There are applicants and 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.
The first line has three integers n, m~(1 \le n, m \le 2 \cdot 10^5) and k~(0 \le k \le 10^9) — the number of applicants, the number of apartments, and the maximum allowed difference.
The next line contains integers a_1, a_2, ..., a_n~(1 \le a_i \le 10^9) — the desired apartment size of each applicant. If the desired size of an applicant is , he or she will accept any apartment whose size is between x - k and x + k inclusively.
The last line contains integers b_1, b_2, ..., b_m~(1 \le b_i \le 10^9) — the size of each apartment.
Print one integer — the number of applicants who will get an apartment.
Example 1