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;

const int MOD = 1e9 + 7;
const int MAX = 1e5 + 10;
int n;
long long a[MAX], b[MAX];
pair<long long, bool> ab[MAX * 2];

int main() {
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        scanf("%lld", a + i);
    }
    sort(a, a + n);
    for (int i = 0; i < n; i++) {
        scanf("%lld", b + i);
    }
    sort(b, b + n);
    long long ans = 1;

    for (int i = 0; i < n; i++) {
        ab[i] = make_pair(a[i], false);
    }
    for (int i = 0; i < n; i++) {
        ab[n + i] = make_pair(b[i], true);
    }
    sort(ab, ab + 2 * n);
    int cnt = 0;
    for (int i = 0; i < n * 2; i++) {
        if (ab[i].second) {
            // com
            if (cnt > 0) {
                (ans *= cnt) %= MOD;
            }
            cnt--;
        } else {
            // el
            if (cnt < 0) {
                (ans *= -cnt) %= MOD;
            }
            cnt++;
        }
    }

    printf("%d\n", ans);
    return 0;
}
