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
mod = 10**9+7

n = int(input())
s = []
for i in range(2):
    for j in range(n):
        a = int(input())
        s.append((a, i))
s.sort()

ans = 1
l = []
cur = None
for num, c in s:
    if not l:
        l.append(s[i])
        cur = c
    elif c == cur:
        l.append(num)
    else:
        ans *= len(l)
        ans %= mod
        l.pop()
print(ans)