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 PYTHON3):

Solution:
from sys import stdin as si
from collections import Counter as c


class Solution:

    def __init__(self):
        self.track = []

    def lovetriangle(self,m,i):

        if len(self.track)==2:
            if m[i] -1 == self.track[0]:
                print ('YES')
                exit(0)
            else:
                return

        else:
            self.track.append(i)
            self.lovetriangle(m,m[i]-1)
            self.track.pop(-1)








if __name__ == '__main__':
    #for i in range(int(si.readline().strip())):
    n = si.readline().strip()
    m = list(map(int, si.readline().strip().split()))
    S = Solution()
    for i in range(len(m)):
        S.lovetriangle(m,i)
    else:
        print ('NO')


'''
http://codeforces.com/contest/939/problem/A
'''