Idempotent functions

Some time ago Leonid have known about idempotent functions. Idempotent function defined on a set {1, 2, …, n} is such function , that for any  the formula g(g(x)) = g(x) holds.

Let’s denote as f ^(k)(x) the function f applied k times to the value x. More formally, f ⁽¹⁾(x) = f(x), f ^(k)(x) = f(f ^(k - 1)(x)) for each k > 1.

You are given some function . Your task is to find minimum positive integer k such that function f ^(k)(x) is idempotent.

Input

In the first line of the input there is a single integer n (1 ≤ n ≤ 200) — the size of function f domain.

In the second line follow f(1), f(2), …, f(n) (1 ≤ f(i) ≤ n for each 1 ≤ i ≤ n), the values of a function.

Output

Output minimum k such that function f ^(k)(x) is idempotent.

Examples

input

4
1 2 2 4

output

1

input

3
2 3 3

output

2

input

3
2 3 1

output

3

Note

In the first sample test function f(x) = f ⁽¹⁾(x) is already idempotent since f(f(1)) = f(1) = 1, f(f(2)) = f(2) = 2, f(f(3)) = f(3) = 2, f(f(4)) = f(4) = 4.

In the second sample test:

• function f(x) = f ⁽¹⁾(x) isn’t idempotent because f(f(1)) = 3 but f(1) = 2;
• function f(x) = f ⁽²⁾(x) is idempotent since for any x it is true that f ⁽²⁾(x) = 3, so it is also true that f ⁽²⁾(f ⁽²⁾(x)) = 3.

In the third sample test:

• function f(x) = f ⁽¹⁾(x) isn’t idempotent because f(f(1)) = 3 but f(1) = 2;
• function f(f(x)) = f ⁽²⁾(x) isn’t idempotent because f ⁽²⁾(f ⁽²⁾(1)) = 2 but f ⁽²⁾(1) = 3;
• function f(f(f(x))) = f ⁽³⁾(x) is idempotent since it is identity function: f ⁽³⁾(x) = x for any  meaning that the formula f ⁽³⁾(f ⁽³⁾(x)) = f ⁽³⁾(x) also holds.

Solution:

import java.io.Reader;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;

/**
* Built using CHelper plug-in
* Actual solution is at the top
* @author Niyaz Nigmatullin
*/
public class Main {
public static void main(String[] args) {
InputStream inputStream = System.in;
OutputStream outputStream = System.out;
FastScanner in = new FastScanner(inputStream);
FastPrinter out = new FastPrinter(outputStream);
TaskC solver = new TaskC();
solver.solve(1, in, out);
out.close();
}
}

class TaskC {
public void solve(int testNumber, FastScanner in, FastPrinter out) {
int n = in.nextInt();
int[] f = new int[n];
for (int i = 0; i < n; i++) f[i] = in.nextInt() - 1;
        int[] was = new int[n];
        int[] d = new int[n];
        BigInteger ans = BigInteger.ONE;
        for (int i = 0; i < n; i++) {
            Arrays.fill(was, 0);
            int p = i;
            int c = 0;
            while (was[p] == 0) {
                d[p] = c++;
                was[p] = 1;
                p = f[p];
            }
            BigInteger cycle = BigInteger.valueOf(c - d[p]);
            ans = ans.divide(ans.gcd(cycle)).multiply(cycle);
        }
        for (int q = 1; q <= 2 * n; q++) {
            boolean bad = false;
            for (int i = 0; i < n; i++) {
                int v = i;
                for (int j = 0; j < q; j++) v = f[v];
                int u = v;
                for (int j = 0; j < q; j++) u = f[u];
                if (v != u) {
                    bad = true;
                }
            }
            if (!bad) {
                out.println(q);
                return;
            }
        }
        out.println(ans);
    }
}

class FastScanner extends BufferedReader {

    public FastScanner(InputStream is) {
        super(new InputStreamReader(is));
    }

    public int read() {
        try {
            int ret = super.read();
//            if (isEOF && ret < 0) {
//                throw new InputMismatchException();
//            }
//            isEOF = ret == -1;
            return ret;
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    static boolean isWhiteSpace(int c) {
        return c >= 0 && c <= 32;
    }

    public int nextInt() {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int ret = 0;
        while (c >= 0 && !isWhiteSpace(c)) {
if (c < '0' || c > '9') {
throw new NumberFormatException("digit expected " + (char) c
+ " found");
}
ret = ret * 10 + c - '0';
c = read();
}
return ret * sgn;
}

public String readLine() {
try {
return super.readLine();
} catch (IOException e) {
return null;
}
}

}

class FastPrinter extends PrintWriter {

public FastPrinter(OutputStream out) {
super(out);
}

}