<p>Given a string <code>s</code>, find <em>the longest palindromic <strong>subsequence</strong>&#39;s length in</em> <code>s</code>.</p>

<p>A <strong>subsequence</strong> is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.</p>

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

<pre>
<strong>Input:</strong> s = &quot;bbbab&quot;
<strong>Output:</strong> 4
<strong>Explanation:</strong> One possible longest palindromic subsequence is &quot;bbbb&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;cbbd&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> One possible longest palindromic subsequence is &quot;bb&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists only of lowercase English letters.</li>
</ul>

class Solution:

    def solve(self,left,right,s):
        
        print(left , right)

        if left>right:
            return 0
        if left==right:
            return 1
        
        if Solution.dp[left][right]>0:
            return Solution.dp[left][right]
        if s[left]==s[right]:

            Solution.dp[left][right]=self.solve(left+1,right-1,s)+2

        else:

            Solution.dp[left][right]=max(self.solve(left+1,right,s),self.solve(left,right-1,s))

        return Solution.dp[left][right]

    def longestPalindromeSubseq(self, s: str) -> int:
        n = len(s)
        # Correct DP initialization to avoid shared references
        Solution.dp = [[0] * n for _ in range(n)]

        result = self.solve(0, n - 1, s)
        # print(self.dp)
        return result

        
        
        


        
        
       

       
        



            
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