Coconut Pairs

You work at a coconut factory, and your job is to package coconuts into pairs for shipping. Two coconuts can be paired together if the absolute difference between their diameters is at most $k$. Each coconut can be used in at most one pair.

Given the diameters of $n$ coconuts, what is the maximum number of disjoint pairs you can form?

Input

The first line contains two integers $n$ and $k$, the number of coconuts and the maximum allowed diameter difference for a valid pair.

The second line contains $n$ integers, the diameters $d_1, d_2, \ldots, d_n$ of the coconuts.

Output

A single integer: the maximum number of disjoint coconut pairs.

Constraints

• $1 \le n \le 10^5$
• $0 \le k \le 10^9$
• $1 \le d_i \le 10^9$

Example 1

6 2
1 3 5 2 4 6

3

Explanation

We can have $3$ pairs of coconuts by pairing coconuts $1$ and $2$ $(1, 3)$, coconuts $3$ and $6$ $(5, 6)$, and coconuts $4$ and $5$ $(2, 4)$.

Example 2

5 1
1 5 3 2 4

2

Example 3

7 0
1 3 1 2 2 5 4

2