Alice and Bob take turns playing a game, with Alice going first. You are given an integer array stones.

On each turn, the active player removes any stone from stones. A player loses immediately if the sum of the values of all removed stones so far is divisible by $3$. If all stones are removed and the total sum of removed stones is never divisible by $3$, Bob wins.

Assuming both players play optimally, return true if Alice wins, or false if Bob wins.

Constraints:

• $1 \leq$ stones.length $\leq 10^5$

• $1 \leq$ stones[i] $\leq 10^4$

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.