Description: 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 Format: 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 Format: 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. 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.