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 <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
typedef unsigned int uint;
using namespace std;

const ll mod = 1000000007;

int main() {
    cin.sync_with_stdio(false);
    cin.tie(0);

    int N;
    cin >> N;
    ll A[N], B[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);

    ll ans = 1LL, a = 0, b = 0;
    for (int i = 0; i < 2 * N; i++) {
        if (b == N || A[a] < B[b]) {
            if (a < b) ans = ans * (b - a) % mod;
            a++;
        } else {
            if (b < a) ans = ans * (a - b) % mod;
            b++;
        }
    }

    cout << ans << "\n";
    return 0;
}