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 <algorithm>
#include <vector>
#include <iomanip>
 
static const int MOD = 1000000007;
using ll = long long;
using u32 = unsigned;
using namespace std;
 
template<class T>
constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;
 
int main() {
    int n;
    cin >> n;
    vector<pair<int, int>> v(2*n);
    for (int i = 0; i < n; ++i) {
        int a; scanf("%d", &a);
        v[i] = make_pair(a, 0);
    }
    for (int i = 0; i < n; ++i) {
        int a; scanf("%d", &a);
        v[n+i] = make_pair(a, 1);
    }
    sort(v.begin(), v.end());
    int k = v[0].second, u = 1;
    ll ans = 1;
    for (int i = 1; i < 2*n; ++i) {
        if(u == 0){
            k = v[i].second;
            u = 1;
            continue;
        }
        if(v[i].second == k) u++;
        else {
            (ans *= u) %= MOD;
            u--;
        }
    }
    cout << ans << "\n";
    return 0;
}