Flat Subsequence

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N K A_1 A_2 : A_N

outputFormat

Output

Print the answer.

Example

Input

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

Output

7

样例

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

7