Maximum Substring Removal Score

You are given a string s of lowercase English letters and two integers pointsAB and pointsBA. You may repeatedly apply either operation, any number of times and in any order:

• Remove one occurrence of the substring "ab" and gain pointsAB points.
• Remove one occurrence of the substring "ba" and gain pointsBA points.

Removing a substring joins the characters on its two sides, which may create new removable substrings.

Return the maximum total points you can gain.

Examples

Example 1

Input: s = "cdbcbbaaabab", pointsAB = 4, pointsBA = 5
Output: 19
Explanation: Removing "ba" occurrences (5 points each) before "ab"
occurrences (4 points each) yields the maximum of 19 points.

Example 2

Input: s = "aabbaaxybbaabb", pointsAB = 5, pointsBA = 4
Output: 20
Explanation: Removing "ab" occurrences (5 points each) first is optimal here,
for a total of 20 points.