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 long long ll;

const ll MOD = 1e9+7;
const ll INF = 1e18+7;

signed main(){
	ll n;
	cin >> n;
	vector<ll> a(n), b(n);
	for(auto& x : a)
		cin >> x;
	for(auto& x : b)
		cin >> x;
	vector<pair<ll,ll>> v;
	for(ll i = 0; i < n; ++i)
		v.emplace_back(a[i], 0);
	for(ll i = 0; i < n; ++i)
		v.emplace_back(b[i], 1);
	sort(v.begin(), v.end());
	vector<ll> t(2, 0);
	sort(v.begin(), v.end());
	ll ans = 1;
	for(auto& p : v){
		ll x = p.second;
		if(t[!x]){
			ans = (ans * t[!x]) % MOD;
			--t[!x];
		}
		else
			++t[x];
	}
	cout <<ans << endl;
}

