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:

import java.io.*;
import java.math.BigInteger;
import java.util.*;
public class TestClass {
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String args[] ) throws Exception {
    	
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        String s[] = in.readLine().split(" ");
        int f[] = new int[n+1];
        int m=0;
        ArrayList ind = new ArrayList();
        for(int i=1;i<=n;i++)
        {
        	f[i] = Integer.parseInt(s[i-1]);
        	if(f[i]==i)
        	{
        		m++;
        		ind.add(i);
        	}
        }
        if(m==0)
        {
        	out.println(-1);
        	out.close();
        	System.exit(0);
        }
        int h[] = new int[m+1];
        for(int i=1;i<=m;i++)
        {
        	h[i] = (int)ind.get(i-1);
        }
        int hinv[] = new int[n+1];
        for(int i=1;i<=m;i++)
        {
        	hinv[h[i]] = i; 
        }
        int g[] = new int[n+1];
        for(int i=1;i<=n;i++)
        {
        	int l = hinv[f[i]];
        	if(l==0)
        	{
        		out.println(-1);
            	out.close();
            	System.exit(0);
        	}
        	else
        	{
        		g[i] = l;  
        	}
        }
        out.println(m);
        for(int i=1;i<=n;i++)
        {
        	out.print(g[i]+" ");
        }
        out.println();
        for(int i=1;i<=m;i++)
        {
        	out.print(h[i]+" ");
        }
        out.close();
    }
   
   
}