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())
A = [int(input()) for _ in range(N)]
B = [int(input()) for _ in range(N)]
mod = 10**9+7

from bisect import bisect_right as br
from bisect import bisect_left  as bl

A.sort(reverse=True)
B.sort(reverse=True)


ans = 1

def mbr(ls, a):
    ok = N
    ng = 0
    mid = (ok+ng)//2
    while abs(ok-ng) > 1:
        if ls[mid] >= a:
            ng = mid
        else:
            ok = mid
        mid = (ok+ng)//2

    return ok

for i in range(N):
    a,b = A[i], B[i]
    if a > b:
        idx = mbr(A,b)
        ans = ans * (idx-i) % mod
    else:
        idx = mbr(B,a)
        ans = ans * (idx-i) % mod
print( ans % mod)