<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>

static const int _ = [] {
    std::cin.tie(0);
    std::ios::sync_with_stdio(0);
    return 0;
}();


class Solution {
public:
    int maximumGain(string &s, int x, int y) {
        int totalScore = 0;
        string highPriorityPair = x > y ? "ab" : "ba";
        string lowPriorityPair = x <= y ? "ab" : "ba";

        string stringAfterFirstPass = removeSubstring(s, highPriorityPair);
        int removedPairsCount = (s.length() - stringAfterFirstPass.length()) / 2;
        totalScore += removedPairsCount * max(x, y);

        string stringAfterSecondPass = removeSubstring(stringAfterFirstPass, lowPriorityPair);
        removedPairsCount = (stringAfterFirstPass.length() - stringAfterSecondPass.length()) / 2;
        totalScore += removedPairsCount * min(x, y);

        return totalScore;
    }

private:
    string removeSubstring(const string &input, const string &targetPair) {
        stack<char> charStack;

        for (char currentChar: input) {
            if (currentChar == targetPair[1] && !charStack.empty() && charStack.top() == targetPair[0]) {
                charStack.pop();  // Remove the matching character from the stack
            } else {
                charStack.push(currentChar);
            }
        }

        string remainingChars;
        while (!charStack.empty()) {
            remainingChars += charStack.top();
            charStack.pop();
        }
        reverse(remainingChars.begin(), remainingChars.end());
        
        return remainingChars;
    }
};
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