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.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.*;
import java.util.*;
public class Main {

	public static void main(String[] args) {
		FastScanner sc=new FastScanner();
		PrintWriter pw=new PrintWriter(System.out);
		while(sc.hasNext()){
			int n=sc.nextInt();
			int[]f=new int[n+1];
			int[]g=new int[n+1];
			int[]h=new int[n+1];
			int[]index=new int[n+1];
			HashMap<Integer,Integer>map=new HashMap<Integer,Integer>();
			int count=0;
			int m=0;
			for(int i=1;i<=n;i++){
				f[i]=sc.nextInt();
				if(index[f[i]]==0){
					index[f[i]]=++m;
					h[m]=f[i];
				}
				g[i]=index[f[i]];
			}
			boolean flag=true;
			//judge
			for(int i=1;i<=m;i++){
				if(g[h[i]]!=i) {
					flag=false;
					break;
				}
			}
			if(flag){
				pw.println(m);
				for(int i=1;i<=n;i++) pw.print(g[i]+" ");
				pw.println();
				for(int i=1;i<=m;i++) pw.print(h[i]+" ");
			}
			else 
				pw.println(-1);
			pw.flush();
		}

	}

}
class FastScanner {
    BufferedReader br;
    StringTokenizer st;
    public FastScanner() {
        try	{
            br = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer("");
        } catch (Exception e){e.printStackTrace();}
    }
    public boolean hasNext() {
        while (!st.hasMoreTokens()) {
            String line = nextLine();
            if (line == null) {
                return false;
            }
            st= new StringTokenizer(line);
        }
        return true;
    }
    public String next() {
        if (st.hasMoreTokens())	return st.nextToken();
        try {st = new StringTokenizer(br.readLine());}
        catch (Exception e) {e.printStackTrace();}
        return st.nextToken();
    }

    public int nextInt() {return Integer.parseInt(next());}

    public long nextLong() {return Long.parseLong(next());}

    public double nextDouble() {return Double.parseDouble(next());}

    public String nextLine() {
        String line = "";
        try {line = br.readLine();}
        catch (Exception e) {e.printStackTrace();}
        return line;
    }

    public Integer[] nextIntegerArray(int n) {
        Integer[] a = new Integer[n];
        for(int i = 0; i < n; i++) a[i] = nextInt();
        return a;
    }

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

    public char[] nextCharArray() {
        return nextLine().toCharArray();
    }
}