<p>Given the string <code>s</code>, return the size of the longest substring containing each vowel an even number of times. That is, &#39;a&#39;, &#39;e&#39;, &#39;i&#39;, &#39;o&#39;, and &#39;u&#39; must appear an even number of times.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;eleetminicoworoep&quot;
<strong>Output:</strong> 13
<strong>Explanation: </strong>The longest substring is &quot;leetminicowor&quot; which contains two each of the vowels: <strong>e</strong>, <strong>i</strong> and <strong>o</strong> and zero of the vowels: <strong>a</strong> and <strong>u</strong>.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;leetcodeisgreat&quot;
<strong>Output:</strong> 5
<strong>Explanation:</strong> The longest substring is &quot;leetc&quot; which contains two e&#39;s.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;bcbcbc&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> In this case, the given string &quot;bcbcbc&quot; is the longest because all vowels: <strong>a</strong>, <strong>e</strong>, <strong>i</strong>, <strong>o</strong> and <strong>u</strong> appear zero times.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 5 x 10^5</code></li>
	<li><code>s</code>&nbsp;contains only lowercase English letters.</li>
</ul>

class Solution:
    def findTheLongestSubstring(self, s: str) -> int:
        # Initialize a list to store the first position we encounter a given state
        # State is represented as a bitmask integer of size 32 (for 5 vowels, each can be on/off)
        positions = [inf] * 32

        # The starting state (all vowels have even counts) is at index 0
        positions[0] = -1

        # List of vowels for reference
        vowels = 'aeiou'

        # `state` to keep track of the count of vowels encountered (even/odd as a bitmask)
        # `max_length` to keep track of the length of the longest valid substring so far
        state = max_length = 0

        # Iterate over the string characters with their index
        for index, char in enumerate(s):
            # Check if the current character is a vowel
            for j, vowel in enumerate(vowels):
                # Toggle the corresponding bit if we encounter a vowel
                if char == vowel:
                    state ^= 1 << j

            # Calculate max length using current index and first index where current state was seen
            max_length = max(max_length, index - positions[state])
            # Update the position for this state if it's the first time we're seeing this state
            positions[state] = min(positions[state], index)

        return max_length
683