GitHub: https://github.com/BunnyHeist/CSEC
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 the 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 a1,a2,…,an: 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.
Output
Print one integer: the number of applicants who will get an apartment.
Constraints
1≤n,m≤2⋅105
0≤k≤109
1≤ai, bi≤109
Example
Input:
4 3 5
60 45 80 60
30 60 75
Output:
2
