<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=[-1]*(n*n)
        def solve(i,j):
            if(i>j):
                return 0
            if i==j:
                dp[i*n+j]=1
                return 1
            if i<n-1 :
                if dp[(i+1)*n+j]==-1:
                    a=solve(i+1,j)
                else:
                    a=dp[(i+1)*n+j]
            else:
                a=-1
            r=j
            while s[r]!=s[i]:
                r-=1
            if r>i:
                if dp[(i+1)*n+r-1]==-1:
                    b=solve(i+1,r-1)+2
                else:
                    b=dp[(i+1)*n+r-1]+2
            else:
                b=1
            dp[i*n+j]=max(a,b)
            return dp[i*n+j]
        out=solve(0,n-1)
        return out

        
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