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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Artsem {
	
	static Map<Integer, Integer> values;
	static Map<Integer, Integer> IDs;
	static Map<Integer, Integer> f;
	
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int IDcounter = 0;
		f = new HashMap<Integer, Integer>(n + 1);
		IDs = new HashMap<Integer, Integer>(n + 1);
		values = new HashMap<Integer, Integer>(n+1);
		for(int i = 1; i<=n; i++){
			f.put(i, sc.nextInt());
		}
		
		for(int i = 1; i<=n; i++){
			int result = f.get(i);
			Integer ID = IDs.get(result);
			if(ID == null){
				// New value
				IDcounter += 1;
				ID = IDcounter;
				values.put(ID, result);
				IDs.put(result, ID);
			}
		}
		
		boolean fail = false;
		//Test
		for(int i = 1; i<=n; i++){
			if(h(g(i)) != f(i)){
				fail = true;
				break;
			}
		}
		for(int i = 1; i<=IDcounter; i++){
			if(g(h(i)) != i){
				fail = true;
				break;
			}
		}
		
		if(fail){
			System.out.println(-1);
		}else{
			System.out.println(IDcounter);
			for(int i = 1; i<=n; i++){
				System.out.print(g(i) + " ");
			}
			System.out.println();
			for(int i = 1; i<=IDcounter; i++){
				System.out.print(h(i) + " ");
			}
			System.out.println();
		}
	}
	
	static int g(int n){
		Integer id = IDs.get(f(n));
		return id;
	}
	
	static int h(int id){
		return values.get(id);
	}
	
	static int f(int n){
		return f.get(n);
	}
	
	
}