




class 						lowercase							:

     def __init__(  self		,     _a		,     _a				)						->							str:
           _A							:     List[str]			=						name
           _A							:     Union[str, Any]			=						val

     def __str__(  self				)						->							Dict:
           return F'''{self.__class__.__name__}({self.name}, {self.val})'''



     def __lt__(  self		,     _a				)						->							int:
           return self.val < other.val







class 						lowercase							:

     def __init__(  self		,     _a				)						->							Union[str, Any]:
           _A							:     str			=						{}
           _A							:     int			=						{}
           _A							:     Any			=						self.build_heap(lowerCAmelCase__				)

     def __getitem__(  self		,     _a				)						->							Optional[Any]:
           return self.get_value(lowerCAmelCase__				)

     def 					a__	(  self		,     _a				)						->							Any:
           return (idx - 1) // 2

     def 					a__	(  self		,     _a				)						->							Dict:
           return idx * 2 + 1

     def 					a__	(  self		,     _a				)						->							List[Any]:
           return idx * 2 + 2

     def 					a__	(  self		,     _a				)						->							Optional[int]:
           return self.heap_dict[key]

     def 					a__	(  self		,     _a				)						->							Any:
           _A							:     Tuple			=						len(lowerCAmelCase__				) - 1
           _A							:     List[str]			=						self.get_parent_idx(lowerCAmelCase__				)

           for idx, i in enumerate(lowerCAmelCase__				):
                 _A							:     Union[str, Any]			=						idx
                 _A							:     str			=						i.val

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

     def 					a__	(  self		,     _a		,     _a				)						->							Dict:
           while True:
                 _A							:     Optional[Any]			=						self.get_left_child_idx(lowerCAmelCase__				)  # noqa: E741
                 _A							:     Dict			=						self.get_right_child_idx(lowerCAmelCase__				)

                 _A							:     int			=						idx
                 if l < len(lowerCAmelCase__				) and array[l] < array[idx]:
                       _A							:     List[str]			=						l
                 if r < len(lowerCAmelCase__				) and array[r] < array[smallest]:
                       _A							:     str			=						r

                 if smallest != idx:
                       _A							:     Any			=						array[smallest], array[idx]
                       (
                           _A    
                       )							:     Optional[Any]			=						(
                           self.idx_of_element[array[smallest]],
                           self.idx_of_element[array[idx]],
                       )
                       _A							:     Optional[int]			=						smallest
                 else:
                       break

     def 					a__	(  self		,     _a				)						->							List[str]:
           _A							:     Any			=						self.get_parent_idx(lowerCAmelCase__				)
           while p >= 0 and self.heap[p] > self.heap[idx]:
                 _A							:     List[Any]			=						self.heap[idx], self.heap[p]
                 _A							:     Tuple			=						(
                     self.idx_of_element[self.heap[idx]],
                     self.idx_of_element[self.heap[p]],
                 )
                 _A							:     Union[str, Any]			=						p
                 _A							:     Optional[int]			=						self.get_parent_idx(lowerCAmelCase__				)

     def 					a__	(  self				)						->							List[Any]:
           return self.heap[0]

     def 					a__	(  self				)						->							List[str]:
           _A							:     Tuple			=						self.heap[-1], self.heap[0]
           _A							:     List[str]			=						(
               self.idx_of_element[self.heap[-1]],
               self.idx_of_element[self.heap[0]],
           )

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

     def 					a__	(  self		,     _a				)						->							Optional[Any]:
           self.heap.append(lowerCAmelCase__				)
           _A							:     List[str]			=						len(self.heap				) - 1
           _A							:     List[str]			=						node.val
           self.sift_up(len(self.heap				) - 1				)

     def 					a__	(  self				)						->							int:
           return len(self.heap				) == 0



     def 					a__	(  self		,     _a		,     _a				)						->							Optional[Any]:
           assert (
               self.heap[self.idx_of_element[node]].val > new_value
           ), "newValue must be less that current value"
           _A							:     Any			=						new_value
           _A							:     Tuple			=						new_value
           self.sift_up(self.idx_of_element[node]				)


_snake_case										=       Node("R", -1)
_snake_case										=       Node("B", 6)
_snake_case										=       Node("A", 3)
_snake_case										=       Node("X", 1)
_snake_case										=       Node("E", 4)

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

# Generating Min-Heap from array
_snake_case										=       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()




def 			A_      (    _UpperCAmelCase    ):
						SCREAMING_SNAKE_CASE_: List[str]  		=       [0] * len(_UpperCAmelCase    )
						SCREAMING_SNAKE_CASE_: List[Any]  		=       []
						SCREAMING_SNAKE_CASE_: str  		=       []
						SCREAMING_SNAKE_CASE_: List[str]  		=       0

						for values in graph.values():
												for i in values:
																		indegree[i] += 1

						for i in range(len(_UpperCAmelCase    )    ):
												if indegree[i] == 0:
																		queue.append(_UpperCAmelCase    )

						while queue:
												SCREAMING_SNAKE_CASE_: Optional[int]  		=       queue.pop(0    )
												cnt += 1
												topo.append(_UpperCAmelCase    )
												for x in graph[vertex]:
																		indegree[x] -= 1
																		if indegree[x] == 0:
																								queue.append(_UpperCAmelCase    )

						if cnt != len(_UpperCAmelCase    ):
												print("Cycle exists"    )
						else:
												print(_UpperCAmelCase    )


# Adjacency List of Graph
lowerCAmelCase							:  Any   	=						{0: [1, 2], 1: [3], 2: [3], 3: [4, 5], 4: [], 5: []}



topological_sort(graph)






