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 <stdio.h>
#include <algorithm>
#define mod 1000000007
typedef long long ll;

int main(void) {
  ll i, j, k, n, ans = 1, now = 0;
  scanf("%lld", &n);
  ll a[n], b[n];
  for(i = 0; i < n; ++i) scanf("%lld", &a[i]);
  for(i = 0; i < n; ++i) scanf("%lld", &b[i]);
  std::sort(a, a + n), std::sort(b, b + n);
  for(i = 0; i < n; ++i) {
    if(a[i] < b[i]) {
      while(a[now] < b[i] && now < n) ++now;
      ans *= now - i;
    } else {
      while(b[now] < a[i] && now < n) ++now;
      ans *= now - i;
    }
    ans %= mod;
  }
  printf("%lld", ans);
  return 0;
}