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;
using namespace std;
#define DUMP(x)  cout << #x << " = " << (x) << endl;
#define FOR(i, m, n) for(ll i = m; i < n; i++)
#define IFOR(i, m, n) for(ll i = n - 1; i >= m; i-- )
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
#define FOREACH(x,a) for(auto& (x) : (a) )
#define ALL(v) (v).begin(), (v).end()
#define SZ(x) ll(x.size())

typedef pair<ll,ll> P;
const ll MOD = 1e9+7;

int main(){
  ll N; cin >> N;
  vector<P> ab;
  REP(i,N){
    ll a; cin >> a;
    ab.push_back(make_pair(a,0));
  }
  REP(i,N){
    ll b; cin >> b;
    ab.push_back(make_pair(b,1));
  }
  sort(ALL(ab));
  vector<ll> cnt(2,0);
  ll ans = 1;
  REP(i,2*N){
    ll type = ab[i].second;
    if(cnt[type^1] == 0){
      cnt[type]++;
      continue;
    } 
    (ans *= cnt[type^1] ) %= MOD;
    cnt[type^1]--;
  }
  cout << ans << endl;
}
