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 File {
	
	public static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		String next() {
			while (st == null || !st.hasMoreElements()) {
				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());
		}
	}
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		int max = 1000005;
		int n = sc.nextInt();
		
		int[] f = new int[max];
		int[] g = new int[max];
		int[] h = new int[max];
		
		int m = 0;
		
		for (int i = 1; i <= n; i++) {
			f[i] = sc.nextInt();
			
			// Each value of f for which
			// f(x) = x is like a stable point.
			// m should equal to the number of stable points.
			
			// Each i is certainly unique.
			// So each m is uniquely mapped, as will h and g.
			if (f[i] == i) {
				m++;
				// h will map [m] -> [n], as f
				h[m] = f[i];
				g[h[m]] = m;
			}
		}
				
		// If any value x, f(x) does not equal to any stable point, this is 
		// not possible. Validate.
		for (int i = 1; i <= n; i++) {
			if (g[f[i]] == 0) {
				out.println(-1);
				out.close();
				return;
			}
		}
		
		out.println(m);
		for (int i = 1; i <= n; i++) {
			out.print(g[f[i]] + " ");
		}
		
		out.println();
		for (int i = 1; i <= m; i++) {
			out.print(h[i] + " ");
		}
		
		out.close();
	}
}