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;
constexpr int mod = 1000000007;

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int n; cin >> n;
    vector<int> a(n), b(n);
    for (auto &x: a) cin >> x;
    for (auto &x: b) cin >> x;
    sort(a.begin(), a.end());
    sort(b.begin(), b.end());
    if (a[0] > b[0]) swap(a[0], b[0]);
    auto f = [&](int l, int r) {
        long long ret = 1, rem = 0;
        int j = r-1;
        for (int i = r-1; i >= l; i--) {
            while (l <= j && a[i] < b[j]) rem++, j--;
            ret *= rem--; ret %= mod;
        }
        return ret;
    };
    long long ans = 1; int rg = b[0], lf = 0;
    for (int i = 0; i < n; i++) {
        if (a[i] > b[i]) swap(a[i], b[i]);
        if (rg < a[i]) {
            ans *= f(lf, i); ans %= mod;
            lf = i;
        }
        rg = max(rg, b[i]);
    }
    ans *= f(lf, n);
    cout << ans % mod << "\n";
    return 0;
}