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 ll = long long;

#define mod 1000000007

int main() {
    int N;
    cin >> N;
    vector<int>a(N);
    for (int i = 0; i < N; ++i) {
      cin >> a[i];
    }
    vector<int>b(N);
    for (int i = 0; i < N; ++i) {
      cin >> b[i];
    }

    vector<pair<int, int>>all;
    all.reserve(2*N);
    for (int i = 0; i < N; ++i) {
        all.push_back(make_pair(a[i], 0));
        all.push_back(make_pair(b[i], 1));
    }
    sort(all.begin(), all.end());

    int num = 0;
    int flag = 0;
    ll ans = 1;
    for (int i = 0; i < N*2; ++i) {
        if(num == 0){
            num++;
            flag = all[i].second;
        } else{
            if(all[i].second != flag){
                ans *= num;
                ans %= mod;
                num--;
            } else{
                num++;
            }
        }
    }
    cout << ans;
    return 0;
}