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.IOException;
import java.util.*;

public class Indiv {

    int[] f;
    int[] g;
    int[] h;
    public void solve() throws IOException {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        f = new int[n];
        g = new int[n];
        for (int i = 0; i < n; ++i) {
            f[i] = scanner.nextInt() - 1;
        }

        LinkedList<Integer> mReal = new LinkedList<>();
        HashSet<Integer> mRealSet = new HashSet<>();
        for (int i = 0; i < n; ++i) {
            if (!mRealSet.contains(f[i])) {
                mRealSet.add(f[i]);
                mReal.add(f[i]);
            }
        }

        int m = mReal.size();
        HashMap<Integer, Integer> realToEstim = new HashMap<>();
        h = new int[m];
        int cnt = 0;
        for (int i : mReal) {
            h[cnt] = i;
            realToEstim.put(i, cnt);
            ++cnt;
        }

        for (int i = 0; i < n; ++i) {
            g[i] = realToEstim.get(f[i]);
        }

        if (!check()) {
            System.out.println("-1");
            return;
        }

        System.out.println(m);
        for (int i = 0; i < n; ++i) {
            System.out.print((g[i] + 1) + " ");
        }
        System.out.println("");
        for (int i = 0; i < m; ++i) {
            System.out.print((h[i] + 1) + " ");
        }
    }

    boolean check() {
        for (int i = 0; i < h.length; ++i) {
            if (g[h[i]] != i) {
                return false;
            }
        }
        return true;
    }

    class Pair {
        int estim;
        int real;

        public Pair(int estim, int real) {
            this.estim = estim;
            this.real = real;
        }
    }

    void func(int k, int a, int b) {
        int firstWin = a / k;
        int secondWin = b / k;

        if (firstWin == 0) {
            if (secondWin != 0 && b % k == 0) {
                System.out.println(secondWin);
            } else {
                System.out.println("-1");
            }
        } else if (secondWin == 0) {
            if (a % k == 0) {
                System.out.println(firstWin);
            } else {
                System.out.println("-1");
            }
        } else {
            System.out.println(firstWin + secondWin);
        }
    }

    public void run() {
        try {
            solve();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    public static void main(String[] args) {
        new Indiv().run();
    }
}