codeforces 939 A Love Triangle

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 f_i, where 1 ≤ f_i ≤ n and f_i ≠ 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, ..., f_n (1 ≤ f_i ≤ n, f_i ≠ i), meaning that the i-th plane likes the f_i-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

Copy

5
2 4 5 1 3

Output

YES

Input

Copy

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.

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int M=10000;
int n;
int a[M];
int main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
    {
        cin>>a[i];
    }
    bool f=0;
    for(int i=1;i<=n;i++)
    {
        if(a[a[a[i]]]==i)
            f=1;
    }
    if(f)
        cout<<"YES"<<endl;
    else
        cout<<"NO"<<endl;
    return 0;
}