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 rep(i, N) for (int i = 0; i < (int)N; i++)
using namespace std;
typedef long long ll;
const ll LLINF = 9223372036854775807;
const int INF = pow(2,29);
const int MOD = 1000000007;

int main() {
  ll N; cin >> N;
  map<int,int> pos;
  rep(i,N) { int tmp; cin >> tmp; pos[tmp]=1; }
  rep(i,N) { int tmp; cin >> tmp; pos[tmp]=-1; }
  ll result = 1, count = 0;
  for (auto x: pos) {
    count += x.second;
    if (count*x.second>0) {
      result *= abs(count);
      result %= MOD; 
    }
  }
  cout << result << endl;
  return 0;
}