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.*;
import java.io.*;

public class A {
	FastScanner in;
	PrintWriter out;

	public void solve() throws IOException {
		int n = in.nextInt();
		int[] f = new int[n];
		int m = 0;
		boolean[] was = new boolean[n];
		for (int i = 0; i < n; i++) {
			f[i] = in.nextInt() - 1;
			if (!was[f[i]])
				m++;
			was[f[i]] = true;
		}
		int[] what = new int[m];
		int[] where = new int[n];
		int mp = 0;
		for (int i = 0; i < n; i++) {
			if (was[i]) {
				where[i] = mp;
				what[mp++] = i;
				if (f[i] != i) {
					out.println(-1);
					return;
				}
			}
		}
		out.println(m);
		for (int i = 0; i < n; i++) {
			out.print((where[f[i]] + 1) + " ");
		}
		out.println();
		for (int i = 0; i < m; i++) {
			out.print((what[i] + 1) + " ");
		}
	}

	public void run() {
		try {
			in = new FastScanner();
			out = new PrintWriter(System.out);

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

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

	public static void main(String[] arg) {
		new A().run();
	}
}