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>
#define ALL(c) (c).begin(),(c).end()
#define EACH(i,c) for(auto i=(c).begin();i!=(c).end();++i)
using namespace std;
#define int long long

const long long MOD = 1000000007;

void solve(long long N, std::vector<long long> a, std::vector<long long> b){
    vector<pair<int,int>> c;
    for(auto t: a) {
        c.push_back(make_pair(t, -1LL));
    }
    for(auto t: b) {
        c.push_back(make_pair(t, 1LL));
    }
    sort(ALL(c));

    int q = 0;
    int res = 1;
    for(int i = 0; i < c.size(); ++i) {
        if (q * c[i].second >= 0) {
            q += c[i].second;
        } else {
            res = (res * abs(q)) % MOD;
            q += c[i].second;
        }
    }
    cout << res << endl;
}

signed main(){
    long long N;
    scanf("%lld",&N);
    std::vector<long long> a(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%lld",&a[i]);
    }
    std::vector<long long> b(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%lld",&b[i]);
    }
    solve(N, std::move(a), std::move(b));
    return 0;
}