





from __future__ import annotations


def     SCREAMING_SNAKE_CASE			(      lowerCAmelCase    ,       lowerCAmelCase					):
       _UpperCamelCase              =						position
       _UpperCamelCase              =						[
           (y + 1, x + 2),
           (y - 1, x + 2),
           (y + 1, x - 2),
           (y - 1, x - 2),
           (y + 2, x + 1),
           (y + 2, x - 1),
           (y - 2, x + 1),
           (y - 2, x - 1),
       ]
       _UpperCamelCase              =						[]

       for position in positions:
              _UpperCamelCase              =						position
              if 0 <= y_test < n and 0 <= x_test < n:
                     permissible_positions.append(lowerCamelCase_					)

       return permissible_positions


def     SCREAMING_SNAKE_CASE			(      lowerCAmelCase					):
       return not any(elem == 0 for row in board for elem in row					)


def     SCREAMING_SNAKE_CASE			(      lowerCAmelCase    ,       lowerCAmelCase    ,       lowerCAmelCase					):

       if is_complete(lowerCamelCase_					):
              return True

       for position in get_valid_pos(lowerCamelCase_    ,       len(lowerCamelCase_					)					):
              _UpperCamelCase              =						position

              if board[y][x] == 0:
                     _UpperCamelCase              =						curr + 1
                     if open_knight_tour_helper(lowerCamelCase_    ,       lowerCamelCase_    ,       curr + 1					):
                            return True
                     _UpperCamelCase              =						0

       return False


def     SCREAMING_SNAKE_CASE			(      lowerCAmelCase					):
       _UpperCamelCase              =						[[0 for i in range(lowerCamelCase_					)] for j in range(lowerCamelCase_					)]

       for i in range(lowerCamelCase_					):
              for j in range(lowerCamelCase_					):
                     _UpperCamelCase              =						1
                     if open_knight_tour_helper(lowerCamelCase_    ,       (i, j)    ,       1					):
                            return board
                     _UpperCamelCase              =						0

       _UpperCamelCase              =						f'''Open Kight Tour cannot be performed on a board of size {n}'''
       raise ValueError(lowerCamelCase_					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()













def     SCREAMING_SNAKE_CASE			(      lowerCAmelCase = 1_000					):
       _UpperCamelCase              =						3
       _UpperCamelCase              =						0
       while a < n:
              if a % 3 == 0 or a % 5 == 0:
                     result += a
              elif a % 15 == 0:
                     result -= a
              a += 1
       return result


if __name__ == "__main__":
       print(F'''{solution() = }''')






