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.*;
import java.util.*;
import java.math.BigInteger;
import java.util.Map.Entry;

import static java.lang.Math.*;

public class D extends PrintWriter {

    void run() {
        int n = nextInt();

        int[] f = new int[n];

        for (int i = 0; i < n; i++) {
            f[i] = nextInt() - 1;
        }

        boolean ok = true;

        for (int x = 0; x < n; x++) {
            int y = f[x];
            ok &= f[y] == y;
        }

        if (!ok) {
            println(-1);
            return;
        }

        int[] s = f.clone();

        for (int i = 1; i < n; i++) {
            int j = rnd.nextInt(i);

            s[i] ^= s[j];
            s[j] ^= s[i];
            s[i] ^= s[j];
        }
        Arrays.sort(s);

        int[] t = new int[n];

        int m = 0;

        for (int i = 0; i < n; i++) {
            if (i == 0 || s[i - 1] != s[i]) {
                t[m++] = s[i];
            }
        }

        int[] g = new int[n];
        int[] h = new int[m];

        Arrays.fill(h, -1);

        for (int x = 0; x < n; x++) {
            int y = f[x];
            int z = Arrays.binarySearch(t, 0, m, y);
            g[x] = z;
            h[z] = y;
        }

        println(m);

        for (int x = 0; x < n; x++) {
            print(g[x] + 1);
            print(' ');
        }
        println();

        for (int z = 0; z < m; z++) {
            print(h[z] + 1);
            print(' ');
        }
        println();

    }

    boolean skip() {
        while (hasNext()) {
            next();
        }
        return true;
    }

    int[][] nextMatrix(int n, int m) {
        int[][] matrix = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                matrix[i][j] = nextInt();
        return matrix;
    }

    String next() {
        while (!tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(nextLine());
        return tokenizer.nextToken();
    }

    boolean hasNext() {
        while (!tokenizer.hasMoreTokens()) {
            String line = nextLine();
            if (line == null) {
                return false;
            }
            tokenizer = new StringTokenizer(line);
        }
        return true;
    }

    int[] nextArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++) {
            array[i] = nextInt();
        }
        return array;
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException err) {
            return null;
        }
    }

    public D(OutputStream outputStream) {
        super(outputStream);
    }

    static BufferedReader reader;
    static StringTokenizer tokenizer = new StringTokenizer("");
    static Random rnd = new Random();
    static boolean OJ;

    public static void main(String[] args) throws IOException {
        OJ = System.getProperty("ONLINE_JUDGE") != null;
        D solution = new D(System.out);
        if (OJ) {
            reader = new BufferedReader(new InputStreamReader(System.in));
            solution.run();
        } else {
            reader = new BufferedReader(new FileReader(new File(D.class.getName() + ".txt")));
            long timeout = System.currentTimeMillis();
            while (solution.hasNext()) {
                solution.run();
                solution.println();
                solution.println("----------------------------------");
            }
            solution.println("time: " + (System.currentTimeMillis() - timeout));
        }
        solution.close();
        reader.close();
    }
}