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 $K = 3$.