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 <iostream>
#include <string>
#include <sstream>
#include <iomanip> 
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <functional>
#include <algorithm>
#include <unordered_map>
#include <unordered_set>
#include <bitset>

using namespace std;



int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);

	long long n, i, j, k, MOD = 1000000007, ans, x;
	map<int, int> c;
	cin >> n;
	for (i = 0; i < n; i++) {
		cin >> x;
		c[x] = 1;
	}
	for (i = 0; i < n; i++) {
		cin >> x;
		c[x] = -1;
	}

	ans = 1; x = 0;
	for (auto p : c) {
		if (x == 0) x += p.second;
		else {
			if ((x > 0) && (p.second > 0)) x += p.second;
			else if ((x < 0) && (p.second < 0)) x += p.second;
			else {
				ans = (ans * (abs(x))) % MOD;
				x += p.second;
			}
		}
	}

	cout << ans << "\n";

	return 0;
}
