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:
from __future__ import division, print_function

import os
import sys
from io import BytesIO, IOBase
from sys import stdin,stdout
from collections import Counter
from math import ceil
from bisect import bisect_left 
from bisect import bisect_right
import math

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip


def lessThanX(a, x): 
    i = bisect_left(a, x) 
    if i: 
        return (i-1) 
    else: 
        return -1

def isprime(n):
    for i in range(2,int(math.sqrt(n))+1):
        if n % i == 0 :
            return False
    return True

def BinarySearchFromRight(a, x): 
    i = bisect_right(a, x) 
    if i != len(a)+1 and a[i-1] == x: 
        return (i-1) 
    else: 
        return -1

def BinarySearch(a, x): 
    i = bisect_left(a, x) 
    if i != len(a) and a[i] == x: 
        return i 
    else: 
        return -1

def main():
    n = ip()
    li = ai()
    d = {}
    for i in range(n):
        d[i+1] = li[i]
    c= 0
    for k,v in d.items():
        try:
            if d[d[d[k]]] == k:
                print('YES')
                c += 1;break
        except:
            pass
    if c==0:
        print('NO')

    

# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

ip = lambda: int(sys.stdin.readline().rstrip("\r\n"))
ai = lambda: list(map(int, sys.stdin.readline().split()))
ei = lambda: map(int, sys.stdin.readline().split())

# endregion

if __name__ == "__main__":
    main()