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Time limit 4000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Difficulty Alpha
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 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≤a(i),b(i)≤109
Example
Input:
4 3 5
60 45 80 60
30 60 75
Output:
2
Äëÿ îòïðàâêè ðåøåíèé íåîáõîäèìî âûïîëíèòü âõîä.
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