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
def solve(n, a, b):
    v = []
    for i in range(n):
        v.append((a[i], 1))
        v.append((b[i], -1))
    v = sorted(v, key=lambda _:_[0])
    ans, cnt = 1, 0
    for _, t in v:
        if (cnt != 0) and (cnt * t < 0):
            ans = (ans * abs(cnt)) % MOD
        cnt += t
    return ans

n = int(input())
a = [int(input()) for i in range(n)]
b = [int(input()) for i in range(n)]
print(solve(n, a, b))