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())
MOD = 10 ** 9 + 7
A = []
B = []
for i in range(N):
    A.append((int(input()), 0))

for i in range(N):
    B.append((int(input()), 1))
D = A + B
D = sorted(D)

a = 0
b = 0
ans = 1
for x, i in D:
    if i == 0:
        if b == 0:
            a += 1
        else:
            ans *= b
            b -= 1
    else:
        if a == 0:
            b += 1
        else:
            ans *= a
            a -= 1
    ans %= MOD
print(ans)