<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>

"""

dp(i, j) = dp(i+1, j-1) + 2, max(dp(i+1, j))

"""

def cached(fn):
    cache = {}
    def wrapped(*args):
        if args in cache:
            return cache[args]
        sol = fn(*args)
        cache[args] = sol
        return sol
    return wrapped


@cached
def palindrome(s, i, j):
    if i > j:
        return 0
    elif i == j:
        return 1
    elif s[i] == s[j]:
        return 2 + palindrome(s, i+1, j-1)
    else:
        return max(palindrome(s, i+1, j), palindrome(s, i, j-1))

class Solution:
    def longestPalindromeSubseq(self, s: str) -> int:
        return palindrome(s, 0, len(s)-1)
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