




'''simple docstring'''

def __UpperCAmelCase	(   _UpperCAmelCase		:   int						)      ->      list:

			# bit count represents no. of bits in the gray code
			if bit_count < 0:
						raise ValueError("The given input must be positive"						)

			# get the generated string sequence
			__snake_case			=		gray_code_sequence_string(_UpperCAmelCase						)
			#
			# convert them to integers
			for i in range(len(_UpperCAmelCase						)						):
						__snake_case			=		int(sequence[i]		,				2						)

			return sequence


def __UpperCAmelCase	(   _UpperCAmelCase		:   int						)      ->      list:

			# The approach is a recursive one
			# Base case achieved when either n = 0 or n=1
			if bit_count == 0:
						return ["0"]

			if bit_count == 1:
						return ["0", "1"]

			__snake_case			=		1 << bit_count  # defines the length of the sequence
			# 1<< n is equivalent to 2^n

			# recursive answer will generate answer for n-1 bits
			__snake_case			=		gray_code_sequence_string(bit_count - 1						)

			__snake_case			=		[]

			# append 0 to first half of the smaller sequence generated
			for i in range(seq_len // 2						):
						__snake_case			=		"0" + smaller_sequence[i]
						sequence.append(_UpperCAmelCase						)

			# append 1 to second half ... start from the end of the list
			for i in reversed(range(seq_len // 2						)						):
						__snake_case			=		"1" + smaller_sequence[i]
						sequence.append(_UpperCAmelCase						)

			return sequence


if __name__ == "__main__":
						import doctest

						doctest.testmod()












def  SCREAMING_SNAKE_CASE				(      snake_case						,   snake_case						,   snake_case						,   snake_case							)		->    int:
		# Return True if there is node that has not iterated.
		__lowercase											=     [False] * len(snake_case							)
		__lowercase											=     []
		queue.append(snake_case							)
		__lowercase											=     True

		while queue:
				__lowercase											=     queue.pop(0							)
				for ind in range(len(graph[u]							)							):
						if visited[ind] is False and graph[u][ind] > 0:
								queue.append(snake_case							)
								__lowercase											=     True
								__lowercase											=     u

		return visited[t]



def  SCREAMING_SNAKE_CASE				(      snake_case						,   snake_case						,   snake_case							)		->    Dict:
		# This array is filled by BFS and to store path
		__lowercase											=     [-1] * (len(snake_case							))
		__lowercase											=     0
		while bfs(snake_case						,   snake_case						,   snake_case						,   snake_case							):
				__lowercase											=     float('Inf'							)
				__lowercase											=     sink

				while s != source:
						# Find the minimum value in select path
						__lowercase											=     min(snake_case						,   graph[parent[s]][s]							)
						__lowercase											=     parent[s]

				max_flow += path_flow
				__lowercase											=     sink

				while v != source:
						__lowercase											=     parent[v]
						graph[u][v] -= path_flow
						graph[v][u] += path_flow
						__lowercase											=     parent[v]
		return max_flow


SCREAMING_SNAKE_CASE_   :      Any			=   [
    [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],
]

SCREAMING_SNAKE_CASE_	,SCREAMING_SNAKE_CASE_   :      Optional[Any]			=   0, 5


print(ford_fulkerson(graph, source, sink))




