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  1. # Generated tables
  2. original_dp_table = [[4, 6, 6, 6, 8, 5, 9, 0, 0, 0, 3, 4, 4, 9, 2, 6, 5, 6, 0, 0, 7, 3, 3, 3, 3, 3, 3, 8, 5, 0, 4, 5, 4, 4, 4, 4, 5, 7, 5, 0, 5, 5, 7, 5, 5, 5, 6, 5, 6, 0, 6, 6, 6, 5, 6, 6, 0, 6, 7, 6, 7, 6, 7, 4, 8, 7, 8, 7, 8, 8, 7, 8, 8, 8, 9, 8, 9, 4, 9, 8, 9, 9, 10, 9, 0, 9, 10, 9, 10, 0, 10, 0, 10, 0, 10, 5, 10, 10, 3, 10, 0], [7, 6, 6, 8, 5, 10, 0, 8, 8, 0, 7, 0, 4, 6, 5, 0, 0, 5, 0, 7, 3, 3, 3, 0, 3, 3, 7, 0, 0, 0, 3, 5, 4, 6, 5, 4, 4, 7, 0, 0, 5, 4, 5, 5, 5, 5, 5, 6, 0, 0, 6, 6, 6, 5, 6, 4, 6, 6, 7, 0, 7, 6, 4, 6, 7, 7, 7, 7, 8, 0, 8, 7, 8, 8, 8, 8, 0, 8, 9, 8, 9, 0, 9, 0, 10, 0, 10, 9, 10, 10, 0, 0, 10, 10, 0, 5, 10, 3, 10, 10, 0], [7, 5, 6, 5, 8, 6, 8, 0, 0, 0, 3, 10, 1, 4, 0, 5, 5, 0, 0, 0, 2, 5, 2, 5, 3, 6, 4, 5, 3, 0, 3, 3, 4, 4, 4, 4, 4, 0, 0, 0, 6, 4, 5, 5, 5, 5, 5, 0, 0, 0, 5, 6, 6, 5, 8, 5, 6, 6, 6, 0, 7, 4, 7, 6, 7, 6, 7, 7, 0, 7, 8, 7, 8, 7, 8, 0, 8, 7, 0, 0, 0, 8, 0, 8, 9, 9, 10, 9, 10, 0, 10, 0, 10, 0, 10, 0, 3, 10, 10, 10, 0], [6, 5, 5, 8, 4, 4, 8, 8, 8, 0, 0, 0, 0, 0, 4, 5, 0, 0, 0, 0, 2, 5, 2, 2, 8, 3, 3, 5, 5, 0, 3, 5, 4, 5, 3, 4, 4, 5, 4, 0, 4, 4, 4, 5, 5, 5, 0, 5, 5, 0, 5, 5, 6, 6, 6, 5, 6, 6, 0, 5, 0, 5, 7, 6, 7, 6, 7, 0, 0, 7, 7, 7, 8, 0, 0, 7, 8, 7, 8, 7, 9, 0, 9, 8, 9, 9, 9, 9, 0, 0, 10, 10, 10, 9, 10, 3, 10, 10, 10, 10, 0], [7, 5, 6, 5, 7, 8, 8, 0, 0, 7, 9, 10, 4, 4, 4, 4, 5, 0, 0, 0, 5, 6, 2, 8, 3, 0, 5, 0, 8, 0, 3, 3, 3, 5, 3, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 0, 5, 5, 5, 0, 5, 5, 7, 0, 5, 5, 6, 5, 6, 0, 6, 5, 6, 5, 7, 6, 0, 6, 7, 7, 7, 7, 8, 0, 8, 7, 8, 0, 0, 7, 0, 8, 9, 0, 9, 8, 9, 0, 10, 9, 10, 0, 10, 9, 2, 4, 10, 10, 10, 10, 0], [6, 8, 2, 4, 7, 8, 7, 7, 0, 0, 6, 10, 10, 8, 4, 4, 0, 5, 4, 6, 5, 6, 1, 2, 4, 5, 2, 0, 0, 0, 3, 4, 3, 4, 3, 0, 3, 0, 4, 0, 4, 4, 4, 4, 0, 0, 4, 5, 0, 0, 5, 3, 5, 4, 5, 4, 5, 0, 0, 0, 6, 5, 6, 5, 6, 0, 7, 6, 7, 0, 7, 0, 0, 7, 7, 7, 8, 7, 8, 0, 8, 7, 8, 8, 9, 8, 2, 8, 9, 9, 10, 9, 10, 2, 10, 4, 10, 10, 10, 10, 0], [7, 5, 5, 7, 7, 8, 7, 7, 0, 0, 6, 9, 9, 8, 10, 5, 4, 0, 0, 6, 6, 6, 2, 6, 0, 0, 0, 0, 2, 0, 2, 4, 3, 4, 0, 4, 0, 6, 3, 0, 3, 4, 4, 0, 4, 4, 4, 4, 0, 0, 6, 0, 5, 4, 5, 4, 5, 0, 6, 0, 6, 5, 0, 5, 0, 5, 6, 0, 7, 0, 7, 0, 7, 0, 7, 7, 0, 0, 0, 0, 8, 0, 8, 7, 8, 0, 9, 8, 9, 8, 9, 0, 5, 9, 10, 4, 10, 10, 10, 10, 0], [5, 7, 5, 0, 0, 8, 7, 0, 7, 0, 6, 9, 3, 8, 0, 0, 10, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 3, 0, 3, 0, 3, 0, 3, 3, 0, 4, 4, 4, 0, 0, 4, 0, 0, 4, 4, 4, 5, 4, 0, 4, 5, 4, 5, 4, 6, 0, 6, 5, 6, 0, 6, 6, 0, 6, 7, 6, 7, 6, 0, 0, 7, 7, 8, 0, 8, 7, 0, 0, 8, 8, 9, 8, 9, 1, 9, 8, 10, 3, 10, 10, 10, 10, 0], [6, 7, 5, 6, 0, 0, 0, 7, 7, 6, 10, 9, 9, 4, 7, 4, 0, 0, 10, 5, 1, 0, 0, 0, 7, 0, 1, 0, 0, 0, 0, 0, 2, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 4, 4, 4, 0, 0, 4, 0, 4, 3, 5, 0, 5, 4, 5, 0, 5, 4, 0, 4, 6, 0, 6, 5, 6, 0, 6, 6, 7, 6, 7, 6, 10, 6, 7, 6, 7, 7, 8, 1, 8, 7, 0, 8, 9, 8, 1, 8, 9, 8, 9, 3, 10, 10, 10, 10, 0], [7, 7, 8, 4, 0, 0, 7, 7, 7, 8, 0, 9, 4, 7, 0, 3, 4, 4, 10, 7, 10, 6, 7, 7, 1, 8, 1, 6, 8, 1, 1, 4, 8, 4, 2, 6, 2, 10, 10, 9, 0, 3, 3, 3, 3, 3, 4, 2, 4, 4, 4, 4, 4, 3, 0, 4, 5, 4, 5, 4, 5, 0, 5, 5, 5, 5, 6, 5, 8, 6, 6, 6, 6, 6, 7, 7, 7, 6, 7, 6, 7, 7, 10, 7, 8, 7, 8, 0, 8, 8, 9, 8, 9, 8, 9, 3, 10, 9, 10, 9, 0], [6, 7, 5, 7, 0, 7, 7, 7, 8, 5, 9, 3, 8, 7, 7, 3, 0, 10, 0, 0, 5, 6, 10, 7, 7, 0, 7, 7, 0, 9, 9, 9, 2, 0, 9, 10, 2, 0, 0, 0, 3, 0, 3, 3, 3, 10, 0, 4, 3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 0, 4, 5, 4, 5, 5, 5, 5, 6, 0, 6, 5, 6, 6, 9, 6, 7, 6, 7, 0, 7, 4, 7, 7, 7, 7, 8, 7, 0, 8, 9, 8, 9, 0, 9, 0, 9, 9, 9, 9, 0], [7, 7, 8, 0, 7, 0, 0, 7, 0, 8, 5, 8, 8, 0, 7, 3, 10, 0, 0, 0, 5, 6, 6, 7, 10, 8, 7, 7, 8, 0, 0, 10, 1, 9, 1, 0, 0, 10, 3, 9, 0, 10, 2, 3, 3, 4, 3, 3, 3, 0, 3, 10, 5, 0, 4, 3, 4, 4, 4, 0, 5, 4, 5, 4, 5, 5, 7, 5, 6, 5, 6, 5, 6, 7, 6, 5, 6, 6, 7, 6, 9, 6, 7, 6, 7, 0, 8, 0, 8, 7, 8, 0, 9, 8, 10, 0, 9, 9, 9, 9, 0], [6, 7, 4, 6, 7, 7, 6, 6, 8, 0, 9, 8, 8, 7, 6, 10, 0, 0, 0, 5, 5, 5, 6, 3, 6, 7, 8, 8, 0, 9, 1, 8, 0, 0, 0, 9, 9, 0, 0, 0, 2, 10, 2, 10, 3, 10, 3, 10, 3, 0, 3, 4, 3, 3, 4, 3, 4, 0, 0, 0, 4, 3, 5, 4, 5, 4, 5, 5, 5, 0, 5, 0, 0, 5, 6, 5, 6, 5, 6, 0, 7, 