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 rep(i, m, n) for (int i = m; i < n; ++i)
const int MOD = 1000000007;
template<class T> void mul(T &a, T b) { a = (a * b) % MOD; }

int main() {
    int N; cin >> N;
    using P = pair<int, int>;
    vector<P> A(2 * N);
    rep(i, 0, N) {
        int a; cin >> a;
        A[i] = {a, 0};
    }
    rep(i, 0, N) {
        int a; cin >> a;
        A[i + N] = {a, 1};
    }
    sort(A.begin(), A.end());
    vector<long long> cnt(2);
    long long ans = 1;
    rep(i, 0, 2 * N) {
        cnt[A[i].second]++;
        if(cnt[A[i].second ^ 1]) {
            mul(ans, cnt[A[i].second ^ 1]);
            cnt[A[i].second]--;
            cnt[A[i].second ^ 1]--;
        }
    }
    cout << ans << endl;
    return 0;
}
