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
N = int(input())
L = []
for _ in range(N):
    L.append([int(input()), 0])
for _ in range(N):
    L.append([int(input()), 1])
L.sort()
a = 0
b = 0
ans = 1
for val, ab in L:
    if ab==0:
        if b>0:
            ans = ans * b % mod
            b-=1
        else:
            a+=1
    else:
        if a>0:
            ans = ans * a % mod
            a-=1
        else:
            b+=1
print(ans)