6, 7, 6, 7, 7, 0, 7, 8, 7, 8, 0, 8, 0, 8, 0, 9, 8, 9, 9, 0], [7, 3, 3, 7, 7, 7, 0, 0, 5, 0, 9, 8, 8, 6, 7, 3, 0, 0, 0, 0, 5, 5, 3, 6, 6, 7, 7, 7, 9, 0, 8, 8, 1, 8, 1, 9, 0, 8, 1, 9, 2, 2, 2, 3, 2, 9, 10, 0, 0, 10, 4, 10, 3, 2, 3, 3, 4, 0, 4, 0, 4, 3, 4, 4, 0, 4, 5, 5, 5, 0, 5, 0, 5, 5, 6, 5, 6, 0, 0, 0, 6, 6, 7, 0, 7, 0, 7, 7, 7, 7, 8, 7, 0, 7, 8, 2, 8, 8, 9, 10, 0], [3, 6, 7, 6, 7, 7, 6, 0, 7, 0, 8, 8, 7, 7, 0, 0, 10, 10, 8, 0, 5, 3, 5, 6, 6, 0, 0, 0, 0, 8, 10, 8, 8, 8, 9, 1, 1, 8, 0, 0, 1, 10, 2, 2, 2, 2, 2, 10, 10, 0, 0, 0, 0, 2, 3, 0, 0, 0, 4, 0, 4, 3, 4, 0, 4, 4, 4, 4, 0, 5, 0, 5, 5, 5, 5, 5, 6, 0, 6, 0, 6, 5, 0, 0, 0, 6, 7, 0, 7, 0, 8, 0, 8, 0, 8, 2, 8, 8, 10, 8, 0], [6, 2, 7, 6, 6, 7, 0, 0, 0, 7, 8, 7, 8, 2, 6, 0, 0, 9, 0, 10, 2, 5, 5, 6, 6, 7, 6, 0, 0, 0, 0, 8, 10, 8, 1, 0, 1, 0, 1, 9, 0, 0, 1, 0, 2, 9, 2, 0, 0, 0, 2, 3, 3, 0, 3, 0, 3, 0, 3, 0, 4, 3, 0, 4, 4, 4, 4, 4, 0, 0, 5, 4, 5, 0, 5, 0, 0, 5, 0, 5, 6, 0, 6, 0, 6, 6, 7, 6, 7, 6, 0, 7, 8, 6, 8, 1, 8, 10, 8, 8, 0], [5, 7, 7, 5, 6, 0, 6, 5, 0, 0, 8, 7, 0, 6, 0, 0, 9, 9, 8, 0, 4, 5, 5, 6, 0, 6, 0, 7, 7, 0, 8, 7, 8, 3, 10, 10, 1, 8, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 10, 0, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 5, 4, 5, 0, 5, 4, 5, 5, 0, 5, 0, 5, 6, 6, 6, 6, 7, 0, 7, 0, 7, 6, 8, 1, 10, 8, 8, 8, 0], [4, 5, 6, 7, 0, 7, 5, 5, 0, 0, 8, 1, 7, 6, 6, 10, 9, 9, 0, 0, 4, 4, 0, 5, 6, 0, 6, 6, 0, 0, 7, 8, 0, 7, 0, 8, 10, 8, 1, 0, 1, 0, 1, 0, 0, 0, 2, 9, 2, 10, 2, 0, 2, 0, 0, 0, 3, 0, 3, 10, 0, 0, 3, 0, 4, 0, 4, 0, 4, 4, 4, 0, 4, 4, 0, 4, 5, 4, 5, 0, 5, 0, 6, 5, 6, 6, 6, 6, 1, 6, 7, 6, 7, 6, 7, 1, 8, 7, 8, 8, 0], [4, 6, 7, 5, 6, 7, 5, 5, 7, 7, 3, 7, 8, 0, 5, 10, 9, 0, 8, 10, 4, 4, 5, 5, 0, 0, 6, 0, 6, 0, 8, 5, 7, 8, 0, 8, 8, 8, 10, 0, 9, 9, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 2, 0, 2, 0, 3, 0, 3, 0, 3, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 5, 0, 5, 0, 0, 4, 5, 4, 6, 5, 6, 1, 6, 6, 7, 6, 7, 6, 9, 1, 7, 7, 8, 7, 0], [6, 7, 4, 7, 6, 7, 7, 0, 7, 0, 2, 7, 7, 8, 5, 10, 3, 8, 8, 10, 4, 4, 9, 7, 5, 6, 6, 6, 0, 7, 4, 7, 8, 0, 8, 7, 8, 4, 8, 10, 10, 10, 1, 10, 1, 0, 1, 9, 1, 0, 0, 0, 10, 1, 2, 10, 2, 10, 3, 10, 3, 0, 3, 0, 3, 0, 3, 3, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 8, 5, 6, 6, 6, 6, 7, 7, 7, 10, 7, 7, 7, 7, 0], [7, 4, 7, 6, 6, 6, 7, 0, 0, 0, 7, 7, 8, 6, 9, 0, 9, 8, 0, 0, 7, 10, 0, 5, 5, 5, 6, 6, 6, 0, 7, 8, 7, 8, 7, 9, 4, 8, 9, 7, 9, 10, 10, 10, 10, 8, 1, 0, 0, 10, 2, 0, 0, 10, 2, 10, 2, 0, 0, 0, 2, 10, 3, 10, 4, 3, 3, 3, 3, 0, 4, 0, 4, 3, 4, 4, 4, 4, 6, 0, 5, 4, 5, 4, 5, 7, 5, 5, 6, 0, 6, 6, 8, 5, 7, 10, 7, 7, 7, 9, 0], [4, 6, 7, 6, 6, 6, 7, 0, 0, 0, 1, 5, 7, 8, 5, 9, 8, 8, 7, 0, 10, 5, 8, 5, 5, 5, 5, 6, 0, 7, 7, 7, 8, 7, 8, 3, 8, 8, 0, 0, 8, 9, 4, 10, 10, 10, 1, 9, 10, 0, 1, 10, 1, 10, 0, 10, 0, 10, 2, 10, 2, 0, 2, 0, 3, 0, 3, 3, 3, 10, 4, 3, 4, 3, 4, 3, 4, 0, 4, 0, 4, 4, 5, 4, 7, 0, 5, 5, 5, 0, 6, 7, 6, 5, 6, 10, 7, 6, 9, 7, 0], [6, 6, 7, 7, 5, 7, 0, 4, 4, 6, 6, 5, 7, 5, 8, 9, 8, 0, 0, 9, 4, 10, 8, 4, 5, 5, 5, 0, 6, 0, 7, 7, 7, 8, 7, 8, 7, 8, 8, 0, 9, 0, 8, 8, 8, 10, 10, 10, 1, 10, 1, 10, 1, 10, 1, 0, 1, 10, 2, 10, 2, 10, 3, 10, 2, 0, 3, 0, 3, 0, 3, 0, 3, 3, 4, 0, 0, 0, 4, 3, 0, 0, 4, 0, 5, 0, 5, 5, 5, 0, 0, 5, 6, 5, 6, 6, 6, 8, 7, 6, 0], [6, 6, 7, 6, 6, 3, 0, 0, 6, 0, 6, 5, 2, 7, 8, 9, 8, 7, 7, 0, 3, 10, 8, 4, 4, 5, 0, 0, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 0, 8, 3, 8, 8, 8, 9, 8, 9, 9, 10, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 0, 10, 2, 10, 2, 10, 2, 10, 4, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 5, 0, 5, 0, 5, 5, 6, 5, 6, 6, 8, 6, 6, 6, 0], [6, 6, 6, 7, 3, 6, 0, 0, 6, 0, 7, 0, 6, 7, 8, 9, 0, 0, 0, 0, 10, 3, 8, 4, 4, 0, 5, 5, 0, 0, 6, 7, 5, 7, 7, 7, 7, 7, 7, 0, 8, 8, 8, 7, 8, 10, 0, 8, 9, 9, 10, 10, 10, 1, 1, 10, 1, 10, 1, 10, 2, 0, 0, 10, 2, 10, 2, 0, 2, 0, 3, 0, 3, 0, 4, 0, 3, 3, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 5, 0, 5, 0, 6, 7, 6, 6, 6, 6, 0], [6, 5, 7, 4, 6, 6, 0, 0, 6, 0, 6, 7, 4, 0, 8, 9, 7, 0, 0, 0, 10, 10, 7, 4, 0, 0, 5, 0, 5, 0, 6, 6, 7, 7, 7, 0, 7, 0, 0, 7, 0, 7, 8, 7, 0, 8, 8, 9, 8, 9, 8, 10, 10, 10, 1, 10, 1, 10, 1, 0, 1, 10, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 3, 2, 3, 