<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 {
public:

    int score = 0;

    string score_x( string s, int x ){

        string str = "";
        stack<char> st;

        for( int i=s.size()-1; i>=0; i-- ){

            if( !st.empty() && st.top() == 'b' && s[i] == 'a' ){ score += x; st.pop(); continue; }
            st.push(s[i]);

        }

        int size = st.size();

        for( int i=0; i<size; i++ ){ str += st.top(); st.pop(); }

        return str;

    }

    string score_y( string s, int y ){

        string str = "";
        stack<char> st;

        for( int i=s.size()-1; i>=0; i-- ){

            if( !st.empty() && st.top() == 'a' && s[i] == 'b' ){ score += y; st.pop(); continue; }
            st.push(s[i]);

        }

        int size = st.size();

        for( int i=0; i<size; i++ ){ str += st.top(); st.pop(); }

        return str;

    }

    int maximumGain(string s, int x, int y) {

        if( x > y ){ s = score_x(s,x); s = score_y(s,y);  }
        else{ s = score_y(s,y); s = score_x(s,x); }

        return score;
    }
};
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