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 <string>
#include <vector>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
#include <iostream>
#include <sstream>
#include <cstring>
#include <numeric>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define F0(i,n) for (int i = 0; i < n; i++)
#define F1(i,n) for (int i = 1; i <= n; i++)
#define CL(a,x) memset(x, a, sizeof(x));
#define SZ(x) ((int)x.size())
const double eps = 1e-10;
const int MOD = 1000000007;
int i, j, k, m, n, l;
ll ans;

int main() {
	//freopen("x.in", "r", stdin);
	cin >> n;
	vector<pii> v;
	F0(i, n) {
		cin >> j;
		v.push_back(pii(j, -1));
	}
	F0(i, n) {
		cin >> j;
		v.push_back(pii(j, 1));
	}
	sort(v.begin(), v.end());
	ans = 1;
	int b = 0;
	for (pii p : v) {
		if (p.second == 1) {
			if (b >= 0) b++; else {
				ans = ans * abs(b) % MOD;
				b++;
			}
		}
		else {
			if (b <= 0) b--; else {
				ans = ans * abs(b) % MOD;
				b--;
			}
		}
	}
	cout << ans << endl;
	return 0;
}
