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 int long long
#define uint unsigned int
#define rep(i, a, b) for (int i = a; i < b; i++)
#define repr(i, a, b) for (int i = a; i >= b; i--)
#define all(a) (a).begin(), (a).end()
#define sz(a) (a).size()
#define pb(a) push_back(a)
#define eb(...) emplace_back(__VA_ARGS__)
#define mp(a, b) make_pair(a, b)
#define mt(...) make_tuple(__VA_ARGS__)
using namespace std;
using pii = pair<int, int>;
constexpr int MOD = 1000000007;
constexpr int INF = 1LL << 30;
constexpr double EPS = 1e-10;

int N;
int a[100010], b[100010];
vector<pii> v;

signed main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  
  cin >> N;
  rep(i, 0, N) {
    cin >> a[i];
    v.eb(a[i], 0);
  }
  rep(i, 0, N) {
    cin >> b[i];
    v.eb(b[i], 1);
  }
  sort(all(v));

  int s = 0, ans = 1;
  rep(i, 0, sz(v)) {
    pii vv = v[i];
    if (vv.second == 0) {
      if (s < 0) (ans *= -s) %= MOD;
      s++;
    } else {
      if (s > 0) (ans *= s) %= MOD;
      s--;
    }
  }
  cout << ans << endl;

  return 0;
}