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;

using i64 = long long int;

const i64 MOD = 1e9 + 7;

int main(){
    int n;
    cin >> n;
    vector<pair<i64, int>> v;
    for(int i=0;i<n;++i){
        i64 a;
        cin >> a;
        v.emplace_back(a, 1);
    }
    for(int i=0;i<n;++i){
        i64 b;
        cin >> b;
        v.emplace_back(b, -1);
    }

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

    i64 ans = 1, acc = 0, prev_acc;
    for(auto e : v){
        prev_acc = acc;
        acc += e.second;
        if(abs(acc) < abs(prev_acc))ans = ans * abs(prev_acc) % MOD;
    }

    cout << ans << endl;

    return 0;
}
