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;
int n,x,mx=2,flag,ans=1,MOD=1000000007;
vector< pair< int,int > > v;
int main() {
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&x),
        v.push_back(make_pair(x,0));
    for(int i=1;i<=n;i++)
        scanf("%d",&x),
        v.push_back(make_pair(x,1));
    sort(v.begin(),v.end());
    stack<int> s;
    for(int i=0;i<=2*n;i++) {
        if(s.empty()) {
            flag=v[i].second;
            s.push(flag);
            continue ;
        }
        if(flag!=v[i].second) {
            ans=(1ll*ans*s.size())%MOD;
            s.pop();
        }
        else
            s.push(flag);
    }
    printf("%d",ans);
}
