Alice and Bob are playing a game with a pile of n stones, with Alice taking the first turn.

On each turn, a player must remove a specific number of stones from the pile:

• On the first turn, the player must remove exactly $10$ stones.

• On each subsequent turn, the current player must remove exactly $1$ fewer stone than the number of stones removed in the previous turn.

The game ends when a player is unable to make a valid move because there are not enough stones left in the pile. That player loses the game.

Given the integer n, return true if Alice wins the game assuming both players play optimally, or false otherwise.

Constraints:

• $1 \leq$ n $\leq 50$

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.