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;

typedef pair<int, int> pii;
typedef long long ll;
typedef vector<int> vi;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i,n) rep2(i,0,n)
#define rep2(i,m,n) for(int i=m;i<(n);i++)
#define ALL(c) (c).begin(),(c).end()

const ll MOD = 1000000007;

int N;
int a[100010], b[100010];
pii p[200010];
int num[2];

int main() {
	cin >> N;

	rep(i, N) {
		cin >> a[i];
		p[i] = mp(a[i], 0);
	}

	rep(i, N) {
		cin >> b[i];
		p[N+i] = mp(b[i], 1); 
	}

	sort(p, p+N*2);

	ll ret = 1;
	rep(i, N*2) {
		int t = p[i].se;
		if (num[t^1] == 0) {
			++num[t];
		} else {
			ret = ret * num[t^1] % MOD;
			--num[t^1];
		}
	}

	cout << ret << endl;

	return 0;
}