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.*;
import java.util.*;
import java.math.*;

public class D {
	public static void main(String[] args) throws IOException {

		/**/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		/*/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(new FileInputStream("src/d.in"))));
		/**/
		
		int n = sc.nextInt();
		int[] f = new int[n];
		for (int i = 0; i < n; i++)
			f[i] = sc.nextInt()-1;
		boolean possible = true;
		for (int i = 0; i < n; i++) {
			if (f[f[i]]!=f[i])
				possible = false;
		}
		if (!possible) {
			System.out.println(-1);
			return;
		}
		HashMap<Integer, Integer> nums = new HashMap<Integer, Integer>();
		ArrayList<Integer> h = new ArrayList<Integer>();
		int[] g = new int[n];
		for (int i = 0; i < n; i++) {
			int res = f[i]+1;
			if (!nums.containsKey(res)) {
				nums.put(res, nums.size()+1);
				h.add(res);
			}
			g[i] = nums.get(res);
		}
		StringBuilder ans = new StringBuilder();
		int m = nums.size();
		ans.append(m+"\n");
		for (int i = 0; i < n; i++) {
			ans.append(g[i]+" ");
		}
		ans.append("\n");
		for (int i = 0; i < m; i++) {
			ans.append(h.get(i)+" ");
		}
		System.out.println(ans);
	}
}