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>
#ifdef _WIN32
#include "debug.hpp"
#endif
using namespace std;

#define rep(i, N)  for(int i = 0; i < (N); i++)
#define reps(i, N) for(int i = 1; i <= (N); i++)
#define repr(i, N) for(int i = (N) - 1; i >= 0; i--)
#define pub push_back

template<typename T> 
void chmax(T &a, T b){ a = max(a, b); };
template<typename T> 
void chmin(T &a, T b){ a = min(a, b); };

typedef long long ll;
typedef pair<int, int> P;
const int INF = 100000000;
const ll LINF = 10000000000000000;
const int MOD = 1000000007;
const int dx[9] = { 0, 1,  0, -1, 1,  1, -1, -1, 0};
const int dy[9] = { 1, 0, -1,  0, 1, -1, -1,  1, 0};
//--------------------------------------//
int N;
int a[100000], b[100000];

P p[200000];
void solve(){
	sort(p, p + N * 2);
	ll c = 0;
	ll ans = 1;
	rep(i, N * 2){
		if(abs(c) > abs(c + p[i].second)){
			ans *= abs(c);
			ans %= MOD;
		}
		c += p[i].second;
	}
	cout << ans << endl;
}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cin >> N;
	rep(i, N) {
		cin >> a[i];
		p[i] = P(a[i], 1);
	}
	rep(i, N) {
		cin >> b[i];
		p[i + N] = P(b[i], -1);
	}
		solve();
	return 0;
}
