Divisor Game

Two players take turns playing a game with a starting number N. On each turn, a player selects a positive divisor d of the current number such that 1 ≤ d < N, then subtracts d from N to produce the new number. If a player cannot make a valid move (because no such divisor exists), they lose the game.

Both players play optimally. Given an integer N, determine whether the first player can force a win. Return true if the first player wins, and false otherwise.

Examples
Input: 2
Output: true
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Divisor Game

Two players take turns playing a game with a starting number N. On each turn, a player selects a positive divisor d of the current number such that 1 ≤ d < N, then subtracts d from N to produce the new number. If a player cannot make a valid move (because no such divisor exists), they lose the game.