<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:
        # hashmap, bit masking 
        # bit masking: check if any two subseqs are disjoint
        # ete: 01010001000, cdc: 00001010100 -> 01010001000 & 00001010100 = 0
        # Therefore, ete and cdc are disjoint
        # s.length <= 12, brute force to find all subseqs
        N = len(s)
        palin = {}  # {masking : length}
        for masking in range(1, 2 ** N):    # 2 ** N = 1 << N
            subseq = ""
            # convert masking to subseq string
            for i in range(N):
                if 1 << i & masking:
                    subseq += s[i]  # should be s[N - 1 - i]. Should not matter for pali
            # check if subseq is a palin
            if subseq == subseq[::-1]:
                palin[masking] = len(subseq)
        # iterate over palin and find max prod of the length of the 2 disjoint palin subseq
        res = 0
        for p1 in palin:
            for p2 in palin:
                if not (p1 & p2):   # p1 and p2 are disjoint
                    res = max(res, palin[p1] * palin[p2])
        return res









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