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 JAVA):

Solution:
import java.io.*;
import java.util.*;

import static java.lang.Integer.compare;
import static java.lang.Math.*;
import static java.lang.System.in;
import static java.lang.System.out;
import static java.util.Arrays.deepToString;

/*
 *
 *17/2/18
 *3:35 PM
 *remedy441
 *
 */
public class CF939
{
    public static int mod = (int) (1e9 + 7);
    public static InputReader in;
    public static PrintWriter out;


    public static void solve() throws FileNotFoundException {

    	in = new InputReader(System.in);
    	out = new PrintWriter(System.out);
    	int n = in.ni();
    	int ar[] = new int[n+1];
    	for(int i=1;i<=n;i++)
    	    ar[i]=in.ni();
    	String ans = "NO";
    	for(int i=1;i<=n;i++){
    	    int x = ar[i];
    	    int y = ar[x];
    	    int z = ar[y];
    	    if(z==i) {
                ans = "YES";
                break;
            }
        }
        out.print(ans);
    	out.close();
    }
    public static void main(String[] args) {
    	new Thread(null, new Runnable() {
    		public void run() {
    			try {
    				solve();
    			} catch (Exception e) {
    				e.printStackTrace();
    			}
    		}
    	}, "1", 1 << 26).start();
    }

    static class Pair implements Comparable<Pair> {

    	int x, y, i;

    	Pair(int x, int y, int i) {
    		this.x = x;
    		this.y = y;
    		this.i = i;
    	}

    	Pair(int x, int y) {
    		this.x = x;
    		this.y = y;
    	}

    	public int compareTo(Pair o) {
    		if (this.x != o.x)
    			return compare(this.x, o.x);
    		else
    			return compare(this.y, o.y);
    		//return 0;
    	}

    	public boolean equals(Object o) {
    		if (o instanceof Pair) {
    			Pair p = (Pair) o;
    			return p.x == x && p.y == y && p.i == i;
    		}
    		return false;
    	}

    	public int hashCode() {
    		return new Integer(x).hashCode() * 31 + new Integer(y).hashCode() + new Integer(i).hashCode() * 37;
    	}

    }

    public static long add(long a, long b) {
    	long x = (a + b);
    	while (x >= mod)
    		x -= mod;
    	return x;
    }

    public static long sub(long a, long b) {
    	long x = (a - b);
    	while (x < 0)
    		x += mod;
    	return x;
    }

    public static long mul(long a, long b) {
    	long x = (a * b);
    	while (x >= mod)
    		x -= mod;
    	return x;
    }

    public static boolean isPal(String s) {
    	for (int i = 0, j = s.length() - 1; i <= j; i++, j--) {
    		if (s.charAt(i) != s.charAt(j))
    			return false;
    	}
    	return true;
    }

    public static String rev(String s) {
    	StringBuilder sb = new StringBuilder(s);
    	sb.reverse();
    	return sb.toString();
    }

    public static long gcd(long x, long y) {
    	if (x % y == 0)
    		return y;
    	else
    		return gcd(y, x % y);
    }

    public static int gcd(int x, int y) {
    	if (x % y == 0)
    		return y;
    	else
    		return gcd(y, x % y);
    }

    static int modInverse(int a, int m) {
    	int m0 = m, t, q;
    	int x0 = 0, x1 = 1;
    	if (m == 1)
    		return 0;
    	while (a > 1) {
    		// q is quotient
    		q = a / m;
    		t = m;
    		// m is remainder now, process same as
    		// Euclid's algo
    		m = a % m;
    		a = t;
    		t = x0;
    		x0 = x1 - q * x0;
    		x1 = t;
    	}
    	// Make x1 positive
    	if (x1 < 0)
    		x1 += m0;
    	return x1;
    }

    public static long gcdExtended(long a, long b, long[] x) {

    	if (a == 0) {
    		x[0] = 0;
    		x[1] = 1;
    		return b;
    	}
    	long[] y = new long[2];
    	long gcd = gcdExtended(b % a, a, y);

    	x[0] = y[1] - (b / a) * y[0];
    	x[1] = y[0];

    	return gcd;
    }

    public static long mulmod(long a, long b, long m) {
    	if (m <= 1000000009)
    		return a * b % m;

    	long res = 0;
    	while (a > 0) {
    		if ((a & 1) != 0) {
    			res += b;
    			if (res >= m)
    				res -= m;
    		}
    		a >>= 1;
    		b <<= 1;
    		if (b >= m)
    			b -= m;
    	}
    	return res;
    }

