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.buffer.readline
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getlist():
    return list(map(int, input().split()))
import math
import heapq
from collections import defaultdict, Counter, deque
MOD = 10**9 + 7
INF = 10**15


def main():
    n = getN()
    line = []
    for i in range(n):
        line.append((getN(), "P"))
    for i in range(n):
        line.append((getN(), "C"))

    line.sort()
    pc = 0
    cn = 0
    ans = 1
    # print(line)
    for point in line:
        pt, st = point
        if st == "P":
            if pc == 0 and cn != 0:
                ans *= cn
                ans %= MOD
                cn -= 1
            else:
                pc += 1

        else:
            if cn == 0 and pc != 0:
                ans *= pc
                ans %= MOD
                pc-=1
            else:
                cn += 1

    print(ans)



if __name__ == '__main__':
    main()

"""
9999
3

2916
"""