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Longest Ideal Subsequence

You are given a string s consisting of lowercase letters and an integer k.

You are given a string s consisting of lowercase letters and an integer k. We call a string t ideal if the following conditions are satisfied:

Return the length of the longest ideal string.

A subsequence is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.

Note that the alphabet order is not cyclic. For example, the absolute difference in the alphabet order of 'a' and 'z' is 25, not 1.

Longest Ideal Subsequence diagram

Example 1

Input: s = "acfgbd", k = 2

Output: 4

Explanation: The longest ideal string is "acbd". The length of this string is 4, so 4 is returned. Note that "acfgbd" is not ideal because 'c' and 'f' have a difference of 3 in alphabet order.

Example 2

Input: s = "abcd", k = 3

Output: 4

Explanation: The longest ideal string is "abcd". The length of this string is 4, so 4 is returned.

Constraints

  • 1 <= s.length <= 10^5
  • 0 <= k <= 25
  • s consists of lowercase English letters.

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