Expansion

Chef had with him a permutation $P$ of the integers $\{1, 2, \ldots, N\}$. A permutation of $\{1, 2, \ldots, N\}$ is an array of length $N$ that contains every integer from $1$ to $N$. From this permutation, he created a new array $A$, also of length $N$, by following this process: 1. First, choose a positive integer $X$. 2. Then, for each $1 \le i \le N$, set either $A_i = P_i$ or $A_i = P_i \