-16,-19,-67,-28,61,38,-38,-69,58,-57,46,0,18,47,-48,-3,-18,-30,-58,-27,-56,40,-15,16,20,-13,-7,35,27,68,6,-24,2,31,-37,3,53,-46,-11}

    Returns: -1

  91. {39,49,31,34,60,0,-6,63,29,54,11,-37,-69,30,-25,-29,56,45,43,68,-49,15,-21,-58,1,52,-36,-9,8,42,26,14,36,66,-43,65,20,-12,37,46,-31,23,-14,-23,-8,-56,69,-43,-39,5}

    {39,49,31,34,60,0,-6,63,29,54,11,-37,-69,30,-25,-29,56,45,43,68,-49,15,-21,-58,1,52,-36,-9,8,42,26,14,36,66,-43,65,20,-12,37,46,-31,23,-14,-23,-8,-56,65,25,64,55}

    Returns: 1

  92. {52,33,-46,-16,28,38,59,32,23,67,20,-68,37,54,-7,56,-1,8,46,-25,-69,-59,6,48,69,63,14,-48,25,3,-33,4,-8,57,-32,-62,24,-63,-35,44,27,29,-40,19,45,30,28,-3,-47,32}

    {52,33,-46,-16,28,38,59,32,23,67,20,-68,37,54,-7,56,-1,8,46,-25,-69,-59,6,48,69,63,14,-48,25,3,-33,4,-8,57,-32,-62,24,-63,-35,44,27,29,-40,19,45,30,-12,40,-65,5}

    Returns: 13

  93. {-55,22,-53,-5,62,-68,60,-65,-4,4,-34,-6,-66,-16,-19,-67,-28,61,38,-38,-69,58,-57,46,0,18,47,-48,-3,-18,-30,-58,-27,-56,40,-15,16,20,-13,-7,35,27,68,6,-24,2,31,-37,3,53}

    {-55,22,-53,-5,62,-68,60,-65,-4,4,-34,-6,-66,-16,-19,-67,-28,61,38,-38,-69,58,-57,46,0,18,47,-48,-3,-18,-30,-58,-27,-56,40,-15,16,20,-13,-7,35,27,68,6,-24,2,57,-64,70,64}

    Returns: 5

  94. {57,37,-58,-35,-24,65,59,48,27,19,54,-55,-8,68,-48,56,12,38,-34,42,30,16,-59,62,-18,25,-68,-60,67,-2,44,36,-21,-36,-51,22,53,-56,47,18,-12,-29,-33,-7,-50,-67,39,18,-15,-50}

    {57,37,-58,-35,-24,65,59,48,27,19,54,-55,-8,68,-48,56,12,38,-34,42,30,16,-59,62,-18,25,-68,-60,67,-2,44,36,-21,-36,-51,22,53,-56,47,18,-12,-29,-33,-7,-50,-67,-12,-19,-24,-23}

    Returns: 4

  95. {-14,-11,-66,54,-69,-48,-37,-33,69,-62,-25,-52,-31,-68,-60,66,1,-35,-26,-10,67,56,13,50,30,-32,29,-39,-55,-7,-16,45,52,9,-9,-40,-45,5,-41,-56,-17,8,51,17,70,37,-27,13,63,-37}

    {-14,-11,-66,54,-69,-48,-37,-33,69,-62,-25,-52,-31,-68,-60,66,1,-35,-26,-10,67,56,13,50,30,-32,29,-39,-55,-7,-16,45,52,9,-9,-40,-45,5,-41,-56,-17,8,51,17,70,37,-15,55,24,44}

    Returns: 8

  96. {-22,53,69,24,16,13,-19,0,11,-33,35,21,-40,27,-45,5,-53,7,-62,-59,20,-63,-16,-31,9,-5,44,34,36,3,-47,-9,29,18,-66,-39,33,46,70,-41,42,-61,-6,32,-25,51,-32,-54,9,53}

