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
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)
mod = 10 ** 9 + 7

N = int(input())
AB = []
for _ in range(N):
    AB.append((int(input()), 0))
for _ in range(N):
    AB.append((int(input()), 1))
AB.sort(reverse=True)

ans = 1
Aset = 0
Bset = 0

while AB:
    _, x = AB.pop()
    if x:
        if Bset:
            ans *= Bset
            ans %= mod
            Bset -= 1
        else:
            Aset += 1
    else:
        if Aset:
            ans *= Aset
            ans %= mod
            Aset -= 1
        else:
            Bset += 1

print(ans)