Degree of a permutation

Find the degree of a permutation $p$.

A permutation of $n$ elements is an ordered set of $n$ distinct numbers from $1$ to $n$.

The degree of a permutation $p$ is a minimal positive integer $k$ such that $p^k=\epsilon$, where $\epsilon$ is an identity permutation $(1,2,...,n)$.

Input

The first line contains the order $n(0<n\le 100)$ of a permutation $p$. The second line contains the permutation $p$ itself.

Output

Print the degree of the given permutation.

Examples