    {-22,53,69,24,16,13,-19,0,11,-33,35,21,-40,27,-45,5,-53,7,-62,-59,20,-63,-16,-31,9,-5,44,34,36,3,-47,-9,29,18,-66,-39,33,46,70,-41,42,-61,-6,32,-25,51,-52,-65,-30,-67}

    Returns: 5

  97. {18,-69,-40,53,-10,-21,-49,-57,-7,7,68,-5,-63,-22,-59,69,-62,32,15,-67,-33,-46,50,6,67,-47,-18,16,13,65,-54,9,36,-28,-12,30,34,-68,-9,60,14,57,-58,51,-23,-14,-56,12,-14,27}

    {18,-69,-40,53,-10,-21,-49,-57,-7,7,68,-5,-63,-22,-59,69,-62,32,15,-67,-33,-46,50,6,67,-47,-18,16,13,65,-54,9,36,-28,-12,30,34,-68,-9,60,14,57,-58,51,-23,-14,23,-12,0,57}

    Returns: 7

  98. {-22,66,70,-39,69,30,42,-62,-52,-66,7,60,64,53,46,29,-10,44,-28,-15,14,-59,-32,39,-14,49,37,33,51,-21,-3,65,-45,28,-69,-13,45,15,-24,-34,40,-30,58,-4,-2,52,-66,-26,-65,18}

    {-22,66,70,-39,69,30,42,-62,-52,-66,7,60,64,53,46,29,-10,44,-28,-15,14,-59,-32,39,-14,49,37,33,51,-21,-3,65,-45,28,-69,-13,45,15,-24,-34,40,-30,58,-4,-2,52,64,-53,51,36}

    Returns: 9

  99. {-29,16,-43,57,39,27,58,-3,-61,63,35,-11,14,4,34,6,-62,8,46,-70,60,11,49,-48,-16,-38,-19,42,-34,66,38,-37,40,31,20,-57,-46,32,-30,-23,19,0,-18,-17,22,59,60,-42,2,-34}

    {-29,16,-43,57,39,27,58,-3,-61,63,35,-11,14,4,34,6,-62,8,46,-70,60,11,49,-48,-16,-38,-19,42,-34,66,38,-37,40,31,20,-57,-46,32,-30,-23,19,0,-18,-17,22,59,21,13,33,-1}

    Returns: 15

  100. {40,-15,11,28,-28,36,23,-42,-54,4,-1,6,7,-56,-14,39,14,54,-48,15,-50,-34,-21,-12,27,66,-23,-3,0,17,-33,50,32,55,-67,-64,-30,16,33,-10,49,-40,24,-32,22,-52,54,20,-29,63}

    {40,-15,11,28,-28,36,23,-42,-54,4,-1,6,7,-56,-14,39,14,54,-48,15,-50,-34,-21,-12,27,66,-23,-3,0,17,-33,50,32,55,-67,-64,-30,16,33,-10,49,-40,24,-32,22,-52,46,-14,48,20}

    Returns: 3

  101. {-34,-18,17,-2,-67,-7,10,29,18,-45,12,36,5,15,51,-37,38,-44,70,-56,50,55,33,-38,-22,1,8,37,-15,-40,45,47,-57,-28,2,-69,64,-61,63,54,57,-27,-12,-4,49,41,66,-28,-5,62}

    {-34,-18,17,-2,-67,-7,10,29,18,-45,12,36,5,15,51,-37,38,-44,70,-56,50,55,33,-38,-22,1,8,37,-15,-40,45,47,-57,-28,2,-69,64,-61,63,54,57,-27,-12,-4,49,41,46,-8,14,34}

    Returns: 9

  102. {40,11,19,-5,38,-28,52,-17,-8,59,-60,-29,-61,-15,-70,26,35,-45,67,-21,-39,-13,-36,-19,9,43,21,27,-25,30,66,29,36,1,41,39,-68,-31,0,-64,-59,60,44,-51,17,32,26,-52,28,54}

