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 ll = long long;

const double eps = 1e-10;
const int MOD = 1000000007;
const int INF = 1000000000;
const ll LINF = 1ll<<50;

template<typename T>
void printv(const vector<T>& s) {
  for(int i=0;i<(int)(s.size());++i) {
    cout << s[i];
    if(i == (int)(s.size())-1) cout << endl;
    else cout << " ";
  }
}

int main () {
  cin.tie(0);
  cout << fixed << setprecision(10);

  int n; cin >> n;
  vector<pair<int, int>> v;
  for(int i=0;i<n;++i) {
    ll a; cin >> a;
    v.push_back(make_pair(a, 0));
  }
  for(int i=0;i<n;++i) {
    ll b; cin >> b;
    v.push_back(make_pair(b, 1));
  }
  sort(v.begin(), v.end());
  ll acnt=0, bcnt=0;
  ll res=1;
  for(int i=0;i<2*n;++i) {
    if(v[i].second==0) {
      if(bcnt) {
        res *= bcnt;
        res %= MOD;
        bcnt--;
        continue;
      }
      acnt++;
    } else {
      if(acnt) {
        res *= acnt;
        res %= MOD;
        acnt--;
        continue;
      }
      bcnt++;
    }
  }
  cout << res << endl;
}
