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>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
template<typename A, typename B> inline bool chmax(A &a, B b) { if (a<b) { a=b; return 1; } return 0; }
template<typename A, typename B> inline bool chmin(A &a, B b) { if (a>b) { a=b; return 1; } return 0; }
typedef long long ll;
typedef pair<int, int> pii;
const ll INF = 1ll<<30;
const ll longINF = 1ll<<60;
const ll MOD = 1000000007;
const double EPS = 1e-9;
const bool debug = 0;
//---------------------------------//

int N;
int a[112345], b[112345];

int main() {
	cin >> N;
	REP(i, N) scanf("%d", a + i);
	REP(i, N) scanf("%d", b + i);
	
	vector<pii> v;
	REP(i, N) v.emplace_back(a[i], 0);
	REP(i, N) v.emplace_back(b[i], 1);
	
	sort(ALL(v));
	
	ll ans = 1, cnt = 0;
	for (pii cur : v) {
		if (cur.se == 0) {
			if (cnt < 0) ans = ans * -cnt % MOD;
			cnt++;
		}
		else {
			if (cnt > 0) ans = ans * cnt % MOD;
			cnt--;
		}
	}
	
	cout << ans << endl;
	
	return 0;
}
