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~, and ~k~: 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~: 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~: the size of each apartment.

Output

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

Constraints

• ~1 \le n, m \le 2 \cdot 10^5~
• ~0 \le k \le 10^9~
• ~1 \le a_i, b_i \le 10^9~

Example Input

4 3 5
60 45 80 60
30 60 75

Example Output

2