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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Queue;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(br.readLine());
		}
		int[] b = new int[n];
		for (int i = 0; i < n; i++) {
			b[i] = Integer.parseInt(br.readLine());
		}
		br.close();

		int mod = 1000000007;
		Arrays.sort(a);
		Arrays.sort(b);

		long ans = 1;
		int ai = 0;
		int bi = 0;
		Queue<Integer> qa = new ArrayDeque<>();
		Queue<Integer> qb = new ArrayDeque<>();
		while (ai < n || bi < n) {
			if (ai < n && (bi == n || a[ai] < b[bi])) {
				if (qb.isEmpty()) {
					qa.add(a[ai]);
				} else {
					ans *= qb.size();
					ans %= mod;
					qb.poll();
				}
				ai++;
			} else {
				if (qa.isEmpty()) {
					qb.add(b[bi]);
				} else {
					ans *= qa.size();
					ans %= mod;
					qa.poll();
				}
				bi++;
			}
		}
		System.out.println(ans);
	}
}
