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 <cstdio>
#include <vector>
#include <algorithm>
#define mod 1000000007
using namespace std;

int n;
vector< pair<int, int> > v;

int main() {

    scanf("%d", &n);
    for(int i = 1; i <= n; ++i) {
        int x;
        scanf("%d", &x);
        v.push_back(make_pair(x, 0));
    }
    for(int i = 1; i <= n; ++i) {
        int x;
        scanf("%d", &x);
        v.push_back(make_pair(x, 1));
    }

    sort(v.begin(), v.end());

    int cnt0 = 0, cnt1 = 0, sol = 1;
    for(auto x: v) {
        if(x.second == 0) {
            if(cnt1 > 0) {
                sol = (1LL * sol * cnt1) % mod;
                --cnt1;
            }
            else ++cnt0;
        }
        else {
            if(cnt0 > 0) {
                sol = (1LL * sol * cnt0) % mod;
                --cnt0;
            }
            else ++cnt1;
        }
    }

    printf("%d\n", sol);

    return 0;
}