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 FOR(i,l,r) for(int i = (l);i < (r);i++)
#define ALL(x) (x).begin(),(x).end()
template<typename T> bool chmax(T& a,const T& b){return a < b ? (a = b,true) : false;}
template<typename T> bool chmin(T& a,const T& b){return b < a ? (a = b,true) : false;}
typedef long long ll;

int N;
const int MAX_N = 1e5;
const ll MOD = 1e9 + 7;

int main()
{
	scanf("%d",&N);
	vector< pair<int,bool> > A(N * 2);
	FOR(i,0,N){
		scanf("%d",&A [i].first);
		A [i].second = true;
	}
	FOR(i,0,N){
		scanf("%d",&A [i + N].first);
	}
	sort(ALL(A));

	ll ans = 1,cnt = 0;
	FOR(i,0,N * 2){
		if(A [i].second){
			if(cnt < 0){
				(ans *= abs(cnt)) %= MOD;
			}
			cnt++;
		}
		else{
			if(cnt > 0){
				(ans *= abs(cnt)) %= MOD;
			}
			cnt--;
		}
	}

	printf("%lld\n",ans);

	return 0;
}
