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 <algorithm>
#include <cfloat>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits.h>
#include <map>
#include <math.h>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <string.h>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)
#define int long long
#define ll long long
#define eps LDBL_EPSILON
#define mod 1000000007
#define int long long
#define double long double
#define INF INT_MAX
#define P pair<int,int>
#define prique priority_queue
using namespace std;
int n, a;
vector<P> vec;
signed main() {
	cin >> n;
	rep(i, n) {
		cin >> a;
		vec.push_back({ a,0 });
	}
	rep(i, n) {
		cin >> a;
		vec.push_back({ a,1 });
	}
	sort(vec.begin(), vec.end());
	int ans = 1, p = 0, e = 0;
	rep(i, 2 * n) {
		if (vec[i].second == 0) {
			if (e > p)ans *= (e - p);
			p++;
		}
		else {
			if (p > e)ans *= (p - e);
			e++;
		}
		ans %= mod;
	}
	cout << ans << endl;
}