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
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())
points = []
for i in range(N):
    a = int(input())
    points.append([a,True])
for i in range(N):
    b = int(input())
    points.append([b,False])
points.sort()

ans = 1
an = bn = 0
for x,c in points:
    if c:
        if bn > 0:
            ans = (ans*bn)%mod
            bn -= 1
        else:
            an += 1
    else:
        if an > 0:
            ans = (ans*an)%mod
            an -= 1
        else:
            bn += 1

print(ans%mod)
