<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:
        """
        we know how to find add length palindromes
        """
        def helper(s, l, r, cache):
            if l < 0 or r >= len(s):
                return 0
            length = 1 if l == r else 2

            if (l, r) in cache:
                return cache[(l, r)]


            if s[l] == s[r]:
                length += helper(s, l-1, r+1, cache)
            else:
                length = max(helper(s, l-1, r, cache), helper(s, l, r+1, cache))
            cache[(l,r)] = length
            return cache[(l, r)]



        length = 0
        cache = {}
        for i in range(len(s)):
            length = max(length, helper(s,i,i, cache), helper(s,i,i+1, cache))
        
        return length
        
121293