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.readline
sys.setrecursionlimit(10 ** 7)

MOD = 10 ** 9 + 7

N = int(input())
A,B = [[int(input()) for _ in range(N)] for _ in [0,1]]

AB = [(x,0) for x in A] + [(x,1) for x in B]
AB.sort()

a = 0
b = 0
answer = 1
for x,i in AB:
    if i == 0:
        if b == 0:
            a += 1
            continue
        answer *= b
        b -= 1
    else:
        if a == 0:
            b += 1
            continue
        answer *= a
        a -= 1
    answer %= MOD

print(answer)