<p>The <strong>variance</strong> of a string is defined as the largest difference between the number of occurrences of <strong>any</strong> <code>2</code> characters present in the string. Note the two characters may or may not be the same.</p>

<p>Given a string <code>s</code> consisting of lowercase English letters only, return <em>the <strong>largest variance</strong> possible among all <strong>substrings</strong> of</em> <code>s</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>

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

<pre>
<strong>Input:</strong> s = &quot;aababbb&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
All possible variances along with their respective substrings are listed below:
- Variance 0 for substrings &quot;a&quot;, &quot;aa&quot;, &quot;ab&quot;, &quot;abab&quot;, &quot;aababb&quot;, &quot;ba&quot;, &quot;b&quot;, &quot;bb&quot;, and &quot;bbb&quot;.
- Variance 1 for substrings &quot;aab&quot;, &quot;aba&quot;, &quot;abb&quot;, &quot;aabab&quot;, &quot;ababb&quot;, &quot;aababbb&quot;, and &quot;bab&quot;.
- Variance 2 for substrings &quot;aaba&quot;, &quot;ababbb&quot;, &quot;abbb&quot;, and &quot;babb&quot;.
- Variance 3 for substring &quot;babbb&quot;.
Since the largest possible variance is 3, we return it.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;abcde&quot;
<strong>Output:</strong> 0
<strong>Explanation:</strong>
No letter occurs more than once in s, so the variance of every substring is 0.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>4</sup></code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def largestVariance(self, s: str) -> int:
        max_result = 0  # Store the maximum variance found

        # Loop over each pair of characters 'from' and 'to'
        for from_char in range(ord('a'), ord('z') + 1):
            for to_char in range(ord('a'), ord('z') + 1):
                if from_char == to_char:
                    continue  # Skip if both characters are the same

                dp = 0  # Tracks the maximum variance of current substring
                dp1 = float('-inf')  # Tracks the maximum variance that includes at least one 'to_char'

                # Loop through the string
                for c in s:
                    if ord(c) == from_char:
                        # If current character is 'from_char', increase dp
                        dp = max(1, dp + 1)
                        if dp1 != float('-inf'):
                            dp1 += 1  # Increment dp1 if it has been initialized
                    elif ord(c) == to_char:
                        # If current character is 'to_char', process dp1
                        if dp1 == float('-inf'):
                            dp1 = max(-1, dp - 1)  # Initialize dp1 if needed
                        else:
                            dp1 = max(max(-1, dp - 1), dp1 - 1)  # Update dp1

                        dp -= 1  # Decrease dp for 'to_char'

                    # Update the maximum variance found
                    max_result = max(max_result, dp1)

        return max_result
       
6504