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
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<string>
#include<vector>
#include<queue>
#include<set>
#include<stack>
#include<functional>
#include<list>
#define P pair<int,int>
#define mod 1000000007
using namespace std;

P a[200000];
int hanten[2] = { 1,0 };
signed main() {
	int b; cin >> b;
	for (int c = 0; c < b; c++) {
		int d; scanf("%d", &d);
		a[c] = P(d, 0);
	}
	for (int c = 0; c < b; c++) {
		int d; scanf("%d", &d);
		a[b + c] = P(d, 1);
	}
	sort(a, a + b * 2);
	long long ans = 1;
	int count[2]{};
	for (int i = 0; i < b * 2; i++) {
		int s = a[i].second;
		if (count[hanten[s]] == 0) {
			count[s]++;
		}
		else {
			ans = ans*count[hanten[s]] % mod;
			count[hanten[s]]--;
		}
	}
	cout << ans << endl;
}