<p>The <strong>beauty</strong> of a string is the difference in frequencies between the most frequent and least frequent characters.</p>

<ul>
	<li>For example, the beauty of <code>&quot;abaacc&quot;</code> is <code>3 - 1 = 2</code>.</li>
</ul>

<p>Given a string <code>s</code>, return <em>the sum of <strong>beauty</strong> of all of its substrings.</em></p>

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

<pre>
<strong>Input:</strong> s = &quot;aabcb&quot;
<strong>Output:</strong> 5
<strong>Explanation: </strong>The substrings with non-zero beauty are [&quot;aab&quot;,&quot;aabc&quot;,&quot;aabcb&quot;,&quot;abcb&quot;,&quot;bcb&quot;], each with beauty equal to 1.</pre>

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

<pre>
<strong>Input:</strong> s = &quot;aabcbaa&quot;
<strong>Output:</strong> 17
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;=<sup> </sup>500</code></li>
	<li><code>s</code> consists of only lowercase English letters.</li>
</ul>

class Solution:
    def beautySum(self, s: str) -> int:
        letters = set(s) 
        n = len(s)
        pref = [Counter() for _ in range(n+1)] 
        
        for i, c in enumerate(s):
            pref[i+1][c] += 1
            
            for cc in letters:
                pref[i+1][cc] += pref[i][cc]
        
        ans = 0
        
        for i in range(n):
            for j in range(i, n):
                maxCnt = 0
                minCnt = n
                
                for c in letters:
                    freq = pref[j+1][c] - pref[i][c] 
                    
                    if freq:
                        maxCnt = max(maxCnt, freq) 
                        minCnt = min(minCnt, freq) 
                
                ans += maxCnt - minCnt
        
        return ans
17000