






"""simple docstring"""






def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__				):
				# Return True if there is node that has not iterated.
				A__							 =       [False] * len(lowerCAmelCase__				)
				A__							 =       []
				queue.append(lowerCAmelCase__				)
				A__							 =       True

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

				return visited[t]



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

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

								max_flow += path_flow
								A__							 =       sink

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


SCREAMING_SNAKE_CASE						:						Union[str, 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						:						str					   =       0, 5







print(ford_fulkerson(graph, source, sink))










"""simple docstring"""






class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					A__							 =       name
					A__							 =       val


	def __str__(      self						):


					"""simple docstring"""

					return f'''{self.__class__.__name__}({self.name}, {self.val})'''






	def __lt__(      self  ,					__a						):


					"""simple docstring"""

					return self.val < other.val





class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       {}
					A__							 =       {}
					A__							 =       self.build_heap(__a						)


	def __getitem__(      self  ,					__a						):


					"""simple docstring"""

					return self.get_value(__a						)


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return (idx - 1) // 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 1


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return self.heap_dict[key]


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       len(__a						) - 1
					A__							 =       self.get_parent_idx(__a						)

					for idx, i in enumerate(__a						):
									A__							 =       idx
									A__							 =       i.val

					for i in range(__a  ,					-1  ,					-1						):
									self.sift_down(__a  ,					__a						)
					return array


	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					while True:
									A__							 =       self.get_left_child_idx(__a						)  # noqa: E741
									A__							 =       self.get_right_child_idx(__a						)

									A__							 =       idx
									if l < len(__a						) and array[l] < array[idx]:
													A__							 =       l
									if r < len(__a						) and array[r] < array[smallest]:
													A__							 =       r

									if smallest != idx:
													A__ ,			A__							 =       array[smallest], array[idx]
													(
													    (
													    A__
													) ,			(
													    A__
													) ,			
													)							 =       (
													    self.idx_of_element[array[smallest]],
													    self.idx_of_element[array[idx]],
													)
													A__							 =       smallest
									else:
													break


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       self.get_parent_idx(__a						)
					while p >= 0 and self.heap[p] > self.heap[idx]:
									A__ ,			A__							 =       self.heap[idx], self.heap[p]
									A__ ,			A__							 =       (
									    self.idx_of_element[self.heap[idx]],
									    self.idx_of_element[self.heap[p]],
									)
									A__							 =       p
									A__							 =       self.get_parent_idx(__a						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return self.heap[0]


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					A__ ,			A__							 =       self.heap[-1], self.heap[0]
					A__ ,			A__							 =       (
					    self.idx_of_element[self.heap[-1]],
					    self.idx_of_element[self.heap[0]],
					)

					A__							 =       self.heap.pop()
					del self.idx_of_element[x]
					self.sift_down(0  ,					self.heap						)
					return x


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					self.heap.append(__a						)
					A__							 =       len(self.heap						) - 1
					A__							 =       node.val
					self.sift_up(len(self.heap						) - 1						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return len(self.heap						) == 0






	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					assert (
					    self.heap[self.idx_of_element[node]].val > new_value
					), "newValue must be less that current value"
					A__							 =       new_value
					A__							 =       new_value
					self.sift_up(self.idx_of_element[node]						)





SCREAMING_SNAKE_CASE						:						List[str]					   =       Node('''R''', -1)
SCREAMING_SNAKE_CASE						:						Tuple					   =       Node('''B''', 6)
SCREAMING_SNAKE_CASE						:						List[Any]					   =       Node('''A''', 3)
SCREAMING_SNAKE_CASE						:						int					   =       Node('''X''', 1)
SCREAMING_SNAKE_CASE						:						Union[str, Any]					   =       Node('''E''', 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
SCREAMING_SNAKE_CASE						:						str					   =       MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print('''Min Heap - before decrease key''')
for i in my_min_heap.heap:
					print(i)

print('''Min Heap - After decrease key of node [B -> -17]''')
my_min_heap.decrease_key(b, -17)

# After
for i in my_min_heap.heap:
					print(i)

if __name__ == "__main__":
					import doctest

					doctest.testmod()


