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.*;
import java.util.*;
public class D {
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int[] f = new int[n];
		TreeSet<Integer> set = new TreeSet<Integer>();
		for(int i=0;i<n;i++)
			set.add(f[i] = sc.nextInt());
		int[] idx  = new int[(int)1e5+2];
		int m = set.size();
		int[] h= new int[m];
		for(int i=0;i<h.length;i++)
		{
			h[i] = set.first();
			idx[h[i]] = i+1;
			set.remove(set.first());
		}
		int[] g = new int[n];
		for(int i=0;i<n;i++)
			g[i] = idx[f[i]];
		//checks
		for(int i=0;i<n;i++)
			if(h[g[i]-1]!=f[i])
			{
				System.out.println(-1);
				return;
			}
		
		for(int i=0;i<m;i++)
			if(g[h[i]-1]!= (i+1))
			{
				System.out.println(-1);
				return;
			}
		
		pw.println(m);
		for(int i=0;i<n;i++)
			pw.print(g[i]+" ");
		pw.println();
		for(int i=0;i<m;i++)
			pw.print(h[i]+" ");
		
		pw.flush();
		pw.close();
	}
	static class Scanner{
		StringTokenizer st;BufferedReader br;
		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
		public String next() throws IOException 
		{while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());return st.nextToken();}
		public int nextInt() throws IOException {return Integer.parseInt(next());}
		public long nextLong() throws IOException {return Long.parseLong(next());}
		public String nextLine() throws IOException {return br.readLine();}
		public double nextDouble() throws IOException {return Double.parseDouble(next());}
		public boolean ready() throws IOException {return br.ready();}
	}

}