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
n = int(input())
a = [(int(input()), "a") for i in range(n)]
b = [(int(input()), "b") for i in range(n)]
li = sorted((a+b))
MOD = 10**9 + 7

def solve(li):
    ans = 1
    for i in range(len(li) - 1):
        if abs(li[i]) < abs(li[i+1]):
            ans *= abs(li[i+1])
            ans %= MOD
    return ans

num = 0
ans = 1
tmp = []
for i in range(2*n):
    if li[i][1] == "a":
        num += 1
    else:
        num -= 1
    if num == 0:
        ans *= solve(tmp)
        ans %= MOD
        tmp = []
    else:
        tmp.append(num)
print(ans)