<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 __init__(self):
        self.solution = {}

    def longestPalindromeSubseq(self, s: str) -> int:
        
        if s in self.solution:
            return self.solution[s]

        if len(s)<=1:
            return len(s)
        
        if s[0]==s[-1]:
            self.solution[s] = 2 + self.longestPalindromeSubseq(s[1:-1])
            return self.solution[s]
        
        self.solution[s] = max(self.longestPalindromeSubseq(s[1:]), self.longestPalindromeSubseq(s[:-1]))
        return self.solution[s]
        
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