0, 3, 3, 0, 3, 4, 0, 0, 0, 4, 0, 0, 4, 5, 4, 5, 4, 7, 5, 6, 5, 6, 6, 0], [5, 6, 5, 6, 0, 5, 0, 0, 6, 0, 6, 6, 6, 6, 4, 8, 0, 7, 0, 8, 10, 10, 8, 5, 4, 4, 4, 5, 0, 6, 5, 6, 6, 7, 7, 6, 7, 0, 0, 7, 7, 8, 7, 7, 0, 0, 9, 8, 9, 8, 9, 2, 0, 10, 10, 10, 1, 10, 1, 10, 1, 9, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 0, 4, 4, 0, 5, 0, 5, 5, 5, 5, 5, 5, 6, 5, 0], [6, 2, 6, 6, 5, 0, 6, 7, 0, 5, 6, 6, 6, 0, 0, 0, 7, 7, 6, 0, 10, 10, 4, 0, 0, 4, 4, 5, 5, 0, 6, 6, 0, 5, 6, 7, 0, 6, 7, 7, 6, 7, 8, 0, 7, 6, 8, 9, 8, 9, 0, 0, 9, 0, 9, 10, 10, 9, 1, 10, 1, 10, 1, 10, 2, 10, 1, 10, 2, 10, 0, 2, 2, 0, 2, 0, 3, 0, 4, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 4, 4, 4, 6, 4, 5, 5, 5, 5, 5, 7, 0], [5, 0, 6, 0, 0, 4, 6, 0, 0, 6, 5, 6, 6, 6, 0, 8, 7, 6, 7, 8, 9, 0, 7, 10, 3, 4, 4, 4, 0, 5, 6, 0, 6, 6, 6, 5, 6, 7, 0, 0, 7, 7, 0, 6, 8, 6, 7, 8, 9, 8, 8, 9, 8, 9, 9, 9, 8, 10, 10, 9, 1, 9, 1, 0, 1, 10, 1, 1, 1, 1, 2, 0, 0, 0, 2, 0, 2, 0, 3, 0, 3, 1, 3, 1, 4, 1, 4, 1, 4, 0, 4, 5, 4, 3, 5, 4, 5, 5, 7, 5, 0], [6, 6, 6, 6, 6, 6, 0, 0, 6, 0, 6, 0, 6, 3, 0, 0, 7, 7, 6, 8, 6, 9, 7, 0, 3, 4, 4, 0, 0, 0, 0, 6, 6, 7, 5, 6, 6, 6, 7, 7, 8, 5, 8, 8, 8, 9, 8, 9, 7, 8, 8, 8, 9, 9, 10, 0, 9, 10, 9, 10, 10, 10, 1, 10, 1, 10, 1, 10, 1, 2, 1, 10, 2, 10, 0, 10, 3, 10, 2, 10, 3, 1, 3, 0, 3, 0, 3, 0, 4, 3, 5, 3, 4, 3, 4, 4, 5, 6, 5, 5, 0], [6, 6, 6, 5, 7, 0, 6, 6, 0, 0, 5, 6, 5, 6, 7, 8, 7, 6, 7, 5, 9, 9, 6, 10, 3, 7, 0, 4, 4, 5, 5, 5, 6, 5, 6, 7, 6, 6, 7, 8, 7, 7, 7, 8, 8, 8, 9, 7, 8, 8, 8, 9, 8, 9, 7, 9, 9, 9, 9, 9, 10, 10, 10, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 2, 0, 0, 0, 0, 0, 2, 10, 4, 10, 3, 3, 3, 3, 3, 0, 4, 0, 4, 0, 4, 4, 6, 4, 5, 4, 0], [6, 6, 6, 6, 0, 5, 6, 6, 6, 0, 6, 4, 2, 6, 7, 0, 0, 8, 0, 7, 9, 8, 7, 9, 10, 4, 3, 4, 0, 0, 5, 6, 4, 6, 6, 6, 6, 6, 7, 0, 7, 7, 7, 8, 7, 9, 7, 8, 8, 8, 8, 8, 9, 7, 9, 8, 9, 9, 8, 9, 0, 9, 9, 10, 10, 10, 10, 1, 1, 10, 1, 10, 1, 10, 2, 10, 2, 10, 2, 10, 0, 0, 2, 0, 3, 0, 3, 0, 4, 0, 3, 0, 4, 0, 4, 5, 4, 4, 4, 4, 0], [6, 5, 6, 4, 6, 6, 6, 6, 0, 6, 5, 5, 6, 6, 7, 7, 7, 0, 0, 7, 8, 8, 6, 9, 0, 0, 3, 0, 0, 0, 5, 5, 6, 6, 6, 6, 6, 6, 0, 6, 7, 7, 7, 6, 8, 6, 8, 7, 7, 8, 7, 9, 7, 9, 8, 8, 9, 8, 9, 0, 9, 9, 9, 10, 9, 10, 10, 10, 1, 10, 1, 10, 1, 1, 1, 10, 1, 10, 2, 10, 3, 0, 0, 0, 2, 0, 3, 0, 3, 0, 3, 0, 3, 0, 5, 3, 4, 4, 4, 4, 0], [5, 6, 3, 5, 5, 5, 6, 6, 6, 0, 5, 6, 0, 6, 6, 7, 0, 0, 6, 7, 9, 8, 7, 3, 6, 3, 0, 4, 0, 4, 5, 5, 5, 6, 6, 6, 6, 0, 0, 0, 6, 7, 6, 8, 3, 8, 7, 7, 7, 0, 8, 7, 8, 8, 9, 8, 8, 9, 7, 9, 9, 8, 9, 9, 10, 7, 10, 10, 10, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 2, 10, 2, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 3, 4, 3, 4, 4, 0], [6, 5, 5, 5, 6, 0, 6, 6, 0, 5, 4, 5, 6, 5, 7, 1, 5, 5, 0, 7, 8, 8, 2, 8, 0, 6, 3, 0, 0, 0, 4, 5, 5, 6, 5, 6, 0, 5, 7, 6, 6, 6, 7, 0, 7, 8, 7, 7, 7, 7, 6, 8, 7, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 10, 7, 9, 10, 8, 10, 10, 10, 10, 1, 10, 1, 10, 1, 10, 2, 10, 1, 10, 2, 10, 2, 0, 0, 0, 2, 0, 3, 0, 4, 0, 3, 3, 3, 3, 4, 5, 0], [3, 5, 5, 5, 6, 5, 6, 0, 0, 0, 5, 0, 5, 5, 3, 7, 6, 1, 0, 0, 8, 5, 7, 8, 9, 0, 0, 0, 0, 4, 4, 5, 5, 5, 5, 0, 5, 5, 0, 0, 6, 6, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 7, 0, 8, 8, 8, 8, 8, 7, 0, 9, 9, 9, 10, 9, 10, 0, 10, 10, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 2, 2, 2, 0, 0, 10, 0, 10, 3, 2, 3, 3, 3, 3, 5, 3, 0], [5, 6, 4, 6, 5, 6, 0, 6, 6, 0, 6, 5, 6, 5, 6, 7, 6, 5, 0, 7, 0, 7, 6, 0, 9, 0, 10, 0, 0, 0, 0, 4, 5, 5, 0, 5, 5, 0, 6, 0, 6, 0, 6, 0, 7, 7, 0, 7, 0, 7, 6, 7, 7, 7, 7, 5, 7, 7, 7, 8, 0, 8, 0, 8, 8, 8, 10, 7, 10, 7, 9, 10, 9, 10, 10, 10, 1, 10, 1, 10, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 3, 0, 0, 1, 3, 0, 3, 4, 3, 3, 0], [5, 4, 5, 5, 6, 0, 6, 5, 5, 0, 1, 6, 5, 7, 6, 6, 6, 7, 0, 0, 7, 7, 6, 8, 9, 10, 0, 0, 0, 0, 4, 4, 5, 0, 5, 5, 5, 5, 6, 6, 0, 6, 0, 6, 6, 7, 6, 0, 0, 0, 6, 6, 6, 7, 0, 0, 7, 0, 0, 7, 8, 0, 8, 8, 8, 7, 8, 10, 1, 10, 9, 9, 9, 10, 10, 10, 10, 10, 1, 10, 1, 10, 1, 10, 1, 1, 1, 10, 2, 2, 2, 1, 2, 1, 0, 2, 4, 0, 3, 3, 0], [5, 5, 5, 5, 0, 0, 5, 5, 0, 0, 0, 5, 5, 6, 6, 6, 6, 7, 0, 0, 7, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 4, 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], [9, 0, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 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, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 4, 0, 0, 9, 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], [9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 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, 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, 0, 0]]
