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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.FileInputStream;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
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;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DArtsemAndSaunders solver = new DArtsemAndSaunders();
        solver.solve(1, in, out);
        out.close();
    }

    static class DArtsemAndSaunders {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int[] f = new int[n + 1];
            for (int i = 1; i <= n; i++) f[i] = in.nextInt();
            HashMap<Integer, Integer> h = new HashMap<>();
            int curr_hIndex = 1;
            int[] g = new int[n + 1];
            boolean[] flagOfG = new boolean[n + 1];
            ArrayList<Integer> h_arr = new ArrayList<>();
            h_arr.add(0);
            for (int i = 1; i <= n; i++) {
                if (flagOfG[i]) {
                    int hValue = h_arr.get(g[i]);
                    if (hValue != f[i]) {
                        out.println(-1);
                        out.flush();
                        return;
                    }
                } else if (h.containsKey(f[i])) {
                    int pointedBy = h.get(f[i]);
                    g[i] = pointedBy;
                    flagOfG[i] = true;
                } else {
                    h.put(f[i], curr_hIndex++);
                    if (g[f[i]] != 0) {
                        out.println(-1);
                        out.flush();
                        return;
                    }
                    g[f[i]] = g[i] = curr_hIndex - 1;
                    h_arr.add(f[i]);
                    flagOfG[i] = flagOfG[f[i]] = true;
                }
            }
            out.println(h_arr.size() - 1);
            for (int i = 1; i <= n; i++) out.printsc(g[i]);
            out.println();
            for (int i = 1; i < h_arr.size(); i++) out.printsc(h_arr.get(i));
            out.println();
            out.flush();
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;
        private ArrayList<String> res = new ArrayList<>();
        private StringBuilder sb = new StringBuilder("");

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void println(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                sb.append(objects[i]);
            }
            res.add(sb.toString());
            sb = new StringBuilder("");
        }

        public void printsc(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                sb.append(objects[i]).append(' ');
            }
        }

        public void close() {
//        writer.flush();
            writer.close();
        }

        public void flush() {
            for (String str : res) writer.printf("%s\n", str);
            res.clear();
            sb = new StringBuilder("");
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public InputReader(FileInputStream file) {
            this.stream = file;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = (res << 3) + (res << 1) + c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}