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
import sys

MOD = 10**9 + 7

N = int(input())
As = [int(sys.stdin.readline()) for _ in range(N)] + [10**9 + 1]
Bs = [int(sys.stdin.readline()) for _ in range(N)] + [10**9 + 1]

As.sort()
Bs.sort()

ans = 1
iA = iB = 0
for _ in range(2*N):
    if iA > iB and As[iA] > Bs[iB]:
        ans *= iA - iB
        ans %= MOD
    elif iA < iB and As[iA] < Bs[iB]:
        ans *= iB - iA
        ans %= MOD

    if As[iA] < Bs[iB]:
        iA += 1
    else:
        iB += 1

print(ans)
