<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 checkPalindrom(self, s, i, j,dp):
        if i > j or i >= len(s) or j < 0:
            return 0
        
        if i == j:
            return 1
        
        if dp[(i,j)] != -1:
            return dp[(i,j)]
        
        if s[i] == s[j]:
            dp[(i,j)] = 2 + self.checkPalindrom(s, i + 1, j - 1,dp)
            return dp[(i,j)]
        else:
            dp[(i,j)] = max(self.checkPalindrom(s, i + 1, j,dp),
            self.checkPalindrom(s,i, j - 1,dp))

            return dp[(i,j)]


    def longestPalindromeSubseq(self, s: str) -> int:
        dp = defaultdict(lambda:-1)
        respone = self.checkPalindrom(s,0, len(s) - 1, dp)
        
        return respone




        
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