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.util.HashSet;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		int n = Integer.parseInt(br.readLine());
		int[] f = new int[n + 1];
		int[] g = new int[n + 1];
		int[] h = new int[n + 1];
		HashSet<Integer> fix = new HashSet<>();
		st = new StringTokenizer(br.readLine());
		for (int i = 1; i <= n; i++) {
			f[i] = Integer.parseInt(st.nextToken());
			if (f[i] == i) {
				fix.add(i);
				g[i] = fix.size();
				h[fix.size()] = i;
			}
		}
		for (int i = 1; i <= n; i++) {
			if (!fix.contains(f[i])) {
				System.out.println(-1);
				System.exit(0);
			}
			if (g[i] == 0) {
				g[i] = g[f[i]];
			}
		}
		System.out.println(fix.size());
		for (int i = 1; i <= n; i++) {
			if (i > 1) {
				System.out.print(" ");
			}
			System.out.print(g[i]);
		}
		System.out.println();
		for (int i = 1; i <= fix.size(); i++) {
			if (i > 1) {
				System.out.print(" ");
			}
			System.out.print(h[i]);
		}
		System.out.println();
	}
}