<p>Given a string <code>s</code>, return <em>the longest</em> <span data-keyword="palindromic-string"><em>palindromic</em></span> <span data-keyword="substring-nonempty"><em>substring</em></span> in <code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;babad&quot;
<strong>Output:</strong> &quot;bab&quot;
<strong>Explanation:</strong> &quot;aba&quot; is also a valid answer.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cbbd&quot;
<strong>Output:</strong> &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> consist of only digits and English letters.</li>
</ul>

class Solution:
    def longestPalindrome(self, s: str) -> str:
        n = len(s)
        f = [[True] * (n - i - 1) for i in range(n)]
        k, mx = 0, 1
        for i in range(n - 2, -1, -1):
            for j in range(2, n + 1 - i):
                f[i][j - 2] = False
                if s[i] == s[i + j - 1]:
                    if j <= 3:
                        f[i][j - 2] = True
                    else:
                        f[i][j - 2] = f[i + 1][j - 4]
                if f[i][j - 2] and mx < j:
                    k = i
                    mx = j

        return s[k: k + mx]
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