  3. original_dp_table_swapped = [[8, 7, 4, 5, 0, 0, 0, 9, 0, 0, 4, 4, 2, 0, 9, 4, 0, 0, 0, 0, 3, 8, 4, 0, 4, 4, 4, 4, 10, 0, 5, 4, 5, 4, 0, 10, 1, 4, 6, 0, 6, 0, 5, 0, 4, 4, 4, 5, 0, 0, 4, 0, 0, 0, 0, 0, 6, 4, 0, 0, 4, 4, 0, 6, 0, 5, 4, 4, 4, 0, 8, 7, 4, 4, 4, 8, 4, 8, 7, 0, 7, 7, 7, 4, 9, 7, 7, 7, 4, 0, 10, 10, 10, 7, 7, 6, 6, 6, 10, 5, 0], [4, 4, 7, 5, 7, 0, 9, 0, 0, 0, 4, 4, 0, 9, 3, 7, 0, 3, 0, 0, 8, 3, 3, 3, 0, 4, 4, 10, 0, 0, 4, 4, 5, 0, 3, 5, 5, 3, 0, 0, 0, 4, 6, 4, 4, 4, 4, 4, 0, 0, 0, 4, 0, 4, 0, 5, 4, 4, 0, 0, 4, 1, 6, 4, 4, 4, 4, 4, 0, 6, 4, 7, 4, 4, 4, 4, 8, 4, 0, 0, 0, 7, 0, 8, 0, 0, 7, 0, 0, 0, 10, 7, 10, 7, 6, 6, 6, 10, 5, 5, 0], [3, 7, 3, 7, 0, 9, 6, 0, 0, 3, 4, 4, 10, 3, 0, 3, 0, 0, 0, 7, 3, 3, 3, 3, 3, 0, 9, 0, 0, 0, 4, 3, 0, 10, 3, 4, 5, 0, 5, 0, 4, 3, 6, 3, 4, 4, 3, 0, 0, 0, 4, 4, 4, 1, 5, 4, 4, 0, 0, 0, 1, 5, 4, 4, 4, 4, 4, 4, 7, 0, 4, 0, 4, 0, 4, 7, 0, 7, 0, 0, 7, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 7, 10, 6, 6, 6, 10, 5, 5, 10, 0], [3, 0, 6, 4, 8, 5, 0, 0, 0, 0, 0, 10, 0, 3, 3, 3, 2, 0, 0, 0, 2, 3, 3, 3, 3, 9, 3, 0, 0, 0, 4, 3, 10, 3, 4, 4, 0, 0, 0, 0, 5, 3, 6, 3, 6, 3, 4, 0, 0, 0, 7, 4, 3, 5, 3, 3, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 6, 10, 6, 9, 6, 9, 6, 6, 10, 5, 5, 10, 10, 0], [3, 6, 2, 7, 6, 5, 0, 0, 0, 0, 10, 3, 1, 3, 2, 0, 0, 6, 0, 0, 2, 2, 2, 2, 8, 3, 0, 0, 0, 0, 0, 10, 4, 3, 4, 0, 0, 2, 0, 0, 5, 3, 5, 3, 3, 0, 0, 0, 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 9, 0, 6, 9, 6, 9, 6, 10, 5, 5, 10, 10, 10, 0], [2, 2, 9, 3, 3, 0, 5, 0, 0, 0, 3, 3, 10, 2, 0, 0, 5, 0, 1, 0, 2, 2, 0, 8, 0, 0, 3, 0, 0, 0, 10, 2, 3, 2, 0, 0, 0, 10, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 2, 9, 0, 0, 5, 9, 6, 9, 9, 5, 5, 10, 10, 10, 10, 0], [2, 8, 0, 3, 0, 4, 5, 1, 0, 0, 3, 0, 2, 0, 6, 0, 0, 6, 1, 1, 2, 2, 7, 0, 2, 0, 0, 0, 0, 9, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 7, 0, 5, 0, 0, 8, 5, 10, 5, 5, 10, 10, 10, 10, 10, 0], [7, 5, 0, 3, 0, 0, 1, 8, 1, 6, 0, 2, 0, 0, 8, 0, 5, 7, 1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 9, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 3, 0, 5, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 5, 0, 0, 8, 2, 1, 0, 2, 1, 0, 9, 8, 5, 10, 10, 10, 10, 10, 10, 0], [5, 0, 5, 5, 0, 0, 7, 7, 0, 6, 0, 2, 0, 7, 0, 1, 5, 0, 7, 1, 6, 0, 0, 0, 0, 0, 0, 9, 2, 1, 2, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 2, 0, 0, 0, 7, 0, 1, 1, 0, 1, 1, 6, 1, 1, 8, 1, 0, 0, 9, 5, 8, 4, 10, 10, 10, 9, 10, 10, 0], [5, 5, 5, 0, 0, 0, 4, 7, 8, 5, 6, 0, 9, 4, 5, 4, 4, 6, 5, 6, 8, 8, 0, 8, 8, 1, 8, 8, 9, 1, 2, 10, 2, 10, 3, 0, 3, 10, 3, 1, 10, 0, 4, 0, 0, 4, 1, 3, 5, 4, 5, 0, 5, 4, 4, 1, 0, 4, 6, 4, 0, 4, 7, 0, 0, 0, 7, 1, 6, 0, 1, 5, 4, 5, 1, 5, 4, 1, 4, 4, 4, 1, 7, 8, 5, 8, 4, 10, 8, 8, 8, 4, 7, 4, 10, 10, 9, 10, 10, 10, 0], [5, 4, 4, 0, 8, 4, 3, 0, 0, 6, 0, 9, 0, 0, 4, 4, 4, 5, 5, 0, 7, 8, 9, 8, 0, 7, 1, 7, 1, 10, 9, 1, 9, 10, 2, 0, 3, 10, 0, 0, 3, 3, 3, 3, 4, 4, 3, 4, 4, 0, 0, 0, 0, 3, 5, 4, 6, 4, 6, 0, 4, 4, 1, 4, 7, 4, 0, 5, 7, 0, 8, 4, 8, 1, 6, 4, 4, 4, 4, 0, 4, 6, 4, 7, 10, 4, 10, 7, 8, 0, 0, 0, 7, 0, 10, 9, 10, 10, 10, 10, 0], [4, 4, 4, 0, 3, 0, 0, 0, 8, 0, 9, 10, 0, 3, 4, 4, 4, 4, 5, 0, 7, 7, 7, 8, 7, 1, 1, 7, 1, 9, 0, 10, 2, 10, 2, 0, 0, 0, 10, 10, 0, 3, 3, 3, 3, 10, 4, 1, 4, 0, 4, 1, 3, 3, 5, 0, 5, 4, 0, 0, 6, 0, 6, 4, 6, 0, 5, 4, 0, 0, 7, 4, 1, 5, 8, 4, 8, 7, 4, 0, 6, 0, 0, 7, 0, 7, 0, 0, 0, 0, 0, 0, 7, 0, 9, 10, 10, 10, 10, 10, 0], [4, 0, 8, 4, 7, 7, 0, 6, 7, 8, 5, 10, 0, 3, 3, 3, 3, 0, 0, 0, 6, 7, 7, 6, 7, 7, 10, 7, 9, 8, 9, 0, 0, 0, 0, 0, 2, 10, 2, 10, 2, 3, 3, 3, 10, 3, 3, 0, 4, 0, 0, 10, 4, 3, 5, 3, 0, 0, 4, 0, 6, 4, 6, 5, 6, 4, 6, 0, 0, 0, 0, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 10, 0, 6, 0, 10, 10, 10, 10, 10, 10, 0], [4, 8, 3, 6, 7, 0, 0, 0, 8, 0, 5, 9, 9, 7, 