<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>

import math

class Solution:
    def maxProduct(self, s: str) -> int:
        list1 = list()
        self.dfs(s, "", 0, 0, list1)

        ans = 0
        for i in range(len(list1)):
            for j in range(i+1, len(list1)):
                # print(list1[i], list1[j])
                if(self.match(list1[i][0], list1[j][0])) :
                    ans = max(ans, list1[i][1] * list1[j][1])

        return ans
    
    def match(self, a: int, b: int) -> bool:
        result = True
        while(a > 0 or b > 0):
            if((a % 10) and (b %10)):
                result = False
                break
            a //= 10
            b //= 10
        return result

    def dfs(self, s: str, s1: str, pos: int, num: int, list1: list):
        if pos == len(s):
            match = True
            for i in range(int(len(s1)/2)):
                if s1[i] != s1[len(s1)-i-1]:
                    match = False
                    break

            if match:
                list1.append((num, len(s1)))

            return
        self.dfs(s, s1, pos+1, num*10, list1)
        self.dfs(s, s1+s[pos], pos+1, num*10+1, list1)


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