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 int long long 
#define INF 1e9
#define LINF 1e18

typedef unsigned long long ull;
typedef pair<int, int> P;
typedef pair<int, P> Pi;
typedef pair<P, P> PP;

const int MOD = 1e9 + 7;
const int dy[] = { 0, 0, 1, -1 };
const int dx[] = { 1, -1, 0, 0 };

template <class T> void chmin(T& a, const T& b) { a = min(a, b); }
template <class T> void chmax(T& a, const T& b) { a = max(a, b); }

signed main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    cin >> N;
    vector<P> p(2 * N);
    for(int i = 0; i < N; ++i) {
        cin >> p[i].first;
        p[i].second = 0;
    }
    for(int i = 0; i < N; ++i) {
        cin >> p[i + N].first;
        p[i + N].second = 1;
    }
    sort(p.begin(), p.end());
    int res = 1, cnt = 0;
    for(auto i : p) {
        //cout << i.second << endl;
        int add = i.second ? 1 : -1;
        //cout << add << endl;
        if(cnt != 0 && (cnt > 0) != i.second) {
            res = (res * abs(cnt)) % MOD;
        }
        cnt += add;
    }
    cout << res << endl;
    return 0;
}
