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 <algorithm>
#include <stack>
#include <queue>

using namespace std;

typedef pair<int, int> P;

P p[200000];

const long MOD = 1000000007;

int main(){
    int N;
    queue<long> quea, queb;
    cin >> N;
    for(int i = 0; i < N ; i++){
        int a;
        cin >> a;
        p[i] = P(a, -1);
    }
    for(int i = 0; i < N ; i++){
        int b;
        cin >> b;
        p[i+N] = P(b, 1);
    }
    sort(p, p+2*N);
    long ans = 1;
    long sum = 1;
    int cur = p[0].second;
    for(int i = 1; i < 2*N; i++){
        if(cur == p[i].second){
            sum++;
        }else{
            if(sum == 0){
                sum++;
                cur = p[i].second;
            }else{
                ans *= sum;
                ans %= MOD;
                sum--;
            }
        }
    }
    
    cout << ans << endl;
}