As you could know there are no male planes nor female planes. However, each plane on Earth likes some other plane. There are $*n*$ planes on Earth, numbered from $1$ to $*n*$, and the plane with number $*i*$ likes the plane with number $*f*_{*i*}$, where $1 ≤ *f*_{*i*} ≤ *n*$ and $*f*_{*i*} ≠ *i*$.

We call a love triangle a situation in which plane $*A*$ likes plane $*B*$, plane $*B*$ likes plane $*C*$ and plane $*C*$ likes plane $*A*$. Find out if there is any love triangle on Earth.

Input

The first line contains a single integer $*n*$ ($2 ≤ *n* ≤ 5000$) — the number of planes.

The second line contains $*n*$ integers $*f*_{1}, *f*_{2}, ..., *f*_{*n*}$ ($1 ≤ *f*_{*i*} ≤ *n*$, $*f*_{*i*} ≠ *i*$), meaning that the $*i*$-th plane likes the $*f*_{*i*}$-th.

Output

Output «YES» if there is a love triangle consisting of planes on Earth. Otherwise, output «NO».

You can output any letter in lower case or in upper case.

Note

In first example plane $2$ likes plane $4$, plane $4$ likes plane $1$, plane $1$ likes plane $2$ and that is a love triangle.

In second example there are no love triangles.