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;

using int64 = long long;
const int mod = 1e9 + 7;

int main()
{
  int N;
  cin >> N;
  vector< int > A(N), B(N);
  for(int i = 0; i < N; i++) cin >> A[i];
  for(int i = 0; i < N; i++) cin >> B[i];
  sort(begin(A), end(A));
  sort(begin(B), end(B));

  int64 ret = 1LL;
  int latte = 0, malta = 0;
  int a = 0, b = 0;
  while(latte < N || malta < N) {
    if(malta == N || (latte < N && A[latte] < B[malta])) {
      if(b == 0) ++a;
      else (ret *= b--) %= mod;
      ++latte;
    } else {
      if(a == 0) ++b;
      else (ret *= a--) %= mod;
      ++malta;
    }
  }
  cout << ret << endl;
}
