

"""simple docstring"""






from __future__ import annotations



def   lowercase_	(    _lowercase       :		list							,      _lowercase       :		int | None = None							,      _lowercase       :		int | None = None	):




					'''simple docstring'''






					if start is None:
										UpperCAmelCase			:   Union[str, Any]      =				0

					if end is None:
										UpperCAmelCase			:   Optional[int]      =				len(_lowercase	) - 1

					if start >= end:
										return

					UpperCAmelCase			:   int      =				(start + end) // 2

					slowsort(_lowercase							,      _lowercase							,      _lowercase	)
					slowsort(_lowercase							,      mid + 1							,      _lowercase	)

					if sequence[end] < sequence[mid]:
										UpperCAmelCase      ,							UpperCAmelCase			:   Tuple      =				sequence[mid], sequence[end]

					slowsort(_lowercase							,      _lowercase							,      end - 1	)


if __name__ == "__main__":
	from doctest import testmod

	testmod()





"""simple docstring"""






def   lowercase_	(    _lowercase       :		List[str]							,      _lowercase       :		Tuple							,      _lowercase       :		int							,      _lowercase       :		Optional[Any]	):




					'''simple docstring'''






					UpperCAmelCase			:   int      =				[False] * len(_lowercase	)
					UpperCAmelCase			:   List[str]      =				[]
					queue.append(_lowercase	)
					UpperCAmelCase			:   List[Any]      =				True

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

					return visited[t]



def   lowercase_	(    _lowercase       :		Tuple							,      _lowercase       :		Dict							,      _lowercase       :		Optional[int]	):




					'''simple docstring'''






					UpperCAmelCase			:   List[Any]      =				[-1] * (len(_lowercase	))
					UpperCAmelCase			:   List[Any]      =				0
					while bfs(_lowercase							,      _lowercase							,      _lowercase							,      _lowercase	):
										UpperCAmelCase			:   List[str]      =				float("Inf"	)
										UpperCAmelCase			:   str      =				sink

										while s != source:
															# Find the minimum value in select path
															UpperCAmelCase			:   Tuple      =				min(_lowercase							,      graph[parent[s]][s]	)
															UpperCAmelCase			:   Optional[Any]      =				parent[s]

										max_flow += path_flow
										UpperCAmelCase			:   List[str]      =				sink

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


snake_case_   :   Optional[Any]        =       [
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

snake_case_     ,      snake_case_   :   str        =       0, 5




print(ford_fulkerson(graph, source, sink))


