Problem: 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 fi, where 1 ≤ fi ≤ n and fi ≠ 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 f1, f2, ..., fn (1 ≤ fi ≤ n, fi ≠ i), meaning that the i-th plane likes the fi-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.

Examples

Input

5
2 4 5 1 3


Output

YES


Input

5
5 5 5 5 1


Output

NO

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.

Solution (in PYTHON):

Solution:
# -*- coding:utf-8 -*-
#[n, m] = [int(x) for x in raw_input().split()]
def some_func():
    """
    """
    n = input()
    n_list = [int(x) for x in raw_input().split()]

    for i in range(1,n+1):
        if i != n_list[i-1] and n_list[i-1] != n_list[n_list[i-1]-1]   and i != n_list[n_list[i-1]-1]:
            if i == n_list[ n_list[n_list[i-1]-1]-1]:
                return "YES"
    return "NO"



if __name__ == '__main__':
    print some_func()