clean dp

class Solution:

    def longestPalindrome(self, s: str) -> str:

        n = len(s)
        if n < 1:
            return ''

        longest_palindrome = s[0]

        dp = [[False]*n for _ in range(n)]

        for gap in range(n):

            for start in range(n-gap):

                end = start + gap

                if start == end:
                    dp[start][end] = True
                    continue

                dp[start][end] = s[start] == s[end]

                if end - start > 1:
                    dp[start][end] &= dp[start+1][end-1]

                if dp[start][end] and (end - start + 1) > len(longest_palindrome):
                    longest_palindrome = s[start:end+1]

        return longest_palindrome