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>
using namespace std;

using ll = long long;
#define FOR(i, m, n) for (int i = (m); i < (n); i++)
#define REP(i, n) FOR(i, 0, n)
#define REP1(i, n) FOR(i, 1, (n) + 1)
#define ALL(c) (c).begin(), (c).end()
template<class T> inline bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;}
template<class T> inline bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;}
const int MOD = 1000000007;

int main() {
    int n;
    cin >> n;
    set<pair<int, int>> s;
    int a;
    REP(i, n) {
        cin >> a;
        s.emplace(a, 1);
    }
    int b;
    REP(i, n) {
        cin >> b;
        s.emplace(b, -1);
    }

    ll ans = 1;
    ll c = 0;
    bool st = false;
    int d;
    for (auto p : s) {
        if (!st) {
            st = true;
            d = p.second;
            c++;
        } else {
            if (p.second == d) {
                c++;
            } else {
                ans = ans * c % MOD;
                c--;
            }
            if (c == 0) {
                st = false;
            }
        }
    }

    cout << ans << endl;
}