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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class D {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int n = sc.nextInt(), f[] = new int[n];
		for(int i = 0; i < n; ++i)
			f[i] = sc.nextInt() - 1;
		DSU dsu = new DSU(n, f);
		boolean good = true;
		for(int i = 0; i < n; ++i)
			good &= dsu.union(i, f[i]);
		if(!good)
			out.println(-1);
		else
		{
			out.println(dsu.sets);
			int idx = 1, g[] = new int[n];
			for(int i = 0; i < n; ++i)
				if(dsu.find(i) == i)
					g[i] = idx++;
			for(int i = 0; i < n; ++i)
				out.print(g[dsu.find(i)] + " ");
			out.println();
			for(int i = 0; i < n; ++i)
				if(dsu.find(i) == i)
					out.print(dsu.h[i] + 1 + " ");
			out.println();
		}
		out.flush();
		out.close();
	}
	
	static class DSU
	{
		int[] p, r, h;
		int sets;
		
		DSU(int N, int[] a)
		{
			p = new int[N];
			r = new int[N];
			h = a;
			for(int i = 0; i < N; ++i)
				p[i] = i;
			sets = N;
		}
		
		int find(int x) { return x == p[x] ? x : (p[x] = find(p[x])); }
		
		boolean union(int x, int y)
		{
			x = find(x);
			y = find(y);
			if(x == y)
				return true;
			if(h[x] != h[y])
				return false;
			if(r[x] > r[y])
				p[y] = x;
			else
			{
				p[x] = y;
				if(r[x] == r[y])
					++r[y];
			}
			--sets;
			return true;
		}
	}

	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();} 
	}
}