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())
a = [('a',int(input())) for _ in range(n)]
b = [('b',int(input()))for _ in range(n)]
ab = sorted(a+b, key=lambda x: x[1])
m = []
count = 0
for k,i in ab:
    if k == 'a':
        if count < 0:
            m.append(-count)
        count += 1
    else:
        if count > 0:
            m.append(count)
        count -= 1
ans = 1
for mm in m:
    ans *= mm
    ans %= 10**9+7
print(ans)
