Permutation Game

A permutation p of size n (containing each integer from 1 to n exactly once) represents a board. Two players alternate turns. On each turn, a player picks the leftmost remaining position i. Let x = p[i] be the value at that position. If x is the maximum among all remaining positions, the player wins immediately. Otherwise, all remaining positions with values greater than x are removed from the board, and the turn passes to the other player. Determine whether the first player can force a win given optimal play from both sides.

Examples
Input: [5,[2,3,5,1,4]]
Output: false
Hints

Permutation Game

A permutation p of size n (containing each integer from 1 to n exactly once) represents a board. Two players alternate turns. On each turn, a player picks the leftmost remaining position i. Let x = p[i] be the value at that position. If x is the maximum among all remaining positions, the player wins immediately. Otherwise, all remaining positions with values greater than x are removed from the board, and the turn passes to the other player. Determine whether the first player can force a win given optimal play from both sides.