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 <algorithm>
#include <iostream>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;

const ll MOD = 1000000007;

int main()
{
    int n;
    cin >> n;
    int a[100002], b[100002];
    P p[200002];
    for(int i = 0; i < n; i++){
        cin >> a[i];
        p[i] = P(a[i], 0);
    }
    for(int i = 0; i < n; i++){
        cin >> b[i];
        p[n + i] = P(b[i], 1);
    }
    sort(p, p + n * 2);
    ll r = 0;
    ll ans = 1;
    for(int i = 0; i < n * 2; i++){
        if(p[i].second == 0){
            if(r < 0) ans = ans * -r % MOD;
            r++;
        }
        else{
            if(r > 0) ans = ans * r % MOD;
            r--;
        }
    }
    cout << ans << endl;
}