<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:
        N = len(s)
        dp = [[0] * N for _ in range(N)]
        mx = [[0] * N for _ in range(N)]
        dp[0][0] = 1
        mx[0][0] = 1
        rl =  1
        for en in range(1, N):
            for st in range(en, -1, -1):
                if st != en and s[st] == s[en]:
                    dp[en][st] = mx[en-1][st+1] + 2
                    rl = max(dp[en][st], rl)
                else:
                    dp[en][st] = 1
                
                mx[en][st] = mx[en][st+1] if st < N-1 else 0
                mx[en][st] = max(mx[en-1][st], mx[en][st], dp[en][st])

        return rl

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