<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>

from collections import defaultdict

class Solution:
    def longestPalindromeSubseq(self, s: str) -> int:
        r = defaultdict(lambda:{})
        n = len(s)
        for i in range(n):
            r[i][i] = 1
            r[i][i-1] = 0

        for i in range(n - 1, -1, -1):
            for j in range(i + 1,n):
                if s[i] == s[j]:
                    r[i][j] = r[i+1][j-1] + 2
                else:
                    r[i][j] = max(r[i][j-1], r[i+1][j])
        return r[0][n-1]
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