Permutation Deletion

You are given an array $A$ of length $N$, which initially is a permutation of integers from $1$ to $N$. We want to make the array empty by performing the following operation $N$ times: choose any index $i$ and remove $A_i$ from $A$, which decrements the size of $A$ by $1$. We will perform exactly $N$ such operations. Apparently, there are $N!$ ways to do this. But now we wonder how many ways sa