in python 3

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 1f_in and f_ii.

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 (2n5000) the number of planes.

The second line contains n integers f₁,f₂,...,f_n (1f_in, f_ii), 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

5 2 4 5 1 3 

output

YES 

input

Copy

5 5 5 5 5 1 

output

NO 

input

3

3 1 2

output

yes

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.