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;

const int N = 100005;
const int MOD = 1000000007;
typedef pair<int, int> pii;
#define mp(a,b) make_pair(a,b)
#define se second
#define fi first

int n, x;
vector<pii> a;
int cnt[2];

int main() {
	scanf("%d", &n);
	for (int s = 0; s < 2; s++) {
		for (int i = 1; i <= n; i++) {
			scanf("%d", &x);
			a.push_back(mp(x, s));
		}
	}
	sort(a.begin(), a.end());
	int ans = 1;
	memset(cnt, 0, sizeof(cnt));
	for (int i = 0; i < a.size(); i++) {
		if (cnt[!a[i].se] - cnt[a[i].se] > 0)  
			ans = 1LL * ans * (cnt[!a[i].se] - cnt[a[i].se]) % MOD;
		cnt[a[i].se]++;
	}
	printf("%d\n", ans);
	return 0;
}
