Nim Game II

In this version of Nim, a player may remove 1 or 2 stones from a chosen pile on each turn. The player who takes the last stone wins. Given n piles and their sizes, determine if the first player has a winning strategy.

Examples
Input: [1,1]
Output: false
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Nim Game II

In this version of Nim, a player may remove 1 or 2 stones from a chosen pile on each turn. The player who takes the last stone wins. Given `n` piles and their sizes, determine if the first player has a winning strategy.