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<iostream>
#include<queue>
#include<cassert>
using namespace std;
typedef long long ll;
const ll mod = 1000000007;

int main(){
    int n;
    cin >> n;
    priority_queue<pair<int,int>> pq;
    for(int i = 0; i < n; i++){
        int x;  cin >> x;
        pq.push({-x, 1});
    }
    for(int i = 0; i < n; i++){
        int x;  cin >> x;
        pq.push({-x, -1});
    }
    ll ans = 1, balance = 0;
    while(!pq.empty()){
        pair<int,int> p = pq.top(); pq.pop();
        int i = p.second;
        if(i*(balance) < 0){
            ans *= abs(balance);
            ans %= mod;
        }
        balance += i;
    }
    assert(balance==0);
    cout << ans << endl;
    return 0;
}