You are given an integer array stones, where stones[i] represents the weight of the $i^{th}$ stone.

A game is played as follows: on each turn, any two stones are selected and smashed together. Given two stones with weights x and y where x <= y, the outcome is:

• If x == y, both stones are destroyed.

• If x != y, the stone of weight x is destroyed, and the stone of weight y is replaced with a new stone of weight y - x.

The game ends when at most one stone remains.

Return the smallest possible weight of the remaining stone. If no stones remain, return $0$.

Constraints:

• $1 \leq$ stones.length $\leq 30$

• $1 \leq$ stones[i] $\leq 100$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.