Staircase Nim

There are n piles arranged on stairs (pile 1 on step 1, pile 2 on step 2, etc.). A move consists of moving any positive number of stones from a pile on step i to step i-1. Stones reaching step 0 are removed from the game. The player who makes the last move wins. Determine if the first player has a winning strategy.

Examples
Input: [3,2,1]
Output: true
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Staircase Nim

There are `n` piles arranged on stairs (pile 1 on step 1, pile 2 on step 2, etc.). A move consists of moving any positive number of stones from a pile on step `i` to step `i-1`. Stones reaching step 0 are removed from the game. The player who makes the last move wins. Determine if the first player has a winning strategy.