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 <algorithm>
#include <cstdio>
#include <vector>
#define repeat(i, n) for (int i = 0; (i) < int(n); ++(i))
#define whole(x) begin(x), end(x)
using ll = long long;
using namespace std;

constexpr int mod = 1e9+7;
int main() {
    // input
    int n; scanf("%d", &n);
    vector<int> a(n); repeat (i, n) scanf("%d", &a[i]);
    vector<int> b(n); repeat (i, n) scanf("%d", &b[i]);
    // solve
    vector<pair<int, bool> > events;
    repeat (i, n) {
        events.emplace_back(a[i], false);
        events.emplace_back(b[i], true);
    }
    sort(whole(events));
    ll result = 1;
    int cnt = 0;
    for (auto event : events) {
        int delta = (event.second ? 1 : -1);
        if (cnt != 0 and (cnt > 0) != event.second) {
            result = (result * std::abs(cnt)) % mod;
        }
        cnt += delta;
    }
    // output
    printf("%lld\n", result);
    return 0;
}
