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.Map;
import java.util.Scanner;


public class Java765D {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();

        int g[] = new int[n + 1]; // n -> m
        HashMap<Integer, Integer> map = new HashMap<>(n); // is g


        for (int x = 1; x <= n; x++) {
            int fx = scanner.nextInt();

            if (map.containsKey(x) && x != fx)
                no();

            if (map.containsKey(fx)) {
                g[x] = map.get(fx);
            } else {
                if (fx < x)
                    no();
                int s = map.size() + 1;
                map.put(fx, s);
                g[x] = g[fx] = s;
            }
        }

        System.out.println(map.size());
        for (int i = 1; i <= n; i++)
            System.out.print(g[i] + " ");
        System.out.println();
        int h[] = new int[map.size() + 1];
        for (Map.Entry<Integer, Integer> entry : map.entrySet())
            h[entry.getValue()] = entry.getKey();
        for (int i = 1; i < h.length; i++)
            System.out.print(h[i] + " ");
    }

    private static void no() {
        System.out.println(-1);
        System.exit(0);
    }
}