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 <vector>
#include <algorithm>
using namespace std;

#define REP(i, n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i, m, n) for(int i = (int)(m); i < (int)(n); ++i)

const int MOD = 1e+9 + 7;

int main()
{
    int N;
    cin >> N;
    vector<int> a(N), b(N);    
    REP(i, N) cin >> a[i];
    REP(i, N) cin >> b[i];

    sort(a.begin(), a.end());
    sort(b.begin(), b.end());

    long long ans = 1;  // 最初は a[i] - b[i] で繋がっている 
    REP(i, N){
        int pos = lower_bound(a.begin(), a.end(), b[i]) - a.begin(), n;
        if(a[i] < b[i]) n = pos-i;
        else n = i-pos+1;
        ans *= n;  // a[i] が繋げる可能性があるものは n 通り
        ans %= MOD;
        // cout << i << " " << ans << endl;
    } 
    cout << ans << endl;

    return 0;
}