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.Arrays;
import java.util.Scanner;

public class Main {

	static int MOD = 1000*1000*1000+7;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		int[] b = new int[n];
		for (int i=0;i<n;i++) {
			a[i] = sc.nextInt();
		}
		for (int i=0;i<n;i++) {
			b[i] = sc.nextInt();
		}

		Arrays.sort(a);
		Arrays.sort(b);

		int j = 0;
		int k = 0;

		long ans = 1;
		int status = 0;

		while (j<n || k<n) {
			if (j>=n || (k < n && a[j]>b[k])) {
				if (status > 0) {
					ans = (ans*status)%MOD;
				}
				status--;
				k++;
			} else {
				if (status < 0) {
					ans = (ans*(-status))%MOD;
				}
				status++;
				j++;
			}
		}

		System.out.println(ans);
	}

}
