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 fi first
#define se second

typedef pair<int, int> ii;

const long long MOD = 1E9 + 7;

int n;
long long ans = 1;
vector<ii> a;

int main() {
    ios_base::sync_with_stdio(false);
    cin >> n;
    for (int j = 0; j < 2; ++j)
        for (int i = 1; i <= n; ++i) {
            int t;
            cin >> t;
            a.push_back({t, j});
        }
    sort(a.begin(), a.end());
    int cnt[2] = {0, 0};
    for (ii i : a) {
        if (cnt[i.se ^ 1] == 0) ++cnt[i.se];
        else (ans *= cnt[i.se ^ 1]--) %= MOD;
    }
    cout << ans << "\n";
    return 0;
}