<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 maximumGain(string s, int x, int y) {
        string s1="" , s2="";
        int ans=0;
        if(x>=y) {
            s1="ab";
            s2="ba";
        }
        else {
            s2="ab";
            s1="ba";
        }
        int top1=0;
        stack <char> st1, st2;
        for(int i=0; i<s.length(); i++){
            if(s[i]==s1[1]){
                if(top1>=1){
                    if(st1.top()==s1[0]){
                        st1.pop();
                        top1--;
                        ans+=max(x,y);
                    }
                    else {
                        st1.push(s[i]);
                        top1++;
                    }
                }
                else{
                    st1.push(s[i]);
                    top1++;
                }
            }
            else {
                st1.push(s[i]);
                top1++;
            }
        }
        while(!st1.empty()){
            st2.push(st1.top());
            st1.pop();
        }
        s="";
        while(!st2.empty()){
            s+=st2.top();
            st2.pop();
        }
        top1=0;
        s1=s2;
        for(int i=0; i<s.length(); i++){
            if(s[i]==s1[1]){
                if(top1>=1){
                    if(st1.top()==s1[0]){
                        st1.pop();
                        top1--;
                        ans+=min(x,y);
                    }
                    else {
                        st1.push(s[i]);
                        top1++;
                    }
                }
                else{
                    st1.push(s[i]);
                    top1++;
                }
            }
            else {
                st1.push(s[i]);
                top1++;
            }
        }
        while(!st1.empty()){
            st2.push(st1.top());
            st1.pop();
        }
        s="";
        while(!st2.empty()){
            s+=st2.top();
            st2.pop();
        }
        return ans;
    }
};
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