<p>Given a string <code>s</code>, return <em>the number of <strong>palindromic substrings</strong> in it</em>.</p>

<p>A string is a <strong>palindrome</strong> when it reads the same backward as forward.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within the string.</p>

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

<pre>
<strong>Input:</strong> s = &quot;abc&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> Three palindromic strings: &quot;a&quot;, &quot;b&quot;, &quot;c&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;aaa&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> Six palindromic strings: &quot;a&quot;, &quot;a&quot;, &quot;a&quot;, &quot;aa&quot;, &quot;aa&quot;, &quot;aaa&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 of lowercase English letters.</li>
</ul>

# class Solution:
#     def countSubstrings(self, s: str) -> int:

#         def isPalindrome(substring):
#             length_substring = len(substring)
#             halflength = int(length_substring/2)
#             output = False
#             for idx in range(halflength):
#                 if substring[idx] == substring[-1-idx]:
#                     output = True
#                 else:
#                     output = False
#                     break
#             return output
        
#         def countPalindromicSubstrings(string):
#             count = 0
#             length_string = len(string)
#             for