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 collections import deque
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
import bisect
def isprime(n):
  if n <= 1:
    return False
  else:
    for i in range(2,(int(n**0.5)+2)):
      if n%i == 0:
        return False
    return True

def solve():
  n = int(input())
  a = sorted([int(input()) for _ in range(n)])+[10**9 + 1]
  b = sorted([int(input()) for _ in range(n)])+[10**9 + 1]
  mod = 10**9+7
  ans = 1
  if n == 1:
    print(1)
  else:
    na,nb = 0,0
    for i in range(2*n):
      if na>nb and a[na]>b[nb]:
        ans *= na-nb
        ans %= mod
      elif na<nb and a[na]<b[nb]:
        ans *= nb-na
        ans %= mod
      
      if a[na] < b[nb]:na += 1
      else:nb += 1
  print(ans)
      
    
solve()