Question $3)$ We are given an array of integers stones where stones$[$i$]$ is the weight of the

$i-$th stone. We are playing a game with the stones. On each turn, we choose the heaviest two

stones and smash them together.

Suppose the heaviest two stones have weights $x$ and $y$ with $xy.$ The result of this smash

is:

If $(x==y),$ both stones are destroyed, and

If $(y$ is greater than $x),$ the stone of weight $x$ is destroyed, and the stone of weight $y$ has a new

weight $y-x.$

At the end of the game, there is at most one stone left.

Write an algorithm using a priority queue to return the weight of the last remaining stone.

If there are no stones left, return $0.$ What is the time complexity of your program? Explain

your answer. what is the time complexity of your program?

$(10$ points$)$