

def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__      )  ->					Union[str, Any]:
	# Return True if there is node that has not iterated.
	__lowerCamelCase    :    Optional[Any] 	=			[False] * len(lowerCamelCase__      )
	__lowerCamelCase    :    Dict 	=			[]
	queue.append(lowerCamelCase__      )
	__lowerCamelCase    :    Union[str, Any] 	=			True

	while queue:
		__lowerCamelCase    :    int 	=			queue.pop(0      )
		for ind in range(len(graph[u]      )      ):
			if visited[ind] is False and graph[u][ind] > 0:
				queue.append(lowerCamelCase__      )
				__lowerCamelCase    :    List[Any] 	=			True
				__lowerCamelCase    :    Dict 	=			u

	return visited[t]






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__      )  ->					Tuple:
	# This array is filled by BFS and to store path
	__lowerCamelCase    :    Tuple 	=			[-1] * (len(lowerCamelCase__      ))
	__lowerCamelCase    :    Tuple 	=			0
	while bfs(lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__      ):
		__lowerCamelCase    :    Tuple 	=			float('Inf'      )
		__lowerCamelCase    :    Tuple 	=			sink

		while s != source:
			# Find the minimum value in select path
			__lowerCamelCase    :    List[str] 	=			min(lowerCamelCase__     ,			graph[parent[s]][s]      )
			__lowerCamelCase    :    Union[str, Any] 	=			parent[s]

		max_flow += path_flow
		__lowerCamelCase    :    Union[str, Any] 	=			sink

		while v != source:
			__lowerCamelCase    :    List[Any] 	=			parent[v]
			graph[u][v] -= path_flow
			graph[v][u] += path_flow
			__lowerCamelCase    :    Optional[Any] 	=			parent[v]
	return max_flow


a		=[
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

a		,	a		=0, 5

print(ford_fulkerson(graph, source, sink))







from __future__ import annotations






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)  ->					None:
	__lowerCamelCase    :    int 	=			len(lowerCamelCase__      )

	# If row is equal to the size of the board it means there are a queen in each row in
	# the current board (possible_board)
	if row == n:
		# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
		# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
		boards.append(['. ' * i + 'Q ' + '. ' * (n - 1 - i) for i in possible_board]      )
		return

	# We iterate each column in the row to find all possible results in each row
	for col in range(lowerCamelCase__      ):
		# We apply that we learned previously. First we check that in the current board
		# (possible_board) there are not other same value because if there is it means
		# that there are a collision in vertical. Then we apply the two formulas we
		# learned before:
		#
		# 45º: y - x = b or 45: row - col = b
		# 135º: y + x = b or row + col = b.
		#
		# And we verify if the results of this two formulas not exist in their variables
		# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
		#
		# If any or these are True it means there is a collision so we continue to the
		# next value in the for loop.
		if (
		    col in possible_board
		    or row - col in diagonal_right_collisions
		    or row + col in diagonal_left_collisions
		):
			continue

		# If it is False we call dfs function again and we update the inputs
		depth_first_search(
		    [*possible_board, col]     ,			[*diagonal_right_collisions, row - col]     ,			[*diagonal_left_collisions, row + col]     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					None:
	__lowerCamelCase    :    list[list[str]] 	=			[]
	depth_first_search([]     ,			[]     ,			[]     ,			lowerCamelCase__     ,			lowerCamelCase__      )

	# Print all the boards
	for board in boards:
		for column in board:
			print(lowerCamelCase__      )
		print(''      )

	print(len(lowerCamelCase__      )     ,			'solutions were found.'      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					n_queens_solution(4)




