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 <utility>
#include <algorithm>
#include <map>
#include <set>
#include <vector>
#include <cmath>
#include <cstdlib>
#include <queue>
#include <stack>
#include <iomanip>


using namespace std;

#define REP(i, n) for(ll i = 0;i < n;i++)
#define REPR(i, n) for(ll i = n;i >= 0;i--)
#define FOR(i, m, n) for(ll i = m;i < n;i++)
#define FORR(i, m, n) for(ll i = m;i >= n;i--)
#define REPO(i, n) for(ll i = 1;i <= n;i++)
#define ll long long
#define INF 1999999999
#define MINF -1999999999
#define INF64 1999999999999999999
#define ALL(n) n.begin(),n.end()
#define MOD 1000000007



ll n, ans = 1, a[110000], b[110000], now = 1, nx = MINF, nxi = -1;
vector<pair<ll, ll>> p;
int main() {
	cin >> n;
	REP(i, n)cin >> a[i];
	REP(i, n) cin >> b[i];
	sort(a, a + n);
	sort(b, b + n);
	REP(i, n) {
		if (a[i] > b[i])swap(a[i], b[i]);
		p.push_back(make_pair(a[i], b[i]));
	}
	sort(ALL(p));
	REP(i, n) {
		while (nx < p[i].first) {
			now--;
			nxi++;
			nx = p[nxi].second;
		}
		now++;
		ans *= now;
		ans %= MOD;
	}
	cout << ans << endl;
}
