<p>Given a string <code>s</code>, find two <strong>disjoint palindromic subsequences</strong> of <code>s</code> such that the <strong>product</strong> of their lengths is <strong>maximized</strong>. The two subsequences are <strong>disjoint</strong> if they do not both pick a character at the same index.</p>

<p>Return <em>the <strong>maximum</strong> possible <strong>product</strong> of the lengths of the two palindromic subsequences</em>.</p>

<p>A <strong>subsequence</strong> is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters. A string is <strong>palindromic</strong> if it reads the same forward and backward.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="example-1" src="https://assets.leetcode.com/uploads/2021/08/24/two-palindromic-subsequences.png" style="width: 550px; height: 124px;" />
<pre>
<strong>Input:</strong> s = &quot;leetcodecom&quot;
<strong>Output:</strong> 9
<strong>Explanation</strong>: An optimal solution is to choose &quot;ete&quot; for the 1<sup>st</sup> subsequence and &quot;cdc&quot; for the 2<sup>nd</sup> subsequence.
The product of their lengths is: 3 * 3 = 9.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;bb&quot;
<strong>Output:</strong> 1
<strong>Explanation</strong>: An optimal solution is to choose &quot;b&quot; (the first character) for the 1<sup>st</sup> subsequence and &quot;b&quot; (the second character) for the 2<sup>nd</sup> subsequence.
The product of their lengths is: 1 * 1 = 1.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;accbcaxxcxx&quot;
<strong>Output:</strong> 25
<strong>Explanation</strong>: An optimal solution is to choose &quot;accca&quot; for the 1<sup>st</sup> subsequence and &quot;xxcxx&quot; for the 2<sup>nd</sup> subsequence.
The product of their lengths is: 5 * 5 = 25.
</pre>

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

<ul>
	<li><code>2 &lt;= s.length &lt;= 12</code></li>
	<li><code>s</code> consists of lowercase English letters only.</li>
</ul>

class Solution:
    def maxProduct(self, s: str) -> int:
        @cache
        def subsets(i=0):
            if i == len(s):
                return [0]
            
            res = []

            for mask in subsets(i + 1):
                res.append(mask)
                res.append(mask | (1 << i))
            
            return res
        
        def isPalindrome(mask):
            i, j = 0, 12

            while True:
                while i < j and (mask >> i) & 1 == 0:
                    i += 1
                while j >= i and (mask >> j) & 1 == 0:
                    j -= 1
                
                if j < i:
                    break
                
                if s[i] != s[j]:
                    return False
                
                i, j = i + 1, j - 1
            
            return True

        def numOnes(mask):
            res = 0
            while mask:
                res += mask & 1
                mask >>= 1
            return res

        masks = list(filter(isPalindrome, subsets()))
        counts = list(map(numOnes, masks))

        res = 0
        for i in range(len(masks)):
            for j in range(i + 1, len(masks)):
                if masks[i] & masks[j]:
                    continue
                res = max(res, counts[i] * counts[j])

        return res
20800