

class        A_		:
							def __init__(		self		:			Optional[Any]   ,SCREAMING_SNAKE_CASE__		:			Tuple   ,SCREAMING_SNAKE_CASE__		:			Any):
								__lowerCamelCase				:				Union[str, Any]					       = name
								__lowerCamelCase				:				Optional[int]					       = val
							def __str__(		self		:			str):
								return F"{self.__class__.__name__}({self.name}, {self.val})"


							def __lt__(		self		:			str   ,SCREAMING_SNAKE_CASE__		:			List[str]):
								return self.val < other.val






class        A_		:
							def __init__(		self		:			List[Any]   ,SCREAMING_SNAKE_CASE__		:			Optional[int]):
								__lowerCamelCase				:				Optional[Any]					       = {}
								__lowerCamelCase				:				Union[str, Any]					       = {}
								__lowerCamelCase				:				Any					       = self.build_heap(SCREAMING_SNAKE_CASE__)
							def __getitem__(		self		:			Union[str, Any]   ,SCREAMING_SNAKE_CASE__		:			str):
								return self.get_value(SCREAMING_SNAKE_CASE__)
							def     lowerCAmelCase     (		self		:			Tuple   ,SCREAMING_SNAKE_CASE__		:			Dict):
								return (idx - 1) // 2
							def     lowerCAmelCase     (		self		:			Union[str, Any]   ,SCREAMING_SNAKE_CASE__		:			List[Any]):
								return idx * 2 + 1
							def     lowerCAmelCase     (		self		:			Tuple   ,SCREAMING_SNAKE_CASE__		:			List[str]):
								return idx * 2 + 2
							def     lowerCAmelCase     (		self		:			Tuple   ,SCREAMING_SNAKE_CASE__		:			Tuple):
								return self.heap_dict[key]
							def     lowerCAmelCase     (		self		:			Union[str, Any]   ,SCREAMING_SNAKE_CASE__		:			Tuple):
								__lowerCamelCase				:				Optional[Any]					       = len(SCREAMING_SNAKE_CASE__) - 1
								__lowerCamelCase				:				Any					       = self.get_parent_idx(SCREAMING_SNAKE_CASE__)

								for idx, i in enumerate(SCREAMING_SNAKE_CASE__):
									__lowerCamelCase				:				Tuple					       = idx
									__lowerCamelCase				:				Optional[Any]					       = i.val

								for i in range(SCREAMING_SNAKE_CASE__   ,-1   ,-1):
									self.sift_down(SCREAMING_SNAKE_CASE__   ,SCREAMING_SNAKE_CASE__)
								return array
							def     lowerCAmelCase     (		self		:			Tuple   ,SCREAMING_SNAKE_CASE__		:			Optional[int]   ,SCREAMING_SNAKE_CASE__		:			Any):
								while True:
									__lowerCamelCase				:				str					       = self.get_left_child_idx(SCREAMING_SNAKE_CASE__)  # noqa: E741
									__lowerCamelCase				:				List[str]					       = self.get_right_child_idx(SCREAMING_SNAKE_CASE__)

									__lowerCamelCase				:				str					       = idx
									if l < len(SCREAMING_SNAKE_CASE__) and array[l] < array[idx]:
										__lowerCamelCase				:				Optional[Any]					       = l
									if r < len(SCREAMING_SNAKE_CASE__) and array[r] < array[smallest]:
										__lowerCamelCase				:				List[str]					       = r

									if smallest != idx:
										__lowerCamelCase       , __lowerCamelCase				:				Union[str, Any]					       = array[smallest], array[idx]
										(
										    (
										    __lowerCamelCase
										)       , (
										    __lowerCamelCase
										)       , 
										)				:				int					       = (
										    self.idx_of_element[array[smallest]],
										    self.idx_of_element[array[idx]],
										)
										__lowerCamelCase				:				Optional[int]					       = smallest
									else:
										break
							def     lowerCAmelCase     (		self		:			str   ,SCREAMING_SNAKE_CASE__		:			List[Any]):
								__lowerCamelCase				:				Optional[Any]					       = self.get_parent_idx(SCREAMING_SNAKE_CASE__)
								while p >= 0 and self.heap[p] > self.heap[idx]:
									__lowerCamelCase       , __lowerCamelCase				:				int					       = self.heap[idx], self.heap[p]
									__lowerCamelCase       , __lowerCamelCase				:				Union[str, Any]					       = (
									    self.idx_of_element[self.heap[idx]],
									    self.idx_of_element[self.heap[p]],
									)
									__lowerCamelCase				:				str					       = p
									__lowerCamelCase				:				int					       = self.get_parent_idx(SCREAMING_SNAKE_CASE__)
							def     lowerCAmelCase     (		self		:			List[str]):
								return self.heap[0]
							def     lowerCAmelCase     (		self		:			int):
								__lowerCamelCase       , __lowerCamelCase				:				Tuple					       = self.heap[-1], self.heap[0]
								__lowerCamelCase       , __lowerCamelCase				:				Tuple					       = (
								    self.idx_of_element[self.heap[-1]],
								    self.idx_of_element[self.heap[0]],
								)

								__lowerCamelCase				:				Optional[Any]					       = self.heap.pop()
								del self.idx_of_element[x]
								self.sift_down(0   ,self.heap)
								return x
							def     lowerCAmelCase     (		self		:			str   ,SCREAMING_SNAKE_CASE__		:			Union[str, Any]):
								self.heap.append(SCREAMING_SNAKE_CASE__)
								__lowerCamelCase				:				Optional[int]					       = len(self.heap) - 1
								__lowerCamelCase				:				str					       = node.val
								self.sift_up(len(self.heap) - 1)
							def     lowerCAmelCase     (		self		:			Optional[int]):
								return len(self.heap) == 0


							def     lowerCAmelCase     (		self		:			int   ,SCREAMING_SNAKE_CASE__		:			str   ,SCREAMING_SNAKE_CASE__		:			List[Any]):
								assert (
								    self.heap[self.idx_of_element[node]].val > new_value
								), "newValue must be less that current value"
								__lowerCamelCase				:				List[str]					       = new_value
								__lowerCamelCase				:				Dict					       = new_value
								self.sift_up(self.idx_of_element[node])
a		=Node("""R""", -1)
a		=Node("""B""", 6)
a		=Node("""A""", 3)
a		=Node("""X""", 1)
a		=Node("""E""", 4)

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

# Generating Min-Heap from array
a		=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()








"""simple docstring"""
def 		lowercase							(     _snake_case						:      int     ,   _snake_case						:      int     )     ->str:
	"""simple docstring"""





	if a < 0 or b < 0:
		raise ValueError('''the value of both inputs must be positive'''     )
	__snake_case	:						Tuple						=				str(bin(_snake_case     )     )[2:]  # remove the leading "0b"
	__snake_case	:						List[Any]						=				str(bin(_snake_case     )     )[2:]
	__snake_case	:						Any						=				max(len(_snake_case     )     ,   len(_snake_case     )     )
	return "0b" + "".join(
	    str(int('''1''' in (char_a, char_b)     )     )
	    for char_a, char_b in zip(a_binary.zfill(_snake_case     )     ,   b_binary.zfill(_snake_case     )     )     )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





