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

read = sys.stdin.read

N, *ab = map(int, read().split())
mod = 10 ** 9 + 7
ab = list(zip(ab[:N], [0] * N)) + list(zip(ab[N:], [1] * N))
ab.sort()

remain_pc = 0
remain_power = 0
answer = 1

for x, p in ab:
    if p == 0:
        if remain_power == 0:
            remain_pc += 1
            continue
        answer *= remain_power
        remain_power -= 1
    else:
        if remain_pc == 0:
            remain_power += 1
            continue
        answer *= remain_pc
        remain_pc -= 1
    answer %= mod

print(answer)
