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>

//#define int long long
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
#define X first
#define Y second
#define endl '\n'
#define all(o) o.begin(), o.end()
#define IOS ios::sync_with_stdio(0), cin.tie(0)
inline int sgn(int x){
    return (!x ? 0 : (x > 0 ? 1 : -1));
}
const int mod = 1e9 + 7;
int main(){
    IOS;
    int n;
    cin >> n;
    vector<pii> p;
    for(int i=0; i<n; i++){
        int x;
        cin >> x;
        p.push_back({x, +1});
    }
    for(int i=0; i<n; i++){
        int x;
        cin >> x;
        p.push_back({x, -1});
    }
    sort(all(p));
    int s = 0, ans = 1;
    for(int i=0; i<p.size(); i++){
        int x = p[i].Y;
        if(s && sgn(s) * x == -1)
            ans = 1LL * ans * abs(s) % mod;
        s += x;
    }
    cout << ans << endl;
}
