# 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 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 ${a}_{1},{a}_{2},\dots ,{a}_{n}$: 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 ${b}_{1},{b}_{2},\dots ,{b}_{m}$: the size of each apartment.

Output

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

Constraints
• $1\le n,m\le 2\cdot {10}^{5}$
• $0\le k\le {10}^{9}$
• $1\le {a}_{i},{b}_{i}\le {10}^{9}$
Example

Input:
4 3 560 45 80 6030 60 75

Output:
2