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 <cmath>
#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <algorithm>
#include <utility>
#include <iomanip>

#define int long long int
#define rep(i, n) for(int i = 0; i < (n); ++i)

using namespace std;

typedef pair<int, int> P;

const int INF = 1e15;
const int MOD = 1e9+7;

signed main(){
    int n;
    cin >> n;

    vector<int> x(2*n);
    map<int, bool> y;
    rep(i, n){
        cin >> x[i];
        y[x[i]] = false;
    }
    rep(i, n){
        cin >> x[n+i];
        y[x[n+i]] = true;
    }
    sort(x.begin(), x.end());

    stack<int> a, b;
    int ans = 1;
    rep(i, 2*n){
        if(y[x[i]]){
            if(not a.empty()){
                ans *= a.size();
                ans %= MOD;
                a.pop();
                continue;
            }
            b.push(x[i]);
        }else{
            if(not b.empty()){
                ans *= b.size();
                ans %= MOD;
                b.pop();
                continue;
            }
            a.push(x[i]);
        }
    }
    cout << ans << endl;
    return 0;
}
