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:
'''
    Auther: ghoshashis545 Ashis Ghosh
    College: jalpaiguri Govt Enggineerin College
    Date:24/03/2020
'''
from math import ceil,sqrt,log,gcd
def ii():return int(input())
def si():return input()
def mi():return map(int,input().split())
def li():return list(mi())
def main():
    
    n=ii()
    m={}
    a=li()
    f=0
    for i in range(n):
        m[i+1]=a[i]
    for i in range(n):
        x=a[i]
        y=m[x]
        z=m[y]
        if(y!=i+1 and z==i+1):
            f=1
            break
    if(f):
        print('YES')
    else:
        print('NO')
    
    
    
    
    
    
    
    
    
    
    
    
    






    
if __name__ =="__main__":
    main()