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.ArrayList;
import java.util.Scanner;

public class Main {

    static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        int N = sc.nextInt();
        int[] F = new int[N + 1];

        ArrayList<ArrayList<Integer>> lists = new ArrayList<>(N + 1);
        boolean[] ok = new boolean[N + 1];
        for (int i = 0; i <= N; i++) {
            lists.add(new ArrayList<>());
        }
        for (int i = 1; i <= N; i++) {
            F[i] = sc.nextInt();
            lists.get(F[i]).add(i);
            if (i == F[i]) ok[i] = true;
        }
        ArrayList<Integer> idx = new ArrayList<>();
        for (int i = 1; i <= N; i++) {
            if (lists.get(i).isEmpty()) continue;
            if (!ok[i]) {
                System.out.println("-1");
                return;
            }
            idx.add(i);
        }
        int M = idx.size();
        System.out.println(M);
        int[] G = new int[N + 1];
        for (int i = 1; i <= M; i++) {
            for (Integer pos : lists.get(idx.get(i - 1))) {
                G[pos] = i;
            }
        }
        for (int i = 1; i < N; i++) {
            System.out.print(G[i] + " ");
        }
        System.out.println(G[N]);
        for (int i = 0; i < M - 1; i++) {
            System.out.print(idx.get(i) + " ");
        }
        System.out.println(idx.get(M- 1));
    }

}