You are given a string ’s’ of even length. Split the string into two equal halves, where the first half is ‘a’ and the second half is ‘b’.

Two strings are considered alike if they contain the same number of vowels (a, e, i, o, u, A, E, I, O, U). Return ’true’ if ‘a’ and ‘b’ are alike, otherwise return ‘false’.

You are given a string s and two integers x and y. You can perform two types of operations any number of times:

1. Remove the substring “ab” and gain x points.
2. Remove the substring “ba” and gain y points.

Each time a substring is removed, the characters are deleted from the string, and the corresponding points are added to your total score. Your task is to maximize the total score after applying these operations any number of times.

You are given two strings, a and b, consisting of lowercase letters. In one operation, you can change any character in either string to any lowercase letter. Your goal is to perform the minimum number of operations to satisfy one of the following three conditions:

1. Every character in string a is strictly less than every character in string b alphabetically.
2. Every character in string b is strictly less than every character in string a alphabetically.
3. Both a and b consist of only one distinct character.

Return the minimum number of operations needed to achieve one of these conditions.

You are given a string s consisting of only the characters ‘a’, ‘b’, and ‘c’. Your task is to repeatedly perform the following operation any number of times:

1. Pick a non-empty prefix from the string where all characters are equal.
2. Pick a non-empty suffix from the string where all characters are equal.
3. The prefix and suffix should not intersect, and the characters in both should be the same.
4. Remove the prefix and suffix.

Your goal is to find the minimum length of the string after performing the operation any number of times.