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

<ul>
	<li>Remove substring <code>&quot;ab&quot;</code> and gain <code>x</code> points.

	<ul>
		<li>For example, when removing <code>&quot;ab&quot;</code> from <code>&quot;c<u>ab</u>xbae&quot;</code> it becomes <code>&quot;cxbae&quot;</code>.</li>
	</ul>
	</li>
	<li>Remove substring <code>&quot;ba&quot;</code> and gain <code>y</code> points.
	<ul>
		<li>For example, when removing <code>&quot;ba&quot;</code> from <code>&quot;cabx<u>ba</u>e&quot;</code> it becomes <code>&quot;cabxe&quot;</code>.</li>
	</ul>
	</li>
</ul>

<p>Return <em>the maximum points you can gain after applying the above operations on</em> <code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cdbcbbaaabab&quot;, x = 4, y = 5
<strong>Output:</strong> 19
<strong>Explanation:</strong>
- Remove the &quot;ba&quot; underlined in &quot;cdbcbbaaa<u>ba</u>b&quot;. Now, s = &quot;cdbcbbaaab&quot; and 5 points are added to the score.
- Remove the &quot;ab&quot; underlined in &quot;cdbcbbaa<u>ab</u>&quot;. Now, s = &quot;cdbcbbaa&quot; and 4 points are added to the score.
- Remove the &quot;ba&quot; underlined in &quot;cdbcb<u>ba</u>a&quot;. Now, s = &quot;cdbcba&quot; and 5 points are added to the score.
- Remove the &quot;ba&quot; underlined in &quot;cdbc<u>ba</u>&quot;. Now, s = &quot;cdbc&quot; and 5 points are added to the score.
Total score = 5 + 4 + 5 + 5 = 19.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aabbaaxybbaabb&quot;, x = 5, y = 4
<strong>Output:</strong> 20
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= x, y &lt;= 10<sup>4</sup></code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def maximumGain(self, s: str, x: int, y: int) -> int:
        total_score = 0
        high_priority_pair = "ab" if x > y else "ba"
        low_priority_pair = "ba" if high_priority_pair == "ab" else "ab"

        # First pass: remove high priority pair
        string_after_first_pass = self.remove_substring(s, high_priority_pair)
        removed_pairs_count = (len(s) - len(string_after_first_pass)) // 2

        # Calculate score from first pass
        total_score += removed_pairs_count * max(x, y)

        # Second pass: remove low priority pair
        string_after_second_pass = self.remove_substring(
            string_after_first_pass, low_priority_pair
        )
        removed_pairs_count = (
            len(string_after_first_pass) - len(string_after_second_pass)
        ) // 2

        # Calculate score from second pass
        total_score += removed_pairs_count * min(x, y)

        return total_score

    def remove_substring(self, input: str, target_pair: str) -> str:
        char_stack = []

        # Iterate through each character in the input string
        for current_char in input:
            # Check if current character forms the target pair with the top of the stack
            if (
                current_char == target_pair[1]
                and char_stack
                and char_stack[-1] == target_pair[0]
            ):
                char_stack.pop()  # Remove the matching character from the stack
            else:
                char_stack.append(current_char)

        # Reconstruct the remaining string after removing target pairs
        return "".join(char_stack)
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