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 <bits/stdc++.h>
using namespace std;
using ll = long long;

const ll mod = 1e9 + 7;

int main()
{
	int N;
	cin >> N;
	vector<int> a(N), b(N);
	for (int i = 0; i < N; i++) {
		cin >> a[i];
	}
	for (int i = 0; i < N; i++) {
		cin >> b[i];
	}
	sort(a.begin(), a.end());
	sort(b.begin(), b.end());
	ll res = 1, st = 0;
	for (int i = 0, j = 0; i < N || j < N; ) {
		if (i == N) {
			j++;
			if (st > 0) res = res * abs(st) % mod;
			st--;
		}
		else if (j == N) {
			i++;
			if (st < 0) res = res * abs(st) % mod;
			st++;
		}
		else if (a[i] < b[j]) {
			i++;
			if (st < 0) res = res * abs(st) % mod;
			st++;
		}
		else {
			j++;
			if (st > 0) res = res * abs(st) % mod;
			st--;
		}
	}
	cout << res << endl;
	return 0;
}
