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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;
typedef long long ll;
typedef pair<ll, char> P;
vector<P> V;
string str;
ll n, ans;
const ll mod = 1000000007;

void dfs(ll num, ll moji, ll count){
    if (num == str.length()) return;
    if (count == 0){
        dfs(num + 1, str[num] - 'A', count + 1);
    } else {
        if (str[num] - 'A' == moji){
            dfs(num + 1, moji, count + 1);
        } else {
            (ans *= count) %= mod;
            dfs(num + 1, moji, count - 1);
        }
    }
}

int main(void){
    // Your code here!
    cin >> n;
    for (ll i = 0; i < n; i++){
        ll a;
        cin >> a;
        V.push_back(P(a, 'A'));
    }
    for (ll i = 0; i < n; i++){
        ll b;
        cin >> b;
        V.push_back(P(b, 'B'));
    }
    sort(V.begin(), V.end());
    for (ll i = 0; i < V.size(); i++){
        P p = V[i];
        str += p.second;
    }
    ans = 1;
    dfs(0, 0, 0);
    cout << ans << endl;
}
