


from __future__ import annotations

def 		__lowerCAmelCase   (							_UpperCamelCase       ,			_UpperCamelCase		)    ->				list[tuple[int, int]]:






      '''simple docstring'''

      lowerCamelCase__   ,    lowerCamelCase__:						int							   = position
      lowerCamelCase__:						int							   = [
          (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),
      ]
      lowerCamelCase__:						Dict							   = []

      for position in positions:
            lowerCamelCase__   ,    lowerCamelCase__:						str							   = position
            if 0 <= y_test < n and 0 <= x_test < n:
                  permissible_positions.append(_lowerCAmelCase		)

      return permissible_positions

def 		__lowerCAmelCase   (							_UpperCamelCase		)    ->				bool:






      '''simple docstring'''

      return not any(elem == 0 for row in board for elem in row		)

def 		__lowerCAmelCase   (							_UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase		)    ->				bool:






      '''simple docstring'''

      if is_complete(_lowerCAmelCase		):
            return True

      for position in get_valid_pos(_lowerCAmelCase       ,			len(_lowerCAmelCase		)		):
            lowerCamelCase__   ,    lowerCamelCase__:						str							   = position

            if board[y][x] == 0:
                  lowerCamelCase__:						Optional[Any]							   = curr + 1
                  if open_knight_tour_helper(_lowerCAmelCase       ,			_lowerCAmelCase       ,			curr + 1		):
                        return True
                  lowerCamelCase__:						Tuple							   = 0

      return False

def 		__lowerCAmelCase   (							_UpperCamelCase		)    ->				list[list[int]]:






      '''simple docstring'''

      lowerCamelCase__:						Any							   = [[0 for i in range(_lowerCAmelCase		)] for j in range(_lowerCAmelCase		)]

      for i in range(_lowerCAmelCase		):
            for j in range(_lowerCAmelCase		):
                  lowerCamelCase__:						Dict							   = 1
                  if open_knight_tour_helper(_lowerCAmelCase       ,			(i, j)       ,			1		):
                        return board
                  lowerCamelCase__:						List[Any]							   = 0

      lowerCamelCase__:						Dict							   = f"""Open Kight Tour cannot be performed on a board of size {n}"""
      raise ValueError(_lowerCAmelCase		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()










from __future__ import annotations





def 						_lowerCAmelCase							(     _lowerCAmelCase			)    ->						list[int]:


						'''simple docstring'''






						__snake_case				=		2
						__snake_case				=		[]
						while i * i <= n:
												if n % i:
																		i += 1
												else:
																		n //= i
																		factors.append(_lowerCAmelCase			)
						if n > 1:
												factors.append(_lowerCAmelCase			)
						return factors


if __name__ == "__main__":
	import doctest

	doctest.testmod()





