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;

using pii = pair<int, int>;

using ll = long long;

constexpr ll mod = 1e9 + 7;

int main() {
    int n; cin >> n;
    vector<pii> ps;
    for(int i = 0; i < n; ++i) {
        int a; cin >> a;
        ps.emplace_back(a, 0);
    }
    for(int i = 0; i < n; ++i) {
        int b; cin >> b;
        ps.emplace_back(b, 1);
    }
    sort(begin(ps), end(ps));

    ll ans = 1, acnt = 0;
    for(int i = 0; i < 2 * n; ++i) {
        if(ps[i].second == 0) {
            if(acnt < 0) {
                (ans *= -acnt) %= mod;
            }
            acnt += 1;
        } else {
            if(acnt > 0) {
                (ans *= acnt) %= mod;
            }
            acnt -= 1;
        }
    }

    cout << ans << endl;
}