    public static int abs(int a, int b) {
    	return (int) Math.abs(a - b);
    }

    public static long abs(long a, long b) {
    	return (long) Math.abs(a - b);
    }

    public static int max(int a, int b) {
    	if (a > b)
    		return a;
    	else
    		return b;
    }

    public static int min(int a, int b) {
    	if (a > b)
    		return b;
    	else
    		return a;
    }

    public static long max(long a, long b) {
    	if (a > b)
    		return a;
    	else
    		return b;
    }

    public static long min(long a, long b) {
    	if (a > b)
    		return b;
    	else
    		return a;
    }

    public static long pow(long n, long p, long m) {
    	long result = 1;
    	if (p == 0)
    		return 1;
    	if (p == 1)
    		return n;
    	while (p != 0) {
    		if (p % 2 == 1)
    			result *= n;
    		if (result >= m)
    			result %= m;
    		p >>= 1;
    		n *= n;
    		if (n >= m)
    			n %= m;
    	}
    	return result;
    }

    public static long pow(long n, long p) {
    	long result = 1;
    	if (p == 0)
    		return 1;
    	if (p == 1)
    		return n;
    	while (p != 0) {
    		if (p % 2 == 1)
    			result *= n;
    		p >>= 1;
    		n *= n;
    	}
    	return result;
    }

    public static void debug(Object... o) {
    	System.out.println(deepToString(o));
    }

    static class InputReader {
    	private final InputStream stream;
    	private final byte[] buf = new byte[8192];
    	private int curChar, snumChars;
    	private SpaceCharFilter filter;

    	public InputReader(InputStream stream) {
    		this.stream = stream;
    	}

    	public int snext() {
    		if (snumChars == -1)
    			throw new InputMismatchException();
    		if (curChar >= snumChars) {
    			curChar = 0;
    			try {
    				snumChars = stream.read(buf);
    			} catch (IOException e) {
    				throw new InputMismatchException();
    			}
    			if (snumChars <= 0)
    				return -1;
    		}
    		return buf[curChar++];
    	}

    	public int ni() {
    		int c = snext();
    		while (isSpaceChar(c)) {
    			c = snext();
    		}
    		int sgn = 1;
    		if (c == '-') {
    			sgn = -1;
    			c = snext();
    		}
    		int res = 0;
    		do {
    			if (c < '0' || c > '9')
    				throw new InputMismatchException();
    			res *= 10;
    			res += c - '0';
    			c = snext();
    		} while (!isSpaceChar(c));
    		return res * sgn;
    	}

    	public long nl() {
    		int c = snext();
    		while (isSpaceChar(c)) {
    			c = snext();
    		}
    		int sgn = 1;
    		if (c == '-') {
    			sgn = -1;
    			c = snext();
    		}
    		long res = 0;
    		do {
    			if (c < '0' || c > '9')
    				throw new InputMismatchException();
    			res *= 10;
    			res += c - '0';
    			c = snext();
    		} while (!isSpaceChar(c));
    		return res * sgn;
    	}

    	public int[] nIArr(int n) {
    		int a[] = new int[n];
    		for (int i = 0; i < n; i++) {
    			a[i] = ni();
    		}
    		return a;
    	}

    	public long[] nLArr(int n) {
    		long a[] = new long[n];
    		for (int i = 0; i < n; i++) {
    			a[i] = nl();
    		}
    		return a;
    	}

    	public String readString() {
    		int c = snext();
    		while (isSpaceChar(c)) {
    			c = snext();
    		}
    		StringBuilder res = new StringBuilder();
    		do {
    			res.appendCodePoint(c);
    			c = snext();
    		} while (!isSpaceChar(c));
    		return res.toString();
    	}

    	public String nextLine() {
    		int c = snext();
    		while (isSpaceChar(c))
    			c = snext();
    		StringBuilder res = new StringBuilder();
    		do {
    			res.appendCodePoint(c);
    			c = snext();
    		} while (!isEndOfLine(c));
    		return res.toString();
    	}

    	public boolean isSpaceChar(int c) {
    		if (filter != null)
    			return filter.isSpaceChar(c);
    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    	}

    	private boolean isEndOfLine(int c) {
    		return c == '\n' || c == '\r' || c == -1;
    	}

    	public interface SpaceCharFilter {
    		public boolean isSpaceChar(int ch);
    	}

    }

}