D. Apartments
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

There are $$$n$$$ applicants and $$$m$$$ free apartments. Your task is to distribute the apartments so that as many applicants as possible will get an apartment.

Each applicant has a desired apartment size, and they will accept any apartment whose size is close enough to the desired size.

Input

The first input line has three integers $$$n$$$, $$$m$$$ ($$$1 \leq n,m \leq 2\cdot 10^5$$$), and $$$k$$$ ($$$0 \leq k \leq 10^9$$$): the number of applicants, the number of apartments, and the maximum allowed difference.

The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$): the desired apartment size of each applicant. If the desired size of an applicant is $$$x$$$, they will accept any apartment whose size is between $$$x-k$$$ and $$$x+k$$$.

The last line contains $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$ ($$$1 \leq b_i \leq 10^9$$$): the size of each apartment.

Output

Print one integer: the number of applicants who will get an apartment.

Example
Input
4 3 5
60 45 80 60
30 60 75
Output
2