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;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
const long long mod = 1000000007;
const int inf = 1145141919;
typedef pair<int, int> P;
typedef pair<P, int>PP;
typedef pair<int, char>PC;
struct edge { int to, cost; };
int a[114514], b[114514];
int npr[114514];
signed main() {
	int n; cin >> n;
	rep(i, n)cin >> a[i];
	rep(i, n)cin >> b[i];
	vector<P>V;
	rep(i, n) {
		V.push_back(P(a[i], 0));
		V.push_back(P(b[i], 1));
	}
	sort(V.begin(), V.end());
	npr[0] = 1;
	rep(i, 112000) {
		npr[i + 1] = npr[i] * (i + 1);
		npr[i + 1] %= mod;
	}

	int ans = 1;
	int na = 0, nb = 0;
	rep(i, n + n) {
		if (V[i].second) {
			nb++;
			if(na)ans *= na*nb;
			if (na) {
				na--; nb--;
			}
		}
		else {
			na++;
			if(nb)ans *= na*nb;
			if (nb) {
				na--; nb--;
			}
		}
		ans %= mod;
	}
	cout << ans << endl;
}