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.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

/**
 * Created by Brijesh on 14-02-2017.
 */
public class Main {
    static int e09$7=1000000007;
    static double e_06=0.000001;
    static long INF=1000000000000000L;
    static final String[] EMPTY_ARRAY = new String[0];
    static String d_loc="/home/brijesh/Downloads/";
    static String d_loc2="C:\\Users\\Brijesh\\Downloads\\";
    public static void main (String[] args) throws Exception {
        //BufferedReader br=new BufferedReader(new FileReader(d_loc+"A-small-attempt0.in"));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        StringBuilder sb = new StringBuilder();
        int n=Integer.parseInt(br.readLine());
        int[] f=new int[n+1];
        st=new StringTokenizer(br.readLine());
        ArrayList<ArrayList<Integer>> arrayList=new ArrayList<>();
        for (int i=0;i<=n;i++)
            arrayList.add(new ArrayList<>());
        for (int i=1;i<=n;i++) {
            f[i]=Integer.parseInt(st.nextToken());
            arrayList.get(f[i]).add(i);
        }
        boolean ptd=false;
        for (int i=1;i<=n;i++) {
            if (arrayList.get(i).size()!=0) {
                boolean found=false;
                for (int j=0;j<arrayList.get(i).size();j++) {
                    if (arrayList.get(i).get(j)==i) {
                        found=true;
                        break;
                    }
                }
                if(!found) {
                    ptd=true;
                    System.out.println(-1);
                    return;
                }
            }
        }
        int m=0;
        for (int i=1;i<=n;i++) {
            if (arrayList.get(i).size()!=0) m++;
        }
        int[] g=new int[n+1];
        int[] h=new int[m+1];
        int k=1;
        for (int i=1;i<=n;i++) {
            if (arrayList.get(i).size()!=0) {
                h[k]=i;
                k++;
            }
        }
        k=1;
        for (int i=1;i<=n;i++) {
            if (arrayList.get(i).size()!=0) {
                for (int j=0;j<arrayList.get(i).size();j++) {
                    g[arrayList.get(i).get(j)]=k;
                }
                k++;
            }
        }
        System.out.println(m);
        for (int i=1;i<=n;i++)
            System.out.print(g[i]+" ");
        System.out.println();
        for (int i=1;i<=m;i++)
            System.out.print(h[i]+" ");
        System.out.println();

        System.exit(0);
    }
}