Problem Statement

You are given a length-$N$ integer sequence $A=(A_1,A_2,\dots,A_N)$ and a non-negative integer $D$. We wish to delete as few elements as possible from $A$ to obtain a sequence $B$ that satisfies the following condition:

• $|B_i - B_j|\neq D$ for all $i,j \; (1 \leq i < j \leq |B|)$.

Find the minimum number of deletions required.

Constraints

• $1 \le N \le 2\times 10^5$
• $0 \le D \le 10^6$
• $0 \le A_i \le 10^6$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N D
A_1 A_2 \dots A_N

Output

Print the answer.