    {40,11,19,-5,38,-28,52,-17,-8,59,-60,-29,-61,-15,-70,26,35,-45,67,-21,-39,-13,-36,-19,9,43,21,27,-25,30,66,29,36,1,41,39,-68,-31,0,-64,-59,60,44,-51,17,32,7,39,-68,59}

    Returns: 3

  103. {35,-25,69,-48,18,-27,-6,19,32,37,41,-16,49,-69,-17,-26,-46,31,59,-68,-1,-49,52,42,-40,-53,-64,-51,9,63,-14,8,45,-31,-58,4,-37,-62,39,-20,-34,-23,-21,1,10,-33,59,-55,-57,-12}

    {35,-25,69,-48,18,-27,-6,19,32,37,41,-16,49,-69,-17,-26,-46,31,59,-68,-1,-49,52,42,-40,-53,-64,-51,9,63,-14,8,45,-31,-58,4,-37,-62,39,-20,-34,-23,-21,1,10,-33,-26,-10,32,55}

    Returns: 22

  104. {-65,-31,-12,34,39,-47,-22,25,56,36,50,61,-34,65,16,57,-26,-20,-14,40,-54,2,-37,-44,-7,3,-59,45,-39,31,8,-69,-21,49,53,68,-17,27,-48,52,-32,-36,-29,70,-41,67,-26,13,19,-64}

    {-65,-31,-12,34,39,-47,-22,25,56,36,50,61,-34,65,16,57,-26,-20,-14,40,-54,2,-37,-44,-7,3,-59,45,-39,31,8,-69,-21,49,53,68,-17,27,-48,52,-32,-36,-29,70,-41,67,38,19,2,65}

    Returns: 9

  105. {26,-19,-66,-34,28,42,-26,-51,11,-42,-57,9,47,-43,-58,51,50,-36,-38,-31,-62,23,-8,44,5,-21,56,24,-40,16,12,66,-24,68,-25,54,-69,-55,-63,37,33,-47,41,-61,-52,-10,-8,-46,25,41}

    {26,-19,-66,-34,28,42,-26,-51,11,-42,-57,9,47,-43,-58,51,50,-36,-38,-31,-62,23,-8,44,5,-21,56,24,-40,16,12,66,-24,68,-25,54,-69,-55,-63,37,33,-47,41,-61,-52,-10,-41,63,10,-13}

    Returns: 11

  106. {33,-46,-16,28,38,59,32,23,67,20,-68,37,54,-7,56,-1,8,46,-25,-69,-59,6,48,52,69,63,14,-48,25,3,-33,4,-8,57,-32,-62,24,-63,-35,44,27,29,-40,19,45,30,-3,-47,35,-70}

    {33,-46,-16,28,38,59,32,23,67,20,-68,37,54,-7,56,-1,8,46,-25,-69,-59,6,48,52,69,63,14,-48,25,3,-33,4,-8,57,-32,-62,24,-63,-35,44,27,29,-40,19,45,30,-3,-47,35,70}

    Returns: 71

  107. {-70,70}

    {-70,-69}

    Returns: -1

  108. {-70,70,0}

    {-70,-69,50}

    Returns: 138

  109. {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6}

    {0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6}

    Returns: -1

  110. {-41, -40, 1, -11, -32, -7, 24, -11, 49, -15, -22, 20, -8, 54, 54, 69, 16, -30, 36, -6, -30, 40, 64, 20, -66, -37, -33, -18, -35, 36, 9, 61, -43, 45, 5, 60, -8, -58, 65, -66, 41, 12, 34, -11, -57, -38, 46, 63, -55, 3 }

    {5, -24, -2, -4, 23, 14, 1, 70, -26, 45, 15, 48, 32, -41, 54, -47, -67, -46, -9, -53, 54, 28, -61, 11, 53, 68, -33, 62, 37, -8, -17, -17, 48, 19, -49, 56, -41, 16, 17, -50, 28, 59, 10, 50, 23, -16, 56, 31, -70, -44 }

