Problem: Artsem has a friend Saunders from University of Chicago. Saunders presented him with the following problem.

Let [n] denote the set {1, ..., n}. We will also write f: [x] → [y] when a function f is defined in integer points 1, ..., x, and all its values are integers from 1 to y.

Now then, you are given a function f: [n] → [n]. Your task is to find a positive integer m, and two functions g: [n] → [m], h: [m] → [n], such that g(h(x)) = x for all <image>, and h(g(x)) = f(x) for all <image>, or determine that finding these is impossible.

Input

The first line contains an integer n (1 ≤ n ≤ 105).

The second line contains n space-separated integers — values f(1), ..., f(n) (1 ≤ f(i) ≤ n).

Output

If there is no answer, print one integer -1.

Otherwise, on the first line print the number m (1 ≤ m ≤ 106). On the second line print n numbers g(1), ..., g(n). On the third line print m numbers h(1), ..., h(m).

If there are several correct answers, you may output any of them. It is guaranteed that if a valid answer exists, then there is an answer satisfying the above restrictions.

Examples

Input

3
1 2 3


Output

3
1 2 3
1 2 3


Input

3
2 2 2


Output

1
1 1 1
2


Input

2
2 1


Output

-1

Solution (in JAVA):

Solution:
//Codeforces Round 397 (Div. 2)
import java.io.*;
import java.util.*;

public class TaskD {
	
	public static void main (String[] args) throws IOException {
		FastScanner fs = new FastScanner(System.in);
		PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
		
		int n = fs.nextInt();		
		
        int[] f = new int[n];
		for (int i = 0; i < n; i++) {
            f[i] = fs.nextInt()-1;
        }
        				
		boolean ok = true;
		for (int i = 0; i < n; i++) {
			if (f[i] != f[f[i]]) {
				ok = false;
				break;
			}
		}		
		
		int[] g = new int[n];		
		int m = 0;
		int[] h = new int[n];
		for (int i = 0; i < n; i++) {
			if (g[f[i]] == 0) {
				m++;
				g[f[i]] = m;				
				h[m-1] = f[i]+1;
			}
			g[i] = g[f[i]];
		}
		
		if (ok) {
			pw.println(m);
			for (int i = 0; i < n; i++) {
				pw.print(g[i]);
				pw.print(" ");
			}
			pw.println();
			for (int i = 0; i < m; i++) {
				pw.print(h[i]);
				pw.print(" ");
			}
			pw.println();
		} else {
			pw.println("-1");
		}		
        		
		pw.close();		
	}
	
	static class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;        
        FastScanner(InputStream i) {
            reader = new BufferedReader(new InputStreamReader(i));
            tokenizer = new StringTokenizer("");
        }
        String next() throws IOException {
            while(!tokenizer.hasMoreTokens()) tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }        
    }
}