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.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author ilyakor
 */
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);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.nextInt();
        int[] a = new int[n];
        boolean[] im = new boolean[n];
        for (int i = 0; i < n; ++i) {
            a[i] = in.nextInt() - 1;
            im[a[i]] = true;
        }
        int[] pi = new int[n];
        Arrays.fill(pi, -1);
        for (int i = 0; i < n; ++i) {
            if (!im[i]) continue;
            if (pi[a[i]] != -1) {
                out.printLine(-1);
                return;
            }
            if (a[i] != i) {
                out.printLine(-1);
                return;
            }
            pi[a[i]] = i;
        }
        int[] imInd = new int[n];
        Arrays.fill(imInd, -1);
        int imCnt = 0;
        for (int i = 0; i < n; ++i)
            if (im[i])
                imInd[i] = imCnt++;
        int[] h = new int[imCnt];
        int[] g = new int[n];
        for (int i = 0; i < n; ++i)
            if (im[i])
                h[imInd[i]] = a[i];
        for (int i = 0; i < n; ++i) {
            int x = a[i];
            int y = pi[x];
            int z = imInd[y];
            g[i] = z;
        }
        out.printLine(imCnt);
        for (int i = 0; i < n; ++i)
            out.print((g[i] + 1) + " ");
        out.printLine();
        for (int i = 0; i < imCnt; ++i)
            out.print((h[i] + 1) + " ");
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

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

    public static boolean isSpace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

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

    public int readSkipSpace() {
        int c;
        do {
            c = read();
        } while (isSpace(c));
        return c;
    }

    public int nextInt() {
        int sgn = 1;
        int c = readSkipSpace();
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res = res * 10 + c - '0';
            c = read();
        } while (!isSpace(c));
        res *= sgn;
        return res;
    }

}

class OutputWriter {
    private final PrintWriter writer;

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

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
    }

    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

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

}