<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:
        left = 0
        right = len(s) - 1

        @cache
        def testSubseq(left, right):
            max_len = right - left + 1
            length = 0
            while left >= 0 and left < len(s) and right < len(s) and right >= 0 and s[left] == s[right] and left <= right:
                left += 1
                right -= 1
                length += 2
            print(left, right)
            if left > right:
                return max(max_len, 0)
            else:
                return length + max(testSubseq(left + 1, right), testSubseq(left, right - 1), testSubseq(left + 1, right - 1))
            
        return testSubseq(left, right)
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