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 <cmath>
#include <stack>
#include <iostream>
#include <algorithm>
using namespace std;
int n, a[100009], b[100009], p[200009];
int main() {
	cin >> n;
	for (int i = 0; i < n; i++) cin >> a[i];
	for (int i = 0; i < n; i++) cin >> b[i];
	for (int i = 0; i < 2 * n; i++) p[i] = i;
	sort(p, p + 2 * n, [](int v1, int v2) { return (v1 < n ? a[v1] : b[v1 - n]) < (v2 < n ? a[v2] : b[v2 - n]); });
	int d = 0, ret = 1;
	for (int i = 0; i < 2 * n; i++) {
		int nd = d + (p[i] < n ? 1 : -1);
		if (abs(d) > abs(nd)) ret = 1LL * ret * abs(d) % 1000000007;
		d = nd;
	}
	cout << ret << endl;
	return 0;
}