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:
n = int(input())
lovers = input().split(' ')
lovers = [int(i) for i in lovers]
graph = {}
vis = []
for i in range(1, n+1):
    graph[i] = lovers[i-1]
    vis.append(False)


def find_Tri(start, count, origin):
    #print(start, vis[start-1], count)
    if vis[start-1] and count==3 and start == origin:
        return True
    elif vis[start-1] and count!=3:
        return False
    count+=1
    vis[start-1] = True
    #print(count)
    d = find_Tri(graph[start], count, origin)
    vis[start-1] = False

    return d


if n < 3:
    print('No')
else:
    out = 'No'
    for i in range(1, n+1):
        if find_Tri(i,0,i):
            out = 'Yes'
            break
    print(out)