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.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Scanner;
import java.util.Set;

/**
 *
 * 
 * @author anatolii
 */
public class CodeforcesMain {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        
        Scanner reader = new Scanner(System.in);
        final int n = reader.nextInt();
        int m=0;
        int[] f = new int[n];
        int[] g = new int[n];
        int[] h;
        for(int i=0;i<n;i++){
            f[i] = reader.nextInt();
        }
        
        //find m
        int i;
        boolean no=false;
        boolean flag=true;
        int[] h1=new int[n];
        HashSet<Integer> set = new HashSet<>();
        for(i=0;i<n;i++){
            if(f[f[i]-1]!=f[i]){
                System.out.println(-1);
                return;
            }
            set.add(f[f[i]-1]);
        }
        
        m=set.size();
        h=new int[m];
        int kj=0;
        for(Integer integer : set){
            h[kj++]=integer;
        }
        Arrays.parallelSort(h);
        
        for(i=0; i<m;i++){
            g[h[i]-1]=i+1;
        }
        
        for(int k=0;k<n;k++){
            if(g[k]==0){
                int l=0;
                for(;l<m;l++){
                    if(f[k]==h[l]){
                        break;
                    }
                }
                g[k]=l+1;
            }
        }
        
        System.out.println(m);
        for(i=0;i<n;i++){
            System.out.print(g[i]+" ");
        }
        System.out.println();
        for(i=0;i<m;i++){
            System.out.print(h[i]+" ");
        }
    }
}