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.*;

public class ArtsemAndSaunders {
    public static void main(String[] args) {
        Scanner inp = new Scanner(System.in);
        int N = inp.nextInt();

        int[] f = new int[N+1];
        int[] g = new int[N+1];
        int[] h = new int[N+1];
        int[] hPrime = new int[N+1];

        int next_label = 1;
        for (int i=1; i<=N; i++) {
            f[i] = inp.nextInt();
            if (hPrime[f[i]] == 0) hPrime[f[i]] = next_label++;
            g[i] = hPrime[f[i]];
            h[g[i]] = f[i];
        }

        for (int i=1; i<next_label; i++) {
            if (g[h[i]] != i) {
                System.out.println(-1);
                return;
            }
        }

        System.out.println(next_label-1);
        for (int i=1; i<=N; i++) System.out.print(g[i] + " ");
        System.out.println();
        for (int i=1; i<next_label; i++) System.out.print(h[i] + " ");
    }
}