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.Set;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyBufferedReader in = new MyBufferedReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, MyBufferedReader in, PrintWriter out) {
            int n = in.getAnInt();
            int[] f = in.getALineOfInts(n);

            Map<Integer, Set<Integer>> mappedTo = new HashMap<>();

            for (int i = 0; i < n; i++) {
                int x = f[i];
                if (!mappedTo.containsKey(x)) {
                    mappedTo.put(x, new HashSet<>());
                }
                mappedTo.get(x).add(i + 1);
            }

            int m = 0;
            int[] g = new int[n + 1];
            int[] h = new int[n + 1];
            for (Map.Entry<Integer, Set<Integer>> kvp : mappedTo.entrySet()) {
                int x = kvp.getKey();
                Set<Integer> valsThatMapToIt = kvp.getValue();
                if (!valsThatMapToIt.contains(x)) {
                    out.println(-1);
                    return;
                }

                m++;
                h[m] = x;
                for (int inDom : valsThatMapToIt) {
                    g[inDom] = m;
                }
            }

            out.println(m);

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

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

    }

    static class MyBufferedReader {
        BufferedReader in;

        public MyBufferedReader(InputStream s) {
            this.in = new BufferedReader(new InputStreamReader(s));
        }

        public int getAnInt() {
            int res = -1;
            try {
                res = Integer.parseInt(new StringTokenizer(in.readLine()).nextToken());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return res;
        }

        public int[] getALineOfInts(int numExpected) {
            int[] res = new int[numExpected];
            StringTokenizer st = null;
            try {
                st = new StringTokenizer(in.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
            for (int i = 0; i < numExpected; i++)
                res[i] = Integer.parseInt(st.nextToken());
            return res;
        }

    }
}