<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 g(self, s: str) -> bool:
        if len(s) < 2:
            return True

        return s[0] == s[len(s) - 1] and self.g(s[1:len(s) - 1])

    def f(self, index: int, endIndex, s: str, d: Dict[Tuple[int, int], int]) -> int:
        # print(index, endIndex)
        if index == endIndex:
            return 0
        
        if index == endIndex - 1:
            return 1

        k: Tuple[int, int] = (index, endIndex)

        if k in d.keys():
            return d[k]

        v1: int = self.f(index, endIndex - 1, s, d)
        v2: int = self.f(index + 1, endIndex, s, d)
        v3: int = 2 + self.f(index + 1, endIndex - 1, s, d) if s[index] == s[endIndex - 1] else 0

        d[k] = max(v1, v2, v3)

        return d[k]

    def longestPalindromeSubseq(self, s: str) -> int:
        return self.f(0, len(s), s, dict())
        
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