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>
typedef long long LL;
#define FOR(i,a,b) for(LL i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)

using namespace std;
LL p = 1000000007ll;

int main(void)
{
  LL n;
  cin >> n;
  vector<pair<LL,LL>> a(n*2);
  for(auto &x:a) cin >> x.first;
  REP(i,n) a[i].second = 1;
  REP(i,n) a[n+i].second = -1;
  sort(a.begin(),a.end());
  LL answer=1;
  LL tmp = 0;
  for(auto x:a) {
    LL pat = x.second * tmp;
    if(pat<0) {
      answer *= -pat;
      answer %= p;
    }
    tmp += x.second;
  }
  cout << answer << endl;

  return 0;
}
