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

N = int(input())
mod = 10**9+7

lis = []

for i in range(N):

    a = int(input())
    lis.append([a,1])

for i in range(N):

    b = int(input())
    lis.append([b,-1])

ans = 1

lis.sort()

now = 0
for i in range(2*N):

    nex = lis[i][1]

    if nex == 1:

        if now >= 0:
            now += 1
        else:
            ans *= abs(now)
            now += 1

    else:

        if now <= 0:
            now -= 1
        else:
            ans *= abs(now)
            now -= 1

    ans %= mod

print (ans)