Solve the programming task below in a Python markdown code block.
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.

Example

Input

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


Output

7