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<iostream>
#include<algorithm>
#include<utility>
#include<vector>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;

const int MAX_N = 1e5 + 1;
const ll MOD = 1e9 + 7;

int A[MAX_N], B[MAX_N];

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;
    vector<P> line;
    for (int i = 0; i < N; i++) {
        cin >> A[i];
        line.push_back(P(A[i], 0));
    }
    for (int i = 0; i < N; i++) {
        cin >> B[i];
        line.push_back(P(B[i], 1));
    }
    sort(line.begin(), line.end());
    int a_cnt = 0, b_cnt = 0;
    ll ans = 1;
    for (int i = 0; i < line.size(); i++) {
        if (line[i].second == 0) {
            if (b_cnt > 0) {
                ans = (ans * b_cnt) % MOD;
                b_cnt--;
            }
            else a_cnt++;
        }
        else {
            if (a_cnt > 0) {
                ans = (ans * a_cnt) % MOD;
                a_cnt--;
            }
            else b_cnt++;
        }
    }
    cout << ans << endl;
    return 0;
}