


"""simple docstring"""


def    a__       ( __lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase      )		->		int:
				return len_board * len_board_column * row + column






def    a__       ( __lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase   ,	)		->		bool:

				if board[row][column] != word[word_index]:
								return False

				if word_index == len(__lowercase      ) - 1:
								return True

				_A         =	[(0, 1), (0, -1), (-1, 0), (1, 0)]
				_A         =	len(__lowercase      )
				_A         =	len(board[0]      )
				for direction in traverts_directions:
								_A         =	row + direction[0]
								_A         =	column + direction[1]
								if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
												continue

								_A         =	get_point_key(__lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase      )
								if key in visited_points_set:
												continue

								visited_points_set.add(__lowercase      )
								if exits_word(__lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase   ,	word_index + 1   ,	__lowercase      ):
												return True

								visited_points_set.remove(__lowercase      )

				return False






def    a__       ( __lowercase   ,	__lowercase      )		->		bool:
				_A         =	(
				    "The board should be a non empty matrix of single chars strings."
				)

				_A         =	len(__lowercase      )
				if not isinstance(__lowercase   ,	__lowercase      ) or len(__lowercase      ) == 0:
								raise ValueError(__lowercase      )

				for row in board:
								if not isinstance(__lowercase   ,	__lowercase      ) or len(__lowercase      ) == 0:
												raise ValueError(__lowercase      )

								for item in row:
												if not isinstance(__lowercase   ,	__lowercase      ) or len(__lowercase      ) != 1:
																raise ValueError(__lowercase      )

    # Validate word
				if not isinstance(__lowercase   ,	__lowercase      ) or len(__lowercase      ) == 0:
								raise ValueError(
								    "The word parameter should be a string of length greater than 0."      )

				_A         =	len(board[0]      )
				for i in range(__lowercase      ):
								for j in range(__lowercase      ):
												if exits_word(
												    __lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase   ,	0   ,	{get_point_key(__lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase      )}      ):
																return True

				return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()



"""simple docstring"""


def    a__       ( __lowercase = 20      )		->		int:

				try:
								_A         =	int(__lowercase      )
				except (TypeError, ValueError):
								raise TypeError("Parameter n must be int or castable to int."      )
				if n <= 0:
								raise ValueError("Parameter n must be greater than or equal to one."      )
				_A         =	0
				while 1:
								i += n * (n - 1)
								_A         =	0
								for j in range(2   ,	__lowercase      ):
												if i % j != 0:
																_A         =	1
																break
								if nfound == 0:
												if i == 0:
																_A         =	1
												return i
				return None


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