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;
typedef long long ll;
#define REP(i,n) for(int i=0; i<int(n); i++)
#define FOR(i,m,n) for(int i=int(m); i<int(n); i++)
#define ALL(obj) (obj).begin(),(obj).end()
#define VI vector<int>
#define VLL vector<long long>
#define VVI vector<vector<int>>
#define VVLL vector<vector<long long>>
#define VC vector<char>
#define VS vector<string>
#define VVC vector<vector<char>>
#define fore(i,a) for(auto &i:a)

typedef pair <int, int> P;
template<class T> bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; }
const int  INF = 1 << 30;
const ll INFL = 1223372036854775807;
const ll mod = 1000000007;		








int main() {
	
	int n;
	cin >> n;
	
	vector<pair<int, int>> v;
	REP(i, n) {
		int a;
		cin >> a;
		v.push_back({ a,1 });
	}
	REP(i, n) {
		int b;
		cin >> b;
		v.push_back({ b,-1 });
	}

	sort(ALL(v));

	ll ans = 1;
	ll res = 0;

	REP(i, 2 * n) {
		int j = v[i].second;

		if (res*j<0){
			ans *= abs(res);
			ans %= mod;		
		}
		res += j;
	}

	cout << ans << endl;

	return 0;

}