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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
public class D {
	public static void main(String[] args)throws Throwable {
		MyScanner sc=new MyScanner();
		PrintWriter pw=new PrintWriter(System.out);
		
		int n=sc.nextInt();
		int [] a=new int [n];
		TreeSet<Integer> set=new  TreeSet<Integer>();
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
			set.add(a[i]);
		}
		TreeMap<Integer, Integer> map=new TreeMap<Integer, Integer>();
		int m=set.size();
		int [] g=new int [n];
		int [] h=new int [m];
		int p=0;
		while(!set.isEmpty()){
			int x=set.pollFirst();
			map.put(x, p);
			h[p]=x;
			p++;
		}
		boolean ok=true;
		for(int i=0;i<n;i++){
			if(map.containsKey(a[i]))
				g[i]=map.get(a[i])+1;
			else
				ok=false;
		}
		for(int i=0;i<m;i++){
			if(g[h[i]-1]!=i+1)
				ok=false;
		}
		if(!ok)
			pw.println(-1);
		else{
			pw.println(m);
			for(int i=0;i<n;i++)
				pw.print(g[i]+" ");
			pw.println();
			for(int i=0;i<m;i++)
				pw.print(h[i]+" ");
		}
		
		pw.flush();
		pw.close();
	}
	
	static class pair{
		int x,y;
		pair(int a,int b){
			x=a;
			y=b;
		}
	}
	
	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {br = new BufferedReader(new InputStreamReader(System.in));}
		String next() {while (st == null || !st.hasMoreElements()) {
			try {st = new StringTokenizer(br.readLine());}
			catch (IOException e) {e.printStackTrace();}}
		return st.nextToken();}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine(){String str = "";
		try {str = br.readLine();}
		catch (IOException e) {e.printStackTrace();}
		return str;}
	}
}