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 Int = long long;
constexpr Int MOD = 1e9 + 7;
int main()
{
    vector<pair<int, bool>> A;
    int N; cin >> N;
    for (int i = 0; i < N; i++) {
        int a; cin >> a;
        A.emplace_back(a, true);
    }
    for (int i = 0; i < N; i++) {
        int b; cin >> b;
        A.emplace_back(b, false);
    }
    sort(begin(A), end(A));
    Int ans = 1, cnt = 0;
    for (int i = 0; i < 2*N; i++) {
        if (cnt > 0 && !A[i].second) ans = (ans * abs(cnt)) % MOD;
        if (cnt < 0 &&  A[i].second) ans = (ans * abs(cnt)) % MOD;
        if (A[i].second) cnt++; else cnt--;
    }
    cout << ans << '\n';
    return 0;
}
