<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:
        s1 = s
        s2 = s1[::-1]

        cache = {}

        def top_down(i1,i2):
            if i1 == len(s1) or i2 == len(s2):
                return 0

            if s1[i1] == s2[i2]:
                return 1 + top_down(i1 + 1,i2 + 1)
            
            if (i1,i2) in cache:
                return cache[(i1,i2)]
            
            cache[(i1,i2)] = max(top_down(i1 + 1,i2),top_down(i1,i2 + 1))
            return cache[(i1,i2)]
        
        return top_down(0,0)
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