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.
The first line has three integers n,m (1≤n,m≤2⋅105) and k (0≤k≤109) — the number of applicants, the number of apartments, and the maximum allowed difference.
The next line contains n integers a1,a2,...,an (1≤ai,bi≤109) — 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 b1,b2,...,bm — the size of each apartment.
Print one integer — the number of applicants who will get an apartment.