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 <cstdio>
#include <vector>
#include <algorithm>
using namespace std;

typedef long long llong;

vector<pair<int, int>> E;

const int MOD = 1000 * 1000 * 1000 + 7;

int main() {
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        int x;
        scanf("%d", &x);
        E.emplace_back(x, 1);
    }
    for (int i = 0; i < n; i++) {
        int x;
        scanf("%d", &x);
        E.emplace_back(x, -1);
    }
    sort(E.begin(), E.end());
    int bal = 0;
    int ans = 1;
    for (auto e : E) {
        if (bal > 0 && e.second == -1) {
            ans = ((llong)ans * bal) % MOD;
        } else if (bal < 0 && e.second == 1) {
            ans = ((llong)ans * (-bal)) % MOD;
        }
        bal += e.second;
    }
    printf("%d\n", ans);
}
