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>
//#include <math.h>
using namespace std;

#define INF 1.1e9
#define LINF 1.1e18
#define FOR(i,a,b) for (int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define BIT(x,n) bitset<n>(x)
#define PI 3.14159265358979323846

typedef long long ll;
typedef pair<int,int> P;
//typedef pair<int,P> PP;

//-----------------------------------------------------------------------------

int n,tmp;
vector<P> vec;
const int MOD=1e9+7;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	cin>>n;
	REP(i,2*n) {
		cin>>tmp;
		vec.pb(P(tmp,(int)(i>=n)));
	}
	sort(ALL(vec));
	ll ans=1;
	int cnt_a=0,cnt_b=0;
	for(auto v:vec) {
		if(v.se==0) {
			if(cnt_b==0) cnt_a++;
			else (ans*=cnt_b)%=MOD,cnt_b--;
		}
		if(v.se==1) {
			if(cnt_a==0) cnt_b++;
			else (ans*=cnt_a)%=MOD,cnt_a--;
		}
		//cout<<cnt_a<<' '<<cnt_b<<' '<<ans<<endl;
	}
	cout<<ans<<endl;

	return 0;
}
