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
# cf16-exhibition-final-openA - 1D Matching
import sys
input = sys.stdin.readline

def calc(x, y, total):
    MOD = 10 ** 9 + 7
    if y:
        total = (total * y) % MOD
        y -= 1
    else:
        x += 1
    return x, y, total

def main():
    N = int(input())
    A = tuple(map(int, [input() for _ in range(N)]))
    B = tuple(map(int, [input() for _ in range(N)]))
    C = sorted([(i, 1) for i in A] + [(i, 0) for i in B])
    ans, a, b = 1, 0, 0
    for i, t in C:
        if t:  # laptop
            a, b, ans = calc(a, b, ans)
        else:  # power sources
            b, a, ans = calc(b, a, ans)
    print(ans)


if __name__ == "__main__":
    main()