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 ll;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
  
/* attention
    long longのシフト演算には気をつけよう
    タイポした時のデバッグが死ぬほどきつくなるので変数名は最低3字くらい使った方がいいかも
    sizeは(int)とキャストしよう
    ごちゃごちゃ場合分けを考える前に全探索は考えましたか？
*/

const ll mod = 1e9+7;

int main(){
    cin.tie(0);
	ios::sync_with_stdio(false);

   int n; cin >> n;
   vector<pair<int, int>> c(2*n);
   for(int i=0; i<2*n; ++i){
       int x; cin >> x;
       if(i < n) c[i] = make_pair(x, 1);
       else c[i] = make_pair(x, 2);
   }
   sort(c.begin(), c.end());

    ll a = 0, b = 0;
    int m;
    if(c[0].second == 1){ m = 1; a = 1; }
    else { m = 2; b = 1; }

    ll ans = 1;
    for(int i=1; i<2*n; ++i){
        if(c[i].second == 1){
            if(b > 0) { ans *= b; ans %= mod; --b; }
            else ++a;
        }
        else if(c[i].second == 2){
            if(a > 0) { ans *= a; ans %= mod; --a; }
            else ++b;
        }
    }

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