



'''simple docstring'''

def   __lowerCamelCase  (   lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_						)    ->   int:
		return len_board * len_board_column * row + column



def   __lowerCamelCase  (   lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    )    ->   bool:

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

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

		_a  :   Tuple				 =							[(0, 1), (0, -1), (-1, 0), (1, 0)]
		_a  :   int				 =							len(lowerCAmelCase_						)
		_a  :   Tuple				 =							len(board[0]						)
		for direction in traverts_directions:
				_a  :   Union[str, Any]				 =							row + direction[0]
				_a  :   Dict				 =							column + direction[1]
				if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
						continue

				_a  :   Union[str, Any]				 =							get_point_key(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_						)
				if key in visited_points_set:
						continue

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

				visited_points_set.remove(lowerCAmelCase_						)

		return False



def   __lowerCamelCase  (   lowerCAmelCase_		,    lowerCAmelCase_						)    ->   bool:
		_a  :   List[str]				 =							(
		    'The board should be a non empty matrix of single chars strings.'
		)

		_a  :   List[Any]				 =							len(lowerCAmelCase_						)
		if not isinstance(lowerCAmelCase_		,    lowerCAmelCase_						) or len(lowerCAmelCase_						) == 0:
				raise ValueError(lowerCAmelCase_						)

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

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

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

		_a  :   List[Any]				 =							len(board[0]						)
		for i in range(lowerCAmelCase_						):
				for j in range(lowerCAmelCase_						):
						if exits_word(
						    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    0		,    {get_point_key(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_						)}						):
								return True

		return False


if __name__ == "__main__":
							import doctest

							doctest.testmod()









'''simple docstring'''

def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   tuple[int, int]:
		# base case
		if len(lowerCAmelCase_						) == 1:
				return a[0], a[0]
		else:
				# split A into half.
				_a  :   Union[str, Any]				 =							a[: len(lowerCAmelCase_						) // 2]
				_a  :   List[Any]				 =							a[len(lowerCAmelCase_						) // 2 :]

				# 2 sub problems, 1/2 of original size.
				_a ,      _a  :   Any				 =							max_difference(lowerCAmelCase_						)
				_a ,      _a  :   Any				 =							max_difference(lowerCAmelCase_						)

				# get min of first and max of second
				# linear time
				_a  :   Union[str, Any]				 =							min(lowerCAmelCase_						)
				_a  :   Optional[int]				 =							max(lowerCAmelCase_						)

				# 3 cases, either (small1, big1),
				# (min_first, max_second), (small2, big2)
				# constant comparisons
				if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
						return smalla, biga
				elif biga - smalla > max_second - min_first:
						return smalla, biga
				else:
						return min_first, max_second


if __name__ == "__main__":
							import doctest

							doctest.testmod()




