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())
alist = list(reversed(sorted([int(input()) for _ in range(n)])))
blist = list(reversed(sorted([int(input()) for _ in range(n)])))
INF = pow(10, 9) + 7
a = alist.pop()
b = blist.pop()
aset, bset = 0, 0
ans = 1
while len(alist) > 0 or len(blist) > 0:
  if a < b:
    if bset > 0:
      ans = (ans * bset) % INF
      bset -= 1
    else:
      aset += 1
    a = INF
    if len(alist) > 0:
      a = alist.pop()
  else:
    if aset > 0:
      ans = (ans * aset) % INF
      aset -= 1
    else:
      bset += 1
    b = INF
    if len(blist) > 0:
      b = blist.pop()
print(ans % INF)
