<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 {
private:
   //function for counting pairs
       string removevalid(string s,int ch)
       {    stringstream ss;
            char b,a;
            b='b'-ch;
            a='a'+ch;
             stack<char>st;
             int n=s.size();
            for(int i=0;i<n;i++)
            {
                if(s[i]==b && !st.empty() && st.top()==a )
                 {
                   st.pop() ;
                 }
                 else
                    st.push(s[i]);
            }
            
            while(st.size()!=0)
            {   
                ss<<st.top();
                st.pop();
                // char i=st.top();
                // v+=i;
                // st.pop();
            }
            string v=ss.str();
             reverse(v.begin(),v.end());
             cout<<v<<" string aftr removal \n";
            return v;
       }

public:
    int maximumGain(string s, int x, int y) {
    //required variable
    int pr=0,n=0,si=0,count=0;
    si=s.size();
    x>=y?pr=0:pr=1;
    string temp;

    //first pass
      temp=removevalid(s,pr);
      n=temp.size();
      if(n==0)
      {  si/=2;
        x>=y?count=si*x:count=si*y;
        return count;
      }
      count=(si-n)/2;
      x>=y?count=count*x:count=count*y;
    //Second pass
    pr=!pr;
    temp=removevalid(temp,pr);
     si=temp.size();
     int t;
     t=(n-si)/2;
    x>=y?t*=y:t*=x;
    count+=t;
   return count;
    }
};
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