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

Input

6 2
1 3 5 2 4 6

Output

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

Input

5 1
1 5 3 2 4

Output

2

Example 3

Input

7 0
1 3 1 2 2 5 4

Output

2