题目描述
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
输入格式
见题面
输出格式
见题面
样例输入
10 3
1
5
4
3
8
6
9
7
2
4
样例输出
7