Score : 400 points

Problem Statement

You are given a sequence A_1, A_2, ..., A_N and an integer K.

Print the maximum possible length of a sequence B that satisfies the following conditions:

  • B is a (not necessarily continuous) subsequence of A.
  • For each pair of adjacents elements of B, the absolute difference of the elements is at most K.

Constraints

  • 1 \leq N \leq 300,000
  • 0 \leq A_i \leq 300,000
  • 0 \leq K \leq 300,000
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1
A_2
:
A_N

Output

Print the answer.

Sample Input 1

10 3
1
5
4
3
8
6
9
7
2
4

Sample Output 1

7

For example, B = (1, 4, 3, 6, 9, 7, 4) satisfies the conditions.

  • It is a subsequence of A = (1, 5, 4, 3, 8, 6, 9, 7, 2, 4).
  • All of the absolute differences between two adjacent elements (|1-4|, |4-3|, |3-6|, |6-9|, |9-7|, |7-4|) are at most K = 3.