3, 3, 0, 0, 0, 6, 6, 6, 6, 7, 7, 7, 0, 7, 10, 8, 1, 0, 1, 0, 1, 1, 9, 10, 2, 2, 2, 2, 0, 10, 3, 3, 3, 0, 3, 0, 10, 3, 4, 3, 4, 3, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 6, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 10, 0, 0, 10, 8, 3, 10, 10, 10, 10, 10, 8, 0], [7, 3, 6, 6, 0, 0, 0, 6, 7, 0, 6, 0, 9, 2, 6, 3, 0, 0, 0, 0, 6, 5, 6, 6, 6, 6, 7, 0, 7, 7, 10, 9, 1, 9, 1, 10, 1, 1, 2, 10, 2, 0, 10, 0, 3, 0, 0, 10, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 10, 0, 10, 0, 10, 10, 10, 10, 8, 10, 0], [3, 0, 3, 5, 0, 0, 7, 0, 0, 0, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 4, 6, 6, 3, 6, 6, 0, 7, 6, 7, 7, 9, 10, 9, 9, 9, 1, 9, 1, 10, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 4, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 9, 0, 2, 10, 10, 10, 8, 10, 10, 0], [3, 6, 0, 0, 0, 7, 0, 5, 6, 0, 6, 1, 7, 0, 2, 0, 0, 0, 0, 0, 0, 5, 2, 0, 6, 0, 6, 0, 6, 0, 6, 9, 0, 9, 10, 9, 1, 9, 1, 1, 10, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 6, 9, 0, 10, 2, 10, 10, 8, 10, 10, 10, 0], [2, 5, 0, 0, 6, 5, 0, 5, 0, 0, 3, 7, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 5, 0, 5, 5, 6, 0, 6, 8, 8, 8, 9, 10, 9, 1, 10, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 0, 3, 1, 3, 0, 3, 2, 4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 5, 2, 5, 6, 8, 9, 8, 9, 1, 10, 7, 10, 10, 10, 10, 0], [1, 2, 2, 6, 0, 5, 6, 0, 6, 0, 7, 8, 1, 6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 1, 5, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 10, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 0, 2, 1, 3, 0, 3, 0, 0, 0, 0, 0, 4, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 1, 0, 0, 6, 0, 1, 1, 5, 1, 1, 5, 0, 1, 1, 6, 8, 0, 9, 1, 9, 1, 7, 9, 10, 9, 10, 10, 0], [5, 5, 6, 5, 5, 5, 4, 0, 0, 0, 0, 0, 7, 6, 6, 1, 9, 0, 0, 0, 4, 5, 4, 4, 5, 0, 5, 0, 5, 6, 7, 5, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 1, 1, 10, 10, 1, 10, 2, 10, 0, 10, 2, 1, 3, 10, 3, 10, 2, 3, 3, 0, 4, 3, 0, 0, 0, 4, 5, 4, 5, 0, 4, 5, 6, 4, 6, 5, 1, 4, 7, 5, 7, 4, 7, 1, 6, 7, 8, 8, 8, 8, 9, 6, 9, 9, 9, 9, 10, 9, 0], [4, 6, 4, 0, 0, 4, 5, 0, 0, 0, 4, 7, 6, 6, 0, 10, 3, 0, 0, 0, 4, 4, 4, 5, 4, 4, 4, 0, 4, 6, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 8, 10, 10, 10, 1, 1, 1, 10, 1, 1, 1, 0, 0, 10, 2, 0, 0, 10, 0, 0, 3, 1, 3, 0, 3, 1, 4, 4, 0, 0, 0, 3, 5, 5, 5, 4, 6, 4, 4, 0, 6, 4, 7, 4, 7, 4, 7, 7, 8, 0, 8, 7, 6, 7, 9, 8, 9, 9, 9, 7, 0], [6, 4, 4, 4, 4, 4, 0, 5, 0, 0, 0, 0, 6, 4, 9, 8, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 6, 0, 5, 5, 7, 7, 4, 8, 7, 7, 7, 7, 8, 8, 8, 10, 10, 10, 1, 10, 1, 10, 1, 1, 2, 1, 0, 2, 0, 10, 2, 2, 3, 10, 3, 0, 3, 3, 4, 4, 4, 0, 3, 4, 5, 4, 5, 3, 5, 3, 0, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0, 0, 5, 0, 7, 8, 8, 9, 8, 7, 9, 0], [3, 4, 0, 4, 4, 4, 7, 0, 4, 0, 4, 6, 6, 7, 6, 0, 0, 0, 3, 0, 3, 3, 4, 4, 4, 4, 4, 0, 0, 0, 4, 4, 7, 4, 7, 6, 7, 0, 7, 7, 7, 8, 8, 7, 10, 10, 10, 10, 10, 10, 1, 1, 1, 1, 2, 0, 2, 10, 2, 2, 3, 0, 2, 2, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 8, 8, 8, 6, 9, 8, 0], [3, 3, 6, 6, 3, 5, 0, 0, 0, 0, 7, 0, 5, 5, 5, 0, 0, 0, 0, 0, 3, 3, 3, 4, 4, 3, 4, 0, 0, 0, 4, 4, 6, 6, 6, 3, 0, 0, 0, 0, 8, 7, 7, 7, 7, 10, 10, 10, 10, 10, 1, 10, 1, 1, 1, 10, 2, 10, 2, 10, 0, 10, 2, 0, 3, 0, 3, 0, 0, 0, 4, 4, 4, 0, 4, 0, 5, 0, 5, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 8, 7, 6, 8, 8, 8, 0], [3, 3, 6, 3, 7, 0, 0, 0, 0, 0, 0, 7, 0, 4, 0, 4, 9, 2, 0, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 4, 4, 6, 6, 3, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 6, 9, 9, 9, 10, 10, 10, 1, 10, 1, 1, 1, 1, 2, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 7, 0, 7, 0, 7, 5, 8, 7, 8, 8, 0], [3, 6, 3, 6, 0, 0, 0, 4, 0, 0, 7, 5, 0, 2, 4, 0, 1, 8, 0, 0, 3, 2, 4, 3, 0, 0, 0, 0, 0, 0, 3, 5, 3, 3, 0, 0, 0, 0, 0, 0, 6, 0, 6, 6, 6, 8, 9, 7, 9, 9, 9, 10, 10, 10, 1, 10, 1, 10, 1, 10, 2, 10, 2, 0, 0, 0, 2, 0, 0, 2, 3, 0, 3, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 7, 6, 5, 7, 7, 7, 8, 7, 0], [5, 2, 5, 0, 3, 0, 0, 4, 0, 7, 6, 5, 0, 4, 0, 3, 7, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 6, 6, 6, 7, 6, 9, 6, 9, 9, 9, 9, 9, 10, 10, 10, 1, 10, 10, 1, 1, 1, 