maximum-score-from-removing-substrings

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

• Remove substring "ab" and gain x points.
  
  
  
  
  • For example, when removing "ab" from "cabxbae" it becomes "cxbae".
  
  
  
  


• Remove substring "ba" and gain y points.
  
  
  
  • For example, when removing "ba" from "cabxbae" it becomes "cabxe".
  
  
  
  

Return the maximum points you can gain after applying the above operations on s.

Example 1:

Input: s = "cdbcbbaaabab", x = 4, y = 5
Output: 19
Explanation:
- Remove the "ba" underlined in "cdbcbbaaabab". Now, s = "cdbcbbaaab" and 5 points are added to the score.
- Remove the "ab" underlined in "cdbcbbaaab". Now, s = "cdbcbbaa" and 4 points are added to the score.
- Remove the "ba" underlined in "cdbcbbaa". Now, s = "cdbcba" and 5 points are added to the score.
- Remove the "ba" underlined in "cdbcba". Now, s = "cdbc" and 5 points are added to the score.
Total score = 5 + 4 + 5 + 5 = 19.

Example 2:

Input: s = "aabbaaxybbaabb", x = 5, y = 4
Output: 20

Constraints:

• 1 <= s.length <= 105


• 1 <= x, y <= 104


• s consists of lowercase English letters.