Alice and Bob play a game with an integer array nums written on a chalkboard. Alice takes the first turn.

On each turn, a player selects and removes one element from nums. If removing that element causes the bitwise XOR of all remaining numbers on the chalkboard to become $0$, that player loses.

Additionally, if the bitwise XOR of all elements currently on the chalkboard is already $0$ at the start of a player’s turn, that player wins immediately.

Assuming both players play optimally, return true if Alice wins the game, or false otherwise.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $0 \leq$ nums[i] $< 2^{16}$

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.