Prefix Max Counting

For a permutation $P$, we define $f(P)$ to be it's prefix max array, i.e. $f(P)_i = \max(P_1, P_2, \ldots, P_i)$. Now, you are given a partially filled in permutation $P$ of the integers $[1, N]$, i.e. some elements are $-1$. You want to replace the $-1$ elements with integers in $[1, N]$ to make it a permutation. What are the total number of distinct $f(P)$ possible? Since the answer may be la