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;

#define int long long
const double PI = 3.14159265358979323846;
typedef vector<int> vint;
typedef pair<int, int> pint;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};

int N;
int a[110000], b[110000], dp[110000];


signed main() {
    int mod = 1e9 + 7;

    cin >> N;
    for (int i = 0; i < N; i++)cin >> a[i];
    for (int i = 0; i < N; i++)cin >> b[i];
    sort(a, a + N); sort(b, b + N);
    dp[0] = 1;
    for (int i = 0; i < N; i++) {
        if (a[i] == b[i]) {
            dp[i + 1] = dp[i];
            continue;
        }
        
        int n;
        if (a[i] > b[i])n = i - (lower_bound(a, a + N, b[i]) - a);
        else n = i - (lower_bound(b, b + N, a[i]) - b);
        
        dp[i + 1] = (dp[i] * (n + 1) % mod) % mod;
    }
    cout << dp[N] << endl;
}