<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>

'''
aba
bbaa
ababbabaaaba
abbbaaa ab-5 ba-1

aaabbb bbbaaaaa # ab ba

aaaaaaabba  # ab


aaaabbbbb
'''

def count_abs(s):
    ab_count = 0
    a_seen = 0
    b_seen = 0
    for c in s:
        if c == 'a':
            a_seen += 1
        else:
            ab_count += a_seen > b_seen
            b_seen += a_seen > b_seen
    return ab_count


def group_max_gain(s, x, y):
    count_a = s.count('a')
    count_b = s.count('b')
    total_removals = min(count_a, count_b)
    ab_count = count_abs(s)
    ba_count = count_abs(s[::-1])
    print(ab_count, ba_count)
    if x > y:
        ba_count = min(total_removals - ab_count, ba_count)
    else:
        ab_count = min(total_removals - ba_count, ab_count)
    print(ab_count, ba_count)
    return x * ab_count + y * ba_count
    

class Solution:
    def maximumGain(self, s: str, x: int, y: int) -> int:
        groups = [[]]
        for c in s:
            if c in 'ab':
                groups[-1].append(c)
            elif groups[-1]:
                groups.append([])
        return sum(group_max_gain(''.join(g), x, y) for g in groups)
855