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CSES Problem Set

Apartments


Task | Statistics


CSES - Apartments

Time limit:1.00 s Memory limit:512 MB

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 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
Example

Input:
4 3 5
60 45 80 60
30 60 75


Output:
2