
UpperCamelCase_   	=	[
    [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],
]






def 		_UpperCAmelCase   (	UpperCamelCase:     str			,							UpperCamelCase:     Optional[Any]			,							UpperCamelCase:     int			,							UpperCamelCase:     Tuple  ):






	"""simple docstring"""


	__lowerCAmelCase         =							[False] * len(UpperCamelCase  )
	__lowerCAmelCase         =							[s]
	__lowerCAmelCase         =							True

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

	return visited[t]






def 		_UpperCAmelCase   (	UpperCamelCase:     List[str]			,							UpperCamelCase:     Dict			,							UpperCamelCase:     Tuple  ):






	"""simple docstring"""


	__lowerCAmelCase         =							[-1] * (len(UpperCamelCase  ))
	__lowerCAmelCase         =							0
	__lowerCAmelCase         =							[]
	__lowerCAmelCase         =							[i[:] for i in graph]  # Record original cut, copy.
	while bfs(UpperCamelCase			,							UpperCamelCase			,							UpperCamelCase			,							UpperCamelCase  ):
		__lowerCAmelCase         =							float("Inf"  )
		__lowerCAmelCase         =							sink

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

		max_flow += path_flow
		__lowerCAmelCase         =							sink

		while v != source:
			__lowerCAmelCase         =							parent[v]
			graph[u][v] -= path_flow
			graph[v][u] += path_flow
			__lowerCAmelCase         =							parent[v]

	for i in range(len(UpperCamelCase  )  ):
		for j in range(len(graph[0]  )  ):
			if graph[i][j] == 0 and temp[i][j] > 0:
				res.append((i, j)  )

	return res


if __name__ == "__main__":
					print(mincut(test_graph, source=0, sink=5))








from __future__ import annotations

from math import ceil, floor, sqrt






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 2_0_0_0_0_0_0  ):






	"""simple docstring"""


	__lowerCAmelCase         =							[0]
	__lowerCAmelCase         =							42

	for idx in range(1			,							ceil(sqrt(target * 2  ) * 1.1  )  ):
		triangle_numbers.append(triangle_numbers[-1] + idx  )

	# we want this to be as close as possible to target
	__lowerCAmelCase         =							0
	# the area corresponding to the grid that gives the product closest to target
	__lowerCAmelCase         =							0
	# an estimate of b, using the quadratic formula
	__lowerCAmelCase         =							42
	# the largest integer less than b_estimate
	__lowerCAmelCase         =							42
	# the largest integer less than b_estimate
	__lowerCAmelCase         =							42
	# the triangle number corresponding to b_floor
	__lowerCAmelCase         =							42
	# the triangle number corresponding to b_ceil
	__lowerCAmelCase         =							42

	for idx_a, triangle_a in enumerate(triangle_numbers[1:]			,							1  ):
		__lowerCAmelCase         =							(-1 + sqrt(1 + 8 * target / triangle_a  )) / 2
		__lowerCAmelCase         =							floor(UpperCamelCase  )
		__lowerCAmelCase         =							ceil(UpperCamelCase  )
		__lowerCAmelCase         =							triangle_numbers[b_floor]
		__lowerCAmelCase         =							triangle_numbers[b_ceil]

		if abs(target - triangle_b_first_guess * triangle_a  ) < abs(
		    target - best_product  ):
			__lowerCAmelCase         =							triangle_b_first_guess * triangle_a
			__lowerCAmelCase         =							idx_a * b_floor

		if abs(target - triangle_b_second_guess * triangle_a  ) < abs(
		    target - best_product  ):
			__lowerCAmelCase         =							triangle_b_second_guess * triangle_a
			__lowerCAmelCase         =							idx_a * b_ceil

	return area


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






