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;
typedef long long lint;
typedef pair<int, int> P;

lint MOD = 1e9 + 7;
vector<P> X;

int main(){
    int n; cin >> n;
    for(int i=0;i<n;i++){
        int a; cin >> a;
        X.push_back(P(a, 1));
    }
    for(int i=0;i<n;i++){
        int b; cin >> b;
        X.push_back(P(b, 0));
    }

    sort(X.begin(), X.end());

    int c1 = 0, c2 = 0;
    lint ans = 1;
    for(int i=0;i<2*n;i++){
        if(X[i].second){
            if(c2) ans = (ans*c2) % MOD, c2--;
            else c1++;
        }else{
            if(c1) ans = (ans*c1) % MOD, c1--;
            else c2++;
        }
    }

    cout << ans << endl;
    return 0;
}