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
def main():
    from bisect import bisect_left as bl
    n = int(input())
    a = [int(input()) for _ in [0]*n]
    b = [int(input()) for _ in [0]*n]
    a.sort()
    b.sort()
    for i in range(n):
        if a[i] > b[i]:
            a[i], b[i] = b[i], a[i]
    # print(a)
    # print(b)
    mod = 10**9+7
    ans = 1
    for i in range(n):
        ans = ans*(i+1-bl(b, a[i])) % mod
    print(ans)


main()