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 <string>
#include <vector>
#include <cmath>
#include <utility>
#include <iomanip>
using namespace std;
typedef long long ll;
const ll MOD = 1e9+7;
ll a[100001];
ll b[100001];
ll kai[100001];
int main()
{
	int n;
	ll ans=1;
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>a[i];
	for(int i=0;i<n;i++)
		cin>>b[i];
	kai[0]=1;
	for(int i=1;i<100001;i++)
	{
		kai[i]=kai[i-1]*(ll)i;
		kai[i]%=MOD;
	}
	sort(a,a+n);
	sort(b,b+n);
	a[n]=1e14-1;
	b[n]=1e14-1;
	int acnt=0;
	int bcnt=0;
	int aind=0;
	int bind=0;
	while(!(aind==n && bind==n))
	{
		if(a[aind]<b[bind]){
			aind++;
			if(bcnt>0)
			{
				ans*=(ll)bcnt;
				bcnt--;
				ans%=MOD;
			}else{
				acnt++;
			}
		}else{
			bind++;
			if(acnt>0)
			{
				ans*=(ll)acnt;
				acnt--;
				ans%=MOD;
			}else{
				bcnt++;
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}