2, 1, 2, 0, 0, 0, 2, 2, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 2, 0, 0, 6, 0, 6, 4, 7, 6, 7, 7, 7, 7, 0], [2, 4, 0, 0, 0, 0, 5, 0, 5, 5, 6, 5, 5, 0, 0, 9, 8, 1, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 7, 0, 6, 0, 6, 0, 8, 9, 9, 9, 10, 10, 10, 10, 10, 1, 10, 1, 1, 1, 10, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 3, 1, 0, 0, 3, 0, 4, 0, 4, 0, 0, 0, 5, 0, 5, 5, 0, 5, 5, 5, 6, 6, 7, 6, 7, 5, 0], [4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 8, 10, 8, 8, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 5, 7, 8, 8, 8, 8, 9, 10, 9, 10, 10, 10, 10, 1, 10, 1, 10, 1, 10, 2, 1, 2, 2, 2, 0, 0, 0, 3, 1, 3, 0, 0, 0, 0, 2, 4, 1, 3, 1, 0, 1, 5, 0, 1, 4, 6, 5, 6, 6, 6, 6, 5, 6, 0], [5, 5, 5, 0, 0, 0, 0, 0, 5, 0, 5, 1, 3, 6, 0, 0, 8, 0, 7, 2, 10, 0, 3, 3, 0, 4, 0, 4, 0, 0, 5, 4, 4, 0, 6, 4, 5, 5, 0, 0, 0, 7, 0, 5, 0, 5, 5, 5, 7, 0, 8, 5, 8, 9, 8, 9, 8, 9, 10, 10, 10, 10, 10, 10, 1, 1, 1, 1, 2, 10, 2, 10, 2, 2, 0, 10, 2, 2, 3, 1, 3, 2, 4, 1, 4, 0, 4, 0, 5, 4, 4, 4, 6, 4, 6, 6, 6, 4, 6, 6, 0], [4, 4, 4, 4, 0, 6, 0, 0, 0, 0, 5, 0, 8, 3, 4, 5, 0, 8, 0, 8, 0, 3, 3, 0, 4, 0, 3, 0, 0, 0, 0, 4, 0, 5, 4, 4, 4, 4, 0, 0, 6, 0, 5, 5, 4, 5, 0, 7, 6, 0, 0, 5, 8, 8, 8, 8, 8, 8, 9, 10, 8, 10, 10, 10, 1, 10, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 0, 1, 0, 0, 3, 1, 3, 1, 4, 4, 4, 4, 4, 0, 5, 0, 5, 0, 6, 5, 4, 6, 6, 6, 0], [4, 4, 4, 0, 6, 4, 6, 0, 0, 0, 4, 7, 2, 0, 2, 0, 0, 0, 9, 1, 0, 0, 2, 0, 0, 3, 0, 5, 0, 0, 4, 0, 5, 4, 4, 4, 4, 4, 0, 0, 0, 5, 0, 4, 4, 4, 7, 4, 0, 0, 7, 4, 7, 8, 5, 8, 7, 8, 9, 8, 10, 10, 10, 10, 10, 10, 1, 10, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 0, 0, 0, 0, 3, 0, 4, 0, 3, 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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, 2, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 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, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 3, 0, 9, 0, 0, 0, 0, 3, 3, 9, 3, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 1, 0, 0, 9, 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, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 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, 9, 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, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 0, 0, 0, 0, 0, 0, 9, 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], [9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 1, 0, 0, 0, 9, 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, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 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, 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, 0, 0, 0, 0]]
  4. new_hijink_table = [[8, 7, 7, 7, 5, 5, 0, 0, 0, 0, 4, 4, 4, 4, 5, 6, 3, 0, 0, 0, 3, 4, 3, 4, 4, 4, 4, 5, 4, 0, 4, 4, 4, 4, 4, 5, 5, 4, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 6, 0, 6, 6, 6, 5, 6, 6, 7, 6, 7, 0, 7, 6, 7, 7, 7, 7, 8, 7, 8, 0, 8, 8, 8, 8, 8, 8, 9, 8, 9, 0, 9, 8, 10, 9, 10, 10, 10, 10, 10, 0, 10, 0, 10, 0, 10, 5, 10, 10, 10, 10, 0], [7, 7, 6, 7, 8, 5, 7, 9, 0, 0, 3, 4, 4, 10, 2, 0, 0, 6, 0, 0, 3, 3, 3, 3, 3, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 5, 3, 0, 0, 5, 4, 5, 5, 5, 5, 5, 5, 0, 0, 6, 6, 6, 5, 6, 6, 6, 6, 0, 0, 7, 6, 7, 7, 7, 7, 7, 7, 0, 0, 8, 7, 8, 7, 8, 8, 9, 7, 9, 0, 9, 8, 9, 9, 10, 0, 10, 10, 10, 10, 10, 10, 10, 0, 10, 5, 10, 10, 10, 10, 0], [7, 6, 6, 7, 7, 7, 9, 0, 0, 0, 3, 4, 4, 4, 0, 5, 2, 0, 0, 0, 3, 3, 3, 3, 3, 3, 4, 0, 0, 0, 4, 3, 4, 3, 4, 4, 4, 0, 0, 0, 4, 4, 4, 5, 5, 5, 5, 0, 0, 0, 5, 6, 6, 5, 6, 6, 6, 0, 0, 0, 7, 6, 7, 6, 7, 7, 7, 0, 0, 0, 8, 0, 8, 7, 8, 7, 8, 7, 0, 0, 9, 0, 9, 0, 9, 0, 10, 9, 10, 0, 10, 0, 10, 0, 10, 0, 10, 10, 10, 10, 0], [7, 6, 5, 7, 7, 9, 0, 0, 0, 0, 0, 0, 0, 0, 4, 5, 0, 0, 0, 0, 2, 3, 2, 3, 3, 3, 3, 0, 0, 0, 4, 3, 4, 3, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 5, 5, 0, 0, 0, 5, 6, 6, 5, 6, 6, 6, 0, 0, 0, 6, 6, 6, 0, 7, 6, 7, 0, 0, 0, 7, 0, 8, 0, 8, 0, 8, 0, 0, 0, 9, 0, 9, 0, 9, 9, 9, 9, 10, 9, 10, 10, 10, 10, 10, 5, 10, 10, 10, 10, 0], [7, 6, 6, 6, 7, 7, 0, 0, 0, 0, 10, 10, 1, 4, 4, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 3, 4, 3, 4, 3, 4, 0, 