public class Solution
extends Object
810 - Chalkboard XOR Game\.
Hard
You are given an array of integers `nums` represents the numbers written on a chalkboard.
Alice and Bob take turns erasing exactly one number from the chalkboard, with Alice starting first. If erasing a number causes the bitwise XOR of all the elements of the chalkboard to become `0`, then that player loses. The bitwise XOR of one element is that element itself, and the bitwise XOR of no elements is `0`.
Also, if any player starts their turn with the bitwise XOR of all the elements of the chalkboard equal to `0`, then that player wins.
Return `true` _if and only if Alice wins the game, assuming both players play optimally_.
**Example 1:**
**Input:** nums = [1,1,2]
**Output:** false
**Explanation:**
Alice has two choices: erase 1 or erase 2.
If she erases 1, the nums array becomes [1, 2].
The bitwise XOR of all the elements of the chalkboard is 1 XOR 2 = 3.
Now Bob can remove any element he wants, because Alice will be the one to erase the last element and she will lose.
If Alice erases 2 first, now nums become [1, 1].
The bitwise XOR of all the elements of the chalkboard is 1 XOR 1 = 0.
Alice will lose.
**Example 2:**
**Input:** nums = [0,1]
**Output:** true
**Example 3:**
**Input:** nums = [1,2,3]
**Output:** true
**Constraints:**
* `1 <= nums.length <= 1000`
* 0 <= nums[i] < 216