<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 longestPalindromeSubseq(self, s: str) -> int:
        self.s = s
        self.answers = {}

        def recur(start, end):
            if end - start <= 1:
                return end - start
            if (start, end) in self.answers:
                return self.answers[(start, end)]

            if s[start] == s[end-1]:
                self.answers[(start, end)] = 2 + recur(start+1, end-1)
                return self.answers[(start, end)]
                
            for i in range(end-1, start-1, -1):
                if s[start] == s[i]:
                    break
            if i == start:
                add = 1
            else:
                add = 2
            self.answers[(start, end)] = max(add + recur(start+1, i), recur(start+1, end))
            return self.answers[(start, end)]

        return recur(0, len(s))
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