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 For(i, a, b) for(int (i)=(a); (i)<(b); ++(i))
#define rFor(i, a, b) for(int (i)=(a)-1; (i)>=(b); --(i))
#define rep(i, n) For((i), 0, (n))
#define rrep(i, n) rFor((i), (n), 0)
#define fi first
#define se second
using namespace std;
typedef long long lint;
typedef pair<int, int> pii;

int main(){
    int n;
    scanf("%d", &n);
    pii p[2*n];
    rep(i, n*2){
        int a;
        scanf("%d", &a);
        if(i < n) p[i] = make_pair(a, 0);
        else p[i] = make_pair(a, 1);
    }
    sort(p, p+2*n);
    lint pc = 0;
    lint pw = 0;
    lint ans = 1;
    lint mod = 1e9 + 7;
    rep(i, 2*n){
        if(p[i].se){
            if(pc) ans = ans * (pc--) % mod;
            else ++pw;
        }
        else{
            if(pw) ans = ans * (pw--) % mod;
            else ++pc;
        }
    }
    printf("%lld\n", ans);
}