0, 0, 4, 4, 4, 4, 4, 0, 5, 0, 0, 0, 5, 5, 5, 5, 6, 5, 6, 0, 0, 0, 6, 0, 6, 0, 6, 0, 7, 0, 0, 0, 7, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 0, 9, 0, 9, 0, 10, 0, 10, 0, 10, 4, 10, 10, 10, 10, 0], [6, 6, 6, 5, 5, 9, 8, 0, 0, 0, 2, 10, 10, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 3, 2, 3, 3, 3, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 5, 0, 5, 5, 5, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 0, 8, 0, 9, 0, 9, 9, 9, 9, 0, 9, 10, 9, 10, 4, 10, 10, 10, 10, 0], [6, 6, 5, 5, 5, 4, 8, 8, 0, 0, 2, 2, 3, 9, 10, 10, 0, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 4, 0, 0, 0, 0, 0, 5, 0, 5, 0, 5, 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, 8, 7, 8, 0, 8, 0, 9, 8, 9, 0, 9, 0, 10, 9, 10, 4, 10, 10, 10, 10, 0], [6, 4, 0, 0, 0, 0, 8, 7, 7, 0, 6, 2, 3, 8, 0, 0, 10, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 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, 7, 6, 8, 0, 8, 8, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 10, 4, 10, 10, 10, 10, 0], [5, 4, 5, 5, 0, 0, 7, 7, 0, 6, 6, 9, 9, 8, 4, 0, 0, 0, 10, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 5, 6, 0, 6, 0, 7, 0, 7, 5, 7, 6, 7, 7, 8, 7, 8, 1, 8, 8, 8, 0, 9, 9, 9, 8, 9, 4, 10, 9, 10, 10, 0], [7, 8, 8, 4, 0, 0, 8, 7, 8, 8, 9, 9, 9, 8, 0, 4, 4, 0, 5, 10, 10, 7, 7, 1, 1, 0, 1, 7, 8, 0, 2, 8, 2, 8, 2, 0, 3, 10, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 5, 6, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 9, 8, 9, 3, 9, 9, 10, 9, 0], [7, 8, 5, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 7, 8, 3, 4, 4, 0, 0, 5, 7, 10, 7, 7, 0, 1, 7, 0, 9, 8, 1, 2, 8, 2, 10, 2, 10, 0, 0, 3, 3, 3, 3, 3, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 5, 0, 5, 4, 5, 4, 5, 5, 5, 5, 6, 0, 6, 5, 6, 6, 6, 6, 7, 6, 7, 0, 7, 7, 7, 7, 7, 7, 8, 8, 8, 0, 8, 8, 9, 8, 9, 0, 9, 9, 9, 9, 0], [7, 7, 7, 0, 7, 0, 0, 7, 0, 7, 8, 9, 9, 7, 8, 3, 4, 0, 0, 0, 5, 6, 6, 7, 10, 7, 7, 7, 0, 0, 0, 10, 2, 10, 0, 0, 0, 9, 0, 0, 0, 3, 3, 3, 3, 3, 4, 1, 0, 0, 4, 4, 4, 3, 4, 4, 4, 4, 0, 0, 5, 4, 5, 4, 5, 4, 5, 5, 0, 0, 6, 5, 6, 5, 6, 6, 6, 6, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 8, 7, 8, 0, 8, 0, 9, 0, 9, 9, 9, 9, 0], [7, 7, 7, 6, 7, 7, 0, 7, 7, 7, 8, 9, 9, 7, 7, 3, 0, 0, 0, 0, 5, 6, 6, 6, 6, 7, 8, 0, 0, 0, 1, 8, 0, 9, 0, 0, 2, 0, 2, 0, 2, 3, 3, 3, 3, 3, 3, 0, 4, 0, 4, 3, 4, 3, 4, 3, 4, 0, 4, 0, 4, 4, 4, 4, 5, 4, 5, 0, 5, 0, 5, 0, 6, 0, 6, 6, 6, 0, 0, 0, 6, 0, 7, 0, 7, 0, 7, 7, 7, 0, 8, 0, 8, 0, 9, 0, 9, 8, 9, 9, 0], [6, 7, 0, 7, 7, 7, 0, 0, 7, 0, 9, 9, 8, 7, 7, 0, 0, 0, 0, 0, 5, 5, 6, 6, 6, 6, 0, 0, 9, 8, 1, 8, 1, 9, 1, 9, 0, 0, 2, 0, 2, 2, 2, 3, 3, 3, 3, 0, 3, 0, 3, 3, 4, 3, 4, 3, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 5, 0, 0, 0, 5, 0, 5, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0, 7, 7, 8, 7, 8, 7, 8, 2, 8, 8, 9, 8, 0], [6, 6, 6, 6, 6, 0, 0, 6, 7, 0, 9, 9, 8, 7, 7, 0, 0, 0, 0, 0, 5, 5, 6, 6, 6, 0, 0, 0, 0, 0, 10, 7, 1, 8, 1, 9, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 3, 10, 0, 0, 3, 0, 0, 2, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0, 7, 0, 8, 0, 8, 2, 8, 8, 8, 8, 0], [6, 0, 6, 6, 6, 0, 0, 0, 0, 0, 9, 8, 8, 6, 0, 0, 0, 0, 0, 0, 5, 5, 5, 6, 0, 6, 0, 0, 0, 0, 7, 8, 10, 9, 9, 9, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 3, 2, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 6, 0, 7, 7, 7, 8, 2, 8, 8, 8, 8, 0], [6, 6, 6, 0, 6, 6, 0, 6, 0, 0, 9, 8, 7, 0, 0, 0, 0, 0, 0, 0, 4, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 9, 1, 9, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 3, 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, 5, 6, 6, 6, 6, 7, 0, 7, 0, 7, 6, 8, 1, 8, 8, 8, 8, 0], [2, 5, 5, 5, 5, 0, 5, 5, 0, 0, 8, 7, 0, 0, 0, 0, 0, 0, 0, 0, 4, 5, 0, 0, 0, 0, 0, 6, 0, 7, 0, 7, 0, 8, 0, 8, 10, 0, 1, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 3, 0, 0, 0, 3, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 5, 0, 5, 6, 6, 6, 6, 7, 6, 7, 6, 7, 1, 8, 7, 8, 8, 0], [1, 6, 5, 5, 5, 0, 5, 0, 0, 0, 8, 7, 7, 6, 6, 9, 10, 0, 0, 0, 4, 4, 5, 5, 0, 0, 0, 0, 6, 7, 7, 7, 8, 7, 8, 8, 8, 8, 10, 0, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 3, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, 4, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5, 6, 5, 6, 0, 6, 6, 7, 6, 7, 1, 7, 7, 8, 7, 0], [6, 6, 7, 6, 6, 6, 6, 0, 0, 0, 2, 7, 7, 7, 6, 9, 10, 9, 8, 0, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 1, 10, 1, 10, 1, 10, 2, 10, 0, 10, 2, 1, 2, 10, 3, 10, 3, 10, 3, 0, 3, 3, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 7, 6, 7, -1, 7, 7, 7, 7, 0], [6, 7, 7, 6, 5, 6, 7, 0, 0, 0, 7, 7, 7, 7, 6, 10, 10, 9, 0, 0, 4, 4, 4, 5, 5, 5, 6, 6, 6, 0, 7, 7, 7, 7, 8, 8, 8, 8, 8, 0, 8, 10, 10, 10, 1, 10, 1, 10, 1, 0, 2, 0, 0, 10, 2, 10, 2, 10, 0, 0, 3, 10, 3, 10, 3, 3, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 4, 5, 4, 5, 5, 5, 5, 6, 0, 0, 6, 0, 6, 7, -1, 7, 7, 7, 7, 0], [6, 6, 7, 5, 5, 5, 6, 0, 0, 0, 1, 6, 6, 7, 5, 10, 9, 0, 0, 0, 3, 4, 4, 5, 5, 5, 6, 6, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 8, 8, 8, 10, 10, 10, 1, 10, 1, 10, 1, 10, 2, 10, 0, 10, 0, 10, 2, 10, 3, 0, 3, 0, 3, 3, 3, 3, 4, 0, 4, 3, 4, 4, 4, 3, 4, 3, 0, 0, 4, 4, 5, 0, 5, 0, 5, 0, 5, 0, 0, 6, 0, 5, 6, -1, 7, 6, 7, 7, 0], [6, 6, 6, 6, 6, 6, 6, 0, 4, 0, 7, 6, 6, 6, 5, 9, 0, 0, 0, 0, 3, 4, 4, 4, 5, 5, 5, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 8, 8, 8, 8, 8, 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  5. hijink_3d = [[[4, 8], [6, 7], [7, 7], [6, 7], [8, 0], [5, 0], [9, 0], [0, 9], [0, 0], [0, 0], [3, 2], [4, 4], [11, 2], [9, 0], [11, 9], [6, 4], [5, 0], [5, 0], [0, 0], [0, 0], [8, 3], [11, 8], [3, 4], [3, 0], [3, 0], [3, 4], [11, 4], [10, 4], [5, 10], [0, 0], [4, 5], [4, 4], [4, 5], [4, 4], [4, 0], [11, 4], [4, 6], [11, 4], [5, 6], [0, 0], [5, 0], [5, 0], [11, 5], [5, 4], [5, 4], [5, 4], [5, 4], [4, 4], [6, 0], [0, 0], [6, 4], [5, 0], [6, 0], [5, 0], [6, 0], [6, 0], [0, 6], [6, 4], [7, 0], [6, 0], [7, 4], [6, 4], [7, 0], [4, 6], [7, 0], [7, 0], [7, 4], [7, 4], [8, 4], [7, 0], [7, 8], [7, 7], [8, 4], [7, 4], [8, 4], [8, 4], [9, 11], [4, 8], [9, 4], [8, 0], [9, 4], [8, 7], [9, 7], [9, 11], [0, 9], [9, 11], [10, 0], [9, 11], [10, 11], [10, 0], [10, 0], [0, 10], [10, 0], [10, 0], [10, 11], [5, 7], [10, 5], [10, 10], [10, 10], [10, 10], [0, 0]], [[7, 4], [6, 3], [6, 7], [8, 5], [5, 7], [9, 11], [11, 9], [8, 0], [8, 0], [7, 0], [7, 1], [0, 4], [10, 0], [11, 9], [5, 3], [0, 0], [0, 0], 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  6. pseudo_random = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]
  7.  
  8. def p1_strategy(score, opponent_score):
  9. return random_strat(score, opponent_score)
  10.  
  11. def p2_strategy(score, opponent_score):
  12. return new_hijink(score, opponent_score)
  13.  
  14.  
  15. # Test functions
  16. def always_roll(score, opponent_score):
  17. """Always rolls a set number."""
  18. return 5
  19.  
  20. def original_dp(score, opponent_score):
  21. """Returns the value found in the original DP table, before hijink was implemented."""
  22. return original_dp_table[score][opponent_score]
  23.  
  24. def original_dp_hijink(score, opponent_score):
  25. """Utilizes the original DP tables, but hijinks on its first move."""
  26. if score == 0:
  27. return -1
  28. return original_dp_table[score][opponent_score]
  29.  
  30. def original_dp_swap(score, opponent_score):
  31. """Utilizes the original DP tables, but optimized for swapped dice."""
  32. return original_dp_table_swapped[score][opponent_score]
  33.  
  34. def hijink_3d_average(score, opponent_score):
  35. """Returns the average of the values found in the 3d hijink table."""
  36. return (hijink_3d[score][opponent_score][False] + hijink_3d[score][opponent_score][True]) // 2
  37.  
  38. def new_hijink(score, opponent_score):
  39. """Returns the values found in the new hijink table."""
  40. return new_hijink_table[score][opponent_score]
  41.  
  42. def random_strat(score, opponent_score):
  43. """Utilizes new hijink, but pseudo-randomizes its first move."""
  44. if (score == 0):
  45. if pseudo_random[opponent_score % 2]:
  46. #if (opponent_score % 2 == 0): # Utilizes the opponent_score as a deterministic "random" seed
  47. return -1
  48. return new_hijink_table[score][opponent_score]
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