Apartments

There are $nn$ applicants and $mm$ 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 $nn$, $mm$, and $kk$: the number of applicants, the number of apartments, and the maximum allowed difference.

The next line contains $nn$ integers $a_1,a_2,\dots ,a_{n}a\_1,\; a\_2,\; \backslash ldots,\; a\_n$: the desired apartment size of each applicant. If the desired size of an applicant is $xx$, they will accept any apartment whose size is between $x-kx-k$ and $x+kx+k$.

The last line contains $mm$ integers $b_1,b_2,\dots ,b_{m}b\_1,\; b\_2,\; \backslash ldots,\; b\_m$: the size of each apartment.

Output

Print one integer: the number of applicants who will get an apartment.