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"
 
typedef long long ll;
#define int ll
#define fi first
#define se second
#define SORT(a) sort(a.begin(),a.end())
#define rep(i,n) for(int i = 0;i < (n) ; i++) 
#define REP(i,n) for(int i = 0;i < (n) ; i++) 
#define MP(a,b) make_pair(a,b)
#define pb(a) push_back(a)
#define INF LLONG_MAX/2
 
using namespace std;
int MOD = 1000000007;

signed main(){
    
    int n;
    cin >> n;
    map<int,int> m;
    m[0];
    m[1];
    set<pair<int,int>> s;
    rep(i,n){
        int a;
        cin >> a;
        s.insert(MP(a,0));
    }
    rep(i,n){
        int a;
        cin >> a;
        s.insert(MP(a,1));
    }
    int ans = 1;
    for(auto x:s){
        int p = x.se;
        int q = (x.se+1)%2;
        if(m[q] == 0)m[p]++;
        else{
            ans *= m[q];
            ans %= MOD;
            m[q]--;
        }
    }
    cout << ans << endl;

    return 0;   
}
// g++ -std=c++14 code1.cpp
// rm -r -f test;oj dl https://ddcc2019-final.contest.atcoder.jp/tasks/ddcc2019_final_a
// rm -r -f test;oj dl http://cf16-exhibition-final-open.contest.atcoder.jp/tasks/cf16_exhibition_final_a