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, he or she 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

Output:

2