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.HashSet;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class DArtsemAndSaunders {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] f = new int[n + 1];
            HashSet<Integer> dist = new HashSet<>();
            for (int i = 1; i <= n; i++) {
                f[i] = in.nextInt();
                dist.add(f[i]);
            }
            int m = dist.size();
            int[] g = new int[n + 1];
            int[] h = new int[m + 1];
            Arrays.fill(g, -1);
            int v = 1;
            for (int i = 1; i <= n; i++) {
//            if(g[f[i]] != -1) {
//                out.println(-1);
//                return;
//            }
                // g[f[i]] = g[i];
                // h[i] = f[h[i]]
                if (f[i] == i) {
                    h[v++] = i;
                }
                if (v == m + 1) {
                    break;
                }
            }
            int[] h_inv = new int[n + 1];
            Arrays.fill(h_inv, -1);
            for (int i = 1; i <= m; i++) {
                if (h_inv[h[i]] != -1) {
                    out.println(-1);
                    return;
                }
                h_inv[h[i]] = i;
            }
            for (int i = 1; i <= n; i++) {
                // g[i] = h_inv[f[i]]
                if (h_inv[f[i]] == -1) {
                    out.println(-1);
                    return;
                }
                g[i] = h_inv[f[i]];
            }
            boolean ok = true;
            for (int i = 1; i <= m; i++) {
                if (g[h[i]] != i) {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                for (int i = 1; i <= n; i++) {
                    if (h[g[i]] != f[i]) {
                        ok = false;
                        break;
                    }
                }
            }
            if (!ok) {
                out.println(-1);
                return;
            }
            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] + " ");
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

        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 *= 10;
                res += 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;
        }

    }
}