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 <algorithm>
# include <vector>
# include <string>
# include <set>
# include <map>
# include <cmath>
# include <iomanip>
# include <functional>
# include <utility>
# include <stack>
# include <queue>
# include <list>
# include <bitset>
# include <complex>
#include<limits.h>
#include<unordered_map>
#include<unordered_set>
#include<deque>
#include<cstdio>
const int mod = 1000000007;
typedef long long int ll;
#define rep(i,n) for(int i=0;i<n;++i)
#define ALL(x) x.begin(),x.end()
#define pp pair<ll,ll>
const int INF = 1LL << 30;
const ll LLINF = 1LL << 60;
using namespace std;
int main() {	
	ll n, ans = 1,ct=0,ct2=0;
	cin >> n;
	int nn; 
	pp v[200010];
	rep(i, n) { cin >> nn; v[i] = pp{ nn,0 }; }
	rep(i, n) { cin >> nn; v[i+n] = pp{ nn,1 }; }
	sort(v, v + n * 2);
	//rep(i, n * 2)cout << v[i].first << "," << v[i].second<<endl;
	rep(i, 2 * n) {
		if (v[i].second == 0) {
			if (ct2 == 0)++ct;
			else { ans *= ct2; --ct2; ans %= mod; }
		}
		if (v[i].second == 1) {
			if (ct == 0)++ct2;
			else { ans *= ct; --ct; ans %= mod; }
		}
	}
	cout << ans << endl;
	return 0;
}
