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
def mod_fact(n):
  ret = 1
  for i in range(1, n + 1):
    ret = (ret * i) % MOD
  return ret

n = int(input())
AB = []
for i in range(2 * n):
  AB.append((int(input()), i//n)) # i//n: 0=a, 1=b

AB.sort()

a, b = 0, 0
ans = 1
for i, j in AB:
  if j == 0:
    if b == 0:
      a += 1
    else:
      ans = (ans * b) % MOD
      b -= 1
  else:
    if a == 0:
      b += 1
    else:
      ans = (ans * a) % MOD 
      a -= 1
print(ans % MOD)