Buttons Game

Two players play a game with N buttons arranged in a row. On each turn, a player may press either 1 or 2 adjacent unpressed buttons. Once pressed, a button cannot be used again. The player who presses the last unpressed button wins.

Both players play optimally. Given N, determine whether the first player can force a win.

Examples
Input: 1
Output: true
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Buttons Game

Two players play a game with N buttons arranged in a row. On each turn, a player may press either 1 or 2 adjacent unpressed buttons. Once pressed, a button cannot be used again. The player who presses the last unpressed button wins.