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.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class ArtsemAndSaunders {

    static final int MAX = (int) 1e5 + 1;

    public static void main(String[] args) throws IOException {
	MyScanner sc = new MyScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	int n = sc.nextInt();
	int[] f = new int[n];
	TreeSet<Integer> set = new TreeSet<>();
	for (int i = 0; i < n; i++)
	    set.add(f[i] = sc.nextInt());
	int m = set.size(), idx = 0;
	int[] h = new int[m], hh = new int[MAX];
	for (Integer x : set) {
	    h[idx] = x;
	    hh[x] = ++idx;
	}
	int[] g = new int[n];
	for (int i = 0; i < n; i++)
	    g[i] = hh[f[i]];
	for (int i = 0; i < m; i++)
	    if (g[h[i] - 1] != i + 1) {
		System.out.println(-1);
		return;
	    }
	out.println(m);
	for (int i = 0; i < n; i++) {
	    if (i != n - 1)
		out.printf("%d ", g[i]);
	    else
		out.printf("%d", g[i]);
	}
	out.println();
	for (int i = 0; i < m; i++) {
	    if (i != m - 1)
		out.printf("%d ", h[i]);
	    else
		out.printf("%d", h[i]);
	}
	out.println();
	out.flush();
	out.close();
    }

    static class MyScanner {
	StringTokenizer st;
	BufferedReader br;

	public MyScanner(InputStream s) {
	    br = new BufferedReader(new InputStreamReader(s));
	}

	public MyScanner(String file) throws IOException {
	    br = new BufferedReader(new FileReader(new File(file)));
	}

	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 boolean ready() throws IOException {
	    return br.ready();
	}
    }
}