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
mod = 10 ** 9 + 7
INF = 10 ** 10

N = int(input())
A = [int(input()) for _ in range(N)] + [INF]
B = [int(input()) for _ in range(N)] + [INF]

A.sort()
B.sort()

ans = 1
a = b = 0
i = j = 0
while i < N or j < N:
    if A[i] < B[j]:
        if b > 0:
            ans *= b
            b -= 1
        else:
            a += 1
        i += 1
    else:
        if a > 0:
            ans *= a
            a -= 1
        else:
            b += 1
        j += 1

    ans %= mod

print(ans)