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
from heapq import heappush, heappop

mod = 10 ** 9 + 7

n = int(input())
a = [int(input()) for _ in range(n)]
b = [int(input()) for _ in range(n)]

h = []
for aa in a:
    heappush(h, (aa, True))
for bb in b:
    heappush(h, (bb, False))

ca = 0
cb = 0
ans = 1
while h:
    pos, is_elm_of_a = heappop(h)
    if is_elm_of_a:
        if cb > 0:
            ans *= cb
            ans %= mod
            cb -= 1
        else:
            ca += 1
    else:
        if ca > 0:
            ans *= ca
            ans %= mod
            ca -= 1
        else:
            cb += 1
print(ans)