    Returns: 9

  111. {0, 0 }

    {-70, 70 }

    Returns: 138

  112. {-70, -70, 70, 70, -32, -7, 24, -11, 49, -15, -22, 20, -8, 54, 54, 69, 16, -30, 36, -6, -30, 40, 64, 20, -26, -37, -33, -18, -35, 36, 9, 61, -43, 45, 5, 60, -8, -58, 65, -66, 41, 12, 34, -11, -57, -38, 46, 63, -55, 3 }

    {70, -70, -70, 69, 23, 14, 1, 70, -26, 45, 15, 48, 32, -41, 54, -47, -67, -46, -9, -53, 54, 28, -61, 11, 53, 68, -33, 62, 37, -8, -17, -17, 48, 19, -49, 56, -41, 16, 17, -50, 28, 59, 10, 50, 23, -16, 56, 31, -70, -44 }

    Returns: 9

  113. {0, 70, 70, 0 }

    {0, 0, 70, 70 }

    Returns: 68

  114. {0, 3 }

    {0, 0 }

    Returns: 1

  115. {70, -70 }

    {70, -70 }

    Returns: -1

  116. {-70, 0, 70 }

    {0, 70, -70 }

    Returns: 138

  117. {0, 0, 1, 1 }

    {0, 1, 0, 1 }

    Returns: -1

  118. {-70, -70, 70, 70 }

    {-70, 70, -70, 70 }

    Returns: 138

  119. {-70, 70 }

    {-70, 70 }

    Returns: -1

  120. {-70, -70 }

    {-70, 70 }

    Returns: 138

  121. {-70, 70, -69, 69 }

    {-70, 70, 69, -69 }

    Returns: 137

  122. {-70, 70 }

    {0, 0 }

    Returns: 138

  123. {0, 0 }

    {0, 1 }

    Returns: -1

  124. {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6 }

    {0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6 }

    Returns: -1

  125. {-66, -68, -67, -68, -65, -67, -67, -67, -66, -70, -67, -69, -69, -69, -67, -65, -66, -69, -65, -68, -65, -65, -70, -67, -66, -65, -68, 68, -67, -66, -69, -69, -70, -69, -70, -68, -69, -66, -65, -68, -70, -70, -69, -70, -66, -65, -68, -68, -66, -70 }

    {63, 67, 66, 65, 70, 69, 68, 64, 67, 69, 70, 68, 70, 65, 65, 63, 65, 69, 68, 68, 69, 67, 66, 67, 69, 66, 69, 67, 63, 68, -70, 67, 63, 66, 65, 70, 63, 70, 64, 64, 68, 67, 64, 70, 64, 65, 66, 63, 66, 64 }

    Returns: 131

  126. {0, 1, 2, 0, 1, 2, 0, 1, 2 }

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

    Returns: -1

  127. {0, 1 }

    {0, 1 }

    Returns: -1

  128. {0, 51 }

    {0, 0 }

    Returns: 49

  129. {70, 70 }

    {70, -70 }

    Returns: 138

  130. {0, 0, 0, 1, 1, 1, 2, 2, 2 }

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

    Returns: -1

  131. {70, 70, -70, -70 }

    {70, -70, 70, -70 }

    Returns: 138

  132. {0, 1, 0 }

    {0, 1, 2 }

    Returns: 0

  133. {-70, -69, -68, -67, -69, -70, 70, 70 }

    {-70, -69, -68, -67, -70, 70, -70, 70 }

    Returns: 136

  134. {-70, 69 }

    {0, 0 }

    Returns: 137

  135. {-70, 70, -70, 70 }

    {-70, -70, 70, 70 }

    Returns: 138

  136. {68, 70 }

    {50, 50 }

    Returns: 0

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.
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