

"""simple docstring"""






import math



def   lowercase_	(    _lowercase       :		int	):




					'''simple docstring'''






					UpperCAmelCase			:   Optional[int]      =				[]
					UpperCAmelCase			:   str      =				2
					UpperCAmelCase			:   int      =				int(math.sqrt(_lowercase	)	)  # Size of every segment
					UpperCAmelCase			:   Optional[Any]      =				[True] * (end + 1)
					UpperCAmelCase			:   List[Any]      =				[]

					while start <= end:
										if temp[start] is True:
															in_prime.append(_lowercase	)
															for i in range(start * start							,      end + 1							,      _lowercase	):
																				UpperCAmelCase			:   Union[str, Any]      =				False
										start += 1
					prime += in_prime

					UpperCAmelCase			:   str      =				end + 1
					UpperCAmelCase			:   int      =				min(2 * end							,      _lowercase	)

					while low <= n:
										UpperCAmelCase			:   int      =				[True] * (high - low + 1)
										for each in in_prime:
															UpperCAmelCase			:   Optional[Any]      =				math.floor(low / each	) * each
															if t < low:
																				t += each

															for j in range(_lowercase							,      high + 1							,      _lowercase	):
																				UpperCAmelCase			:   Optional[Any]      =				False

										for j in range(len(_lowercase	)	):
															if temp[j] is True:
																				prime.append(j + low	)

										UpperCAmelCase			:   str      =				high + 1
										UpperCAmelCase			:   int      =				min(high + end							,      _lowercase	)

					return prime




print(sieve(1_0**6))





"""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))


