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Remove Palindromic Subsequences

You are given a string s consisting only of letters 'a' and 'b'.

You are given a string s consisting only of letters 'a' and 'b'. In a single step you can remove one palindromic subsequence from s.

Return the minimum number of steps to make the given string empty.

A string is a subsequence of a given string if it is generated by deleting some characters of a given string without changing its order. Note that a subsequence does not necessarily need to be contiguous.

A string is called palindrome if is one that reads the same backward as well as forward.

Remove Palindromic Subsequences diagram

Example 1

Input: s = "ababa"

Output: 1

Explanation: s is already a palindrome, so its entirety can be removed in a single step.

Example 2

Input: s = "abb"

Output: 2

Explanation: "abb" -> "bb" -> "". Remove palindromic subsequence "a" then "bb".

Example 3

Input: s = "baabb"

Output: 2

Explanation: "baabb" -> "b" -> "". Remove palindromic subsequence "baab" then "b".

Constraints

  • 1 <= s.length <= 1000
  • s[i] is either 'a' or 'b'.

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