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

n = int(input())
lines = sys.stdin.readlines()
aaa = list(map(int, lines[:n]))
bbb = list(map(int, lines[n:]))
coords = [(a, 0) for a in aaa] + [(b, 1) for b in bbb]
coords.sort()
MOD = 10 ** 9 + 7

remain_type = 0
remain_count = 0
ans = 1
for x, t in coords:
    if remain_type == t:
        remain_count += 1
        continue
    if remain_count == 0:
        remain_type = t
        remain_count = 1
        continue
    ans = ans * remain_count % MOD
    remain_count -= 1
print(ans)
