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.HashMap;
import java.util.Scanner;


public class Temp{
	static Scanner scan = new Scanner(System.in);
	public static void main(String args[]) {
		HashMap<Integer, Integer> hMap = new HashMap<Integer, Integer>();
		int n = scan.nextInt();
		boolean possible = false;
		int f[] = new int[n];
		for(int i=0;i<n;i++) {
			f[i] = scan.nextInt();
			if(f[i]==i+1) possible = true;
		}
		if(!possible) {
			System.out.println(-1);
			return;
		}
		int end = 0;
		int h[] = new int[n];
		for(int i=0;i<n;i++) {
			if(f[i]-1==i) {
				h[end++] = f[i];
				hMap.put(f[i], end);
			}
		}
		int g[] = new int[n];
		for(int i=0;i<end;i++) {
			g[h[i]-1] = i+1; 
		}
		for(int i=0;i<n;i++) {
			if(g[i]==0) {
				if(hMap.containsKey(f[i])) {
					g[i] = hMap.get(f[i]);
				}
				else {
					System.out.println(-1);
					return;
				}
			}
		}
		System.out.println(end);
		for(int i=0;i<n;i++) {
			System.out.print(g[i]+" ");
		}
		
		System.out.println();
		for(int i=0;i<end;i++) {
			System.out.print(h[i]+" ");
		}
	}
}