Subsequence

题号：NC294495
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Given an integer sequence $\{a_k\}_{k=1}^n$ of length $n$ , and two non-negative integers $k_1$ and $k_2$ , you need to select a subsequence $\{b_k\}_{k=1}^m$ (where $m$ is the length of the subsequence) that satisfies the following conditions:

When $i$ is odd and $i>1$ , $\mid b_i-b_{i-1}\mid\le k_1$ ;
When $i$ is a positive even number, $\mid b_i-b_{i-1}\mid\ge k_2$ .

Determine the maximum possible length of such a subsequence.

A subsequence of $a$ is an array formed by deleting some elements from $a$ . This includes deleting zero elements (keeping the entire array) or deleting all elements.

输入描述:

The first line contains three integers , , and  (，), representing the length of the sequence, the constraint  for the first condition, and the constraint  for the second condition. 

The second line contains  integers  （）, the given integer sequence.

输出描述:

Output a single integer on a line, representing the maximum length of a valid subsequence.

示例1

输入

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5 2 3
4 2 1 3 4

输出

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