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;

const int64_t MOD = 1e9+7;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}
void mul(int64_t& a, int64_t b){
    a = a*b % MOD;
}

int main(){
    int N;
    cin >> N;
    vector<pair<int, int>> P;
    // パソコンは1、電源は-1をsecondに入れて、座標でソート
    for(int c : {1, -1}) for(int i=0; i<N; i++){
        int x;
        cin >> x;
        P.emplace_back(x, c);
    }
    sort(P.begin(), P.end());

    // sumは「パソコンは1、電源は-1」の累積和。このabsが保留しているパソコンまたは電源の数
    int sum = 0;
    int64_t ans = 1;
    for(auto& p : P){
        int c = p.second;
        // sumとcが異符号ならペアが作れる
        if(sum*c < 0) mul(ans, abs(sum));
        sum += c;
    }
    cout << ans << endl;
    return 0;
}
