Apartments

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 line has three integers $n,m(1\le n,m\le 2\cdot 10^5)$ and $k(0\le k\le 10^9)$ — the number of applicants, the number of apartments, and the maximum allowed difference.

The next line contains $n$ integers $a_1,a_2,...,a_n(1\le a_i,b_i\le 10^9)$ — 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 $b_1,b_2,...,b_m$ — the size of each apartment.

Output

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

Examples