Chalkboard XOR Game

Alice and Bob take turns erasing one number from an array. If after a player's move the XOR of all remaining numbers becomes 0, that player loses. The player who erases the last number also loses (since XOR of an empty set is 0). Determine if Alice can force a win with optimal play.

Examples
Input: [1,1,2]
Output: false
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Chalkboard XOR Game

Alice and Bob take turns erasing one number from an array. If after a player's move the XOR of all remaining numbers becomes 0, that player loses. The player who erases the last number also loses (since XOR of an empty set is 0). Determine if Alice can force a win with optimal play.