Finding All

Define a function $f(x, y)$ for integers $x, y$ such that $-1 \le x, y \le 1$ in the following way: - $f(x, y) = -1$ if $x < y$ - $f(x, y) = 0$ if $x = y$ - $f(x, y) = 1$ if $x > y$ You are given an array $A$ of $N$ integers such that $-1 \le A_i \le 1$, and initially integer $X = 0$. Consider the following process: - For each $i = 1, 2, \ldots, N$, update $X = f(X, A_i)$. Over all possible