Arbitrary Shuffling

You are given a permutation $P$ of the integers $[1, N]$. You can do either of the following operations as many times as you want: - Choose an index $X$ ($1 \le X \le N$) such that $P_X = X$, and **shuffle** the subarray $P[1, X]$. - Choose an index $X$ ($1 \le X \le N$) such that $P_X = X$ and **shuffle** the subarray $P[X, N]$. Here the subarray $P[L, R]$ represents the array $[P_L, P_{L + 1}