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
N = int(input())

white = 0  # 前者
black = 0  # 後者

ans = 1

mod = 10**9 + 7
que = []
for i in range(N):
    x = int(input())
    que.append((x, 0))
for i in range(N):
    y = int(input())
    que.append((y, 1))
que.sort(reverse=True)
for i in range(2*N):
    value, index = que[i]
    if index == 0:
        white += 1
        if black > 0:
            ans *= black
            ans %= mod
            black -= 1
            white -= 1
    else:
        black += 1
        if white > 0:
            ans *= white
            ans %= mod
            white -= 1
            black -= 1
print(ans)