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;
#define sz(x) ((int) (x).size())
#define forn(i,n) for (int i = 0; i < int(n); ++i)
typedef long long ll;
typedef long long i64;
typedef long double ld;
const int inf = int(1e9) + int(1e5);
const ll infl = ll(2e18) + ll(1e10);

int main() {
    #ifdef LOCAL
    assert(freopen("a.in", "r", stdin));
    #else
    #endif
    int n;
    cin >> n;
    vector<pair<int, int>> v;
    forn (i, n) {
        int x;
        cin >> x;
        v.emplace_back(x, 1);
    }
    forn (i, n) {
        int x;
        cin >> x;
        v.emplace_back(x, -1);
    }
    sort(v.begin(), v.end());

    const int mod = 1e9 + 7;
    ll res = 1;
    int bal = 0;
    for (auto p: v) {
        int y = p.second;
        if (y == 1 && bal < 0) {
            res = res * -bal;
            res %= mod;
        } else if (y == -1 && bal > 0) {
            res = res * bal;
            res %= mod;
        }
        bal += y;
    }
    cout << res << '\n';
}
