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:
def inp():
    ls=list(map(int,input().split()))
    return ls
n=int(input())
ls=inp()
flag=True
for i in range(n):
    #print(ls[i], ls[ls[i] - 1], ls[ls[ls[i] - 1]-1])
    if ls[ls[ls[ls[i]-1]-1]-1]==ls[i] and len(set([ls[i],ls[ls[i]-1],ls[ls[ls[i]-1]-1]]))==3:
        print("YES")
        flag=False
        break
if flag:
    print("NO")