<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:
        
        def is_pali(l1):
            l,r = 0, len(l1) -1
            while l <= r:
                if s[l1[l]] != s[l1[r]]:
                    return False
                l+=1
                r-=1
            return True

        res = []
        def backtrack(i, path, bitmask):
            if i == len(s):
                if is_pali(path):
                    res.append(bitmask)
                return            

            #take and dont take
            mask = 1 
            mask<<=i
            path.append(i)
            temp = bitmask
            temp|=mask
            backtrack(i + 1, path, temp)
            path.pop()

            backtrack(i + 1, path, bitmask)
        
        lengths = collections.defaultdict(int)
        backtrack(0, [], 0)
        ans = 1
        def get_length(bitmask):
            mask = 1
            res = 0
            while bitmask:
                if bitmask & 1:
                    res+=1
                bitmask>>=1
            return res
        a = 1
        b = 1
        for i, pali in enumerate(res):
            a = get_length(pali)
            for j in range(i + 1, len(res)):
                if pali & res[j] == 0:
                    b = get_length(res[j])
                    ans = max(ans, a * b)
        
        return ans



        
            

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