<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:
        def tab():
            n = len(s)
            s1 = s[::-1]
            dp = [[0 for _ in range(n+1)] for _ in range(n+1)]
            for i in range(1,n+1):
                for j in range(1,n+1):
                    if s[i-1] == s1[j-1]:
                        dp[i][j] = 1 + dp[i-1][j-1]
                    else:
                        dp[i][j] = max(dp[i][j-1],dp[i-1][j])
            return dp[n][n]


        def fun(i,j):
            if i < 0 or j < 0:
                return 0
            if  dp[i][j] != -1 :
                return dp[i][j]
            unpick = max(fun(i-1, j), fun(i, j-1))
            pick = 0
            if s[i] == s1[j]:
                pick = 1 + fun(i-1, j-1)
            dp[i][j] = max(pick, unpick)
            return dp[i][j]
        
        n = len(s)
        i,j = n-1, n-1
        s1 = s[::-1]
        dp = [[-1 for _ in range(n)] for _  in range(n)]
        return fun(n-1, n-1)
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