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;
 
using tpl = tuple<int, int, int>;
typedef pair<int,int> pii;

void fastStream(){cin.tie(0);std::ios_base::sync_with_stdio(0);}

int N;
int A[100010];
int B[100010];
pii event[200020];
const int mod = 1000000000 + 7;

int main(){

    cin >> N;
    for(int i = 0; i < N; i++){
        cin >> A[i];
        event[i] = pii(A[i], 0);
    }
    for(int i = 0; i < N; i++){
        cin >> B[i];
        event[i + N] = pii(B[i], 1);
    }
    ll ans = 1;
    sort(event, event + 2 * N);
    int tot_a = 0;
    for(int i = 0; i < 2 * N; i++){
        if(event[i].second == 0){
            if(tot_a >= 0) tot_a++;
            else{
                (ans *= abs(tot_a)) %= mod;
                tot_a++;
            }
        }
        else{
            if(tot_a <= 0) tot_a--;
            else{
                (ans *= abs(tot_a)) %= mod;
                tot_a--;
           } 
        }
    }
    cout << ans << endl;

    return 0;
}
