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
input = sys.stdin.readline

mod = 10**9+7

N = int(input())
A = [int(input()) for _ in range(N)]
B = [int(input()) for _ in range(N)]

A.sort(reverse=True)
B.sort(reverse=True)

P = []
while A or B:
    if len(A) == 0:
        b = B.pop()
        P.append(0)
    elif len(B) == 0:
        a = A.pop()
        P.append(1)
    else:
        a = A.pop()
        b = B.pop()
        if a > b:
            P.append(0)
            A.append(a)
        else:
            P.append(1)
            B.append(b)

a = 0
b = 0
ans = 1
for p in P:
    if p == 0:
        if b > 0:
            ans = ans * b % mod
            b -= 1
        else:
            a += 1
    else:
        if a > 0:
            ans = ans * a % mod
            a -= 1
        else:
            b += 1
print(ans)

