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())
mod = pow(10, 9) + 7
x = []
for i in range(2 * n):
    if i < n:
        x.append([int(input()), 0])
    else:
        x.append([int(input()), 1])
x.sort()
ans, cnt0, cnt1 = 1, 0, 0
for i in range(2 * n):
    if x[i][1] == 0:
        if cnt1 >= 1:
            ans *= cnt1
            ans %= mod
            cnt1 -= 1
        else:
            cnt0 += 1
    else:
        if cnt0 >= 1:
            ans *= cnt0
            ans %= mod
            cnt0 -= 1
        else:
            cnt1 += 1
print(ans)