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.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {

        new Main().solve();
    }

    int inf = 2000000000;
    int mod = 1000000007;
    double eps = 0.0000000001;

    PrintWriter out;

    int n;
    int m;

    ArrayList<Pair>[] g;

    void solve() throws IOException {

        Reader in;
        BufferedReader br;

        try {

            //br = new BufferedReader( new FileReader("input.txt") );
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            //br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }


        int n = in.nextInt();
        int[] f = new int[n];

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

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

        int k = 0;
        Arrays.fill(g, -1);

        for (int i = 0; i < n; i++) {

            if (f[i] != f[f[i]]) {

                System.out.println(-1);
                return;
            }

            if (g[i] == -1 && g[f[i]] == -1) {
                g[i] = g[f[i]] = k;
                h[k] = f[i];
                k++;
            }
            else {
                g[i] = g[f[i]] = Math.max(g[i], g[f[i]]);
            }
        }

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

        out.flush();
        out.close();
    }

    class Pair implements Comparable<Pair>{

        int a;
        int b;


        Pair(int a, int b) {

            this.a = a;
            this.b = b;

        }

        public int compareTo(Pair p) {
            if (a > p.a) return 1;
            if (a < p.a) return -1;
            return 0;
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }

    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }


        String nextLine() throws IOException {
            return br.readLine();
        }

    }

}