from __future__ import annotations



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: Tuple				,  __UpperCamelCase					: str			)							->      list[tuple[int, int]]:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__							,  SCREAMING_SNAKE_CASE__    							=   position
  SCREAMING_SNAKE_CASE__    							=   [
      (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),
  ]
  SCREAMING_SNAKE_CASE__    							=   []

  for position in positions:
    SCREAMING_SNAKE_CASE__							,  SCREAMING_SNAKE_CASE__    							=   position
    if 0 <= y_test < n and 0 <= x_test < n:
      permissible_positions.append(UpperCamelCase__			)

  return permissible_positions



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: Union[str, Any]			)							->      bool:







  """simple docstring"""





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



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[Any]				,  __UpperCamelCase					: Union[str, Any]				,  __UpperCamelCase					: str			)							->      bool:







  """simple docstring"""





  if is_complete(UpperCamelCase__			):
    return True

  for position in get_valid_pos(UpperCamelCase__				,  len(UpperCamelCase__			)			):
    SCREAMING_SNAKE_CASE__							,  SCREAMING_SNAKE_CASE__    							=   position

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

  return False



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[str]			)							->      list[list[int]]:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__    							=   [[0 for i in range(UpperCamelCase__			)] for j in range(UpperCamelCase__			)]

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

  SCREAMING_SNAKE_CASE__    							=   f"""Open Kight Tour cannot be performed on a board of size {n}"""
  raise ValueError(UpperCamelCase__			)


if __name__ == "__main__":
   import doctest

   doctest.testmod()




from math import isqrt



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int			)							->      bool:







  """simple docstring"""





  return all(number % divisor != 0 for divisor in range(2				,  isqrt(__UpperCamelCase			) + 1			)			)



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int = 10**6			)							->      int:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__    							=   0
  SCREAMING_SNAKE_CASE__    							=   1
  SCREAMING_SNAKE_CASE__    							=   7
  while prime_candidate < max_prime:
    primes_count += is_prime(__UpperCamelCase			)

    cube_index += 1
    prime_candidate += 6 * cube_index

  return primes_count


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