<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:
        dp= []
        for i in range(1000):
            row = []
            for j in range(1000):
                row.append(0)
            dp.append(row)

        def solve(l,r):
            if l == r +1:
                return 0
            if l == r :
                return 1
            if dp[l][r] > 0:
                return dp[l][r]
            if s[l] == s[r]:
                dp[l][r] = solve(l+1,r-1)+2
            
            dp[l][r] = max(dp[l][r],solve(l+1,r))
            dp[l][r] = max(dp[l][r],solve(l,r-1))

            return dp[l][r]
        
        ans  = solve(0,len(s)-1)
        return ans
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