Description

Bessie the cow, always a fan of shiny objects, has taken up a hobby of mining diamonds in her spare

time! She has collected N diamonds (N≤50,000) of varying sizes, and she wants to arrange some of th

em in a pair of display cases in the barn.Since Bessie wants the diamonds in each of the two cases t

o be relatively similar in size, she decides that she will not include two diamonds in the same case

if their sizes differ by more than K (two diamonds can be displayed together in the same case if th

eir sizes differ by exactly K). Given K, please help Bessie determine the maximum number of diamonds

she can display in both cases together.

给定长度为N的数列a，要求选出两个互不相交的子序列（可以不连续），满足同一个子序列中任意两个元素差的绝

对值不超过K。最大化两个子序列长度的和并输出这个值。1 ≤ N ≤ 50000, 1 ≤ a_i ≤ 10 ^ 9, 0 ≤ K ≤ 10^ 9

Format

Input

The first line of the input file contains N and K (0≤K≤1,000,000,000). The next NN lines each cont

ain an integer giving the size of one of the diamonds. All sizes will be positive and will not excee

d 1,000,000,000

Output

Output a single positive integer, telling the maximum number of diamonds that Bessie can showcase in

total in both the cases.

Samples

7 3
10
5
1
12
9
5
14

5