There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.

Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.

In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.

Input

The input is given from Standard Input in the following format:


N
a_1
:
a_N
b_1
:
b_N


Output

Print the number of ways to minimize the total length of the cables, modulo 10^9+7.

Examples

Input

2
0
10
20
30


Output

2


Input

3
3
10
8
7
12
5


Output

1
import java.util.*;
import java.io.*;

import static java.lang.System.in;

public class Main {
    public static void main(String[] args)throws IOException{
        Scanner sc = new Scanner(System.in);
        long mod = 1000000000+7;
        int n = sc.nextInt();
        int[][] dic = new int[2*n][];
        for(int i=0;i<n;i++){
            int a = sc.nextInt();
            dic[i] = new int[]{a,0};
        }
        for(int i=n;i<2*n;i++){
            int b = sc.nextInt();
            dic[i] = new int[]{b,1};
        }
        Arrays.sort(dic,new myc());
        long ans = 1;
        int[] cnt = new int[2];
        for(int i=0;i<2*n;i++){
            int now = dic[i][1];
            if(cnt[1-now]>0){
                ans = ans*cnt[1-now]%mod;
                cnt[1-now]--;
            }else{
                cnt[now]++;
            }
        }
        System.out.println(ans);
    }
    static class myc implements Comparator<int[]>{
        public int compare(int[] a, int[] b){
            return a[0]-b[0];
        }
    }
}
