Game on Permutation

A permutation p of size n (each integer from 1 to n appears exactly once) defines a game. Two players alternate turns. On each turn, a player must pick an index i (0-indexed) such that for all previously picked indices j, p[i] > p[j] — meaning each pick must have a strictly larger value than every previous pick. A player who cannot make a valid move loses. Both play optimally. Determine whether the first player has a winning strategy.

Examples
Input: [4,[1,4,2,3]]
Output: true
Hints

Game on Permutation

A permutation p of size n (each integer from 1 to n appears exactly once) defines a game. Two players alternate turns. On each turn, a player must pick an index i (0-indexed) such that for all previously picked indices j, p[i] > p[j] — meaning each pick must have a strictly larger value than every previous pick. A player who cannot make a valid move loses. Both play optimally. Determine whether the first player has a winning strategy.