




import heapq





def 	__A	(			__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase					)   -> Optional[Any]:
	a		       =							[(0, start)]  # cost from start node,end node
	a		       =							set()
	while heap:
		((a)       ,				(a))		       =							heapq.heappop(__lowerCamelCase					)
		if u in visited:
			continue
		visited.add(__lowerCamelCase					)
		if u == end:
			return cost
		for v, c in graph[u]:
			if v in visited:
				continue
			a		       =							cost + c
			heapq.heappush(__lowerCamelCase							,    (next_item, v)					)
	return -1


__UpperCamelCase      : Union[str, Any]					      =   {
    "A": [["B", 2], ["C", 5]],
    "B": [["A", 2], ["D", 3], ["E", 1], ["F", 1]],
    "C": [["A", 5], ["F", 3]],
    "D": [["B", 3]],
    "E": [["B", 4], ["F", 3]],
    "F": [["C", 3], ["E", 3]],
}
__UpperCamelCase      : Tuple					      =   {
    "B": [["C", 1]],
    "C": [["D", 1]],
    "D": [["F", 1]],
    "E": [["B", 1], ["F", 3]],
    "F": [],
}
__UpperCamelCase      : str					      =   {
    "B": [["C", 1]],
    "C": [["D", 1]],
    "D": [["F", 1]],
    "E": [["B", 1], ["G", 2]],
    "F": [],
    "G": [["F", 1]],
}

__UpperCamelCase      : Tuple					      =   dijkstra(G, "E", "C")
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

__UpperCamelCase      : Dict					      =   dijkstra(Ga, "E", "F")
print(short_distance)  # E -- 3 --> F == 3

__UpperCamelCase      : Any					      =   dijkstra(Ga, "E", "F")
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
		import doctest

		doctest.testmod()







from itertools import combinations, product





def 	__A	(			__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase					)   -> bool:
	if xa == ya == 0 or xa == ya == 0:
		return False
	a		       =							xa * xa + ya * ya
	a		       =							xa * xa + ya * ya
	a		       =							(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
	return (
	    a_square + b_square == c_square
	    or a_square + c_square == b_square
	    or b_square + c_square == a_square
	)





def 	__A	(			__lowerCamelCase = 50					)   -> int:
	return sum(
	    1
	    for pta, pta in combinations(product(range(limit + 1					)							,    repeat=2					)							,    2					)
	    if is_right(*__lowerCamelCase							,    *__lowerCamelCase					)					)


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

