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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.logging.Level;
import java.util.logging.Logger;


public class Main {
    public static Scanner cin = new Scanner(System.in);
    public static void main(String[] args) {
        InputStream inputStream = null;
        OutputStream outputStream = null;
        inputStream = System.in;
        //outputStream = new PrintStream("");
        outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Slover slove = new Slover();
        slove.slove(in, out);
        out.close();
    }
    public static final int maxn = 100010;
    public static final int[] f = new int[maxn];
    public static final int[] g = new int[maxn];
    public static final int[] h = new int[maxn];
    public static final int[] p = new int[maxn];
    public static final int[] id = new int[maxn];
    public static final Set<Integer> s = new TreeSet<Integer>();
    static class Slover {
        public void slove(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            for (int i = 1; i <= n; ++i) {
                p[i] = i;
                f[i] = in.nextInt();
                s.add(f[i]);
            }
            for (int i = 1; i <= n; ++i) {
                if (f[i] != f[f[i]]) {
                    out.println(-1);
                    out.flush();
                    System.exit(0);
                }
            }
            int m = s.size();
            int cnt = 0;
            for (int i = 1; i <= n; ++i) {
                if (id[f[i]] == 0) {
                    id[f[i]] = ++cnt;
                }
                g[i] = id[f[i]];
                h[id[f[i]]] = f[i];
            }
            out.printf("%d\n", m);
            for (int i = 1; i <= n; ++i) {
                out.printf("%d ", g[i]);
            }
            out.println("");
            for (int i = 1; i <= m; ++i) {
                out.printf("%d ", h[i]);
            }
            out.println("");
            out.flush();
        }
    }


    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String s = reader.readLine();
                    if(s == null) return null;
                    tokenizer = new StringTokenizer(s);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public boolean hasNext() {
            try {
                return reader.ready();
            } catch (IOException ex) {
                Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
            }
            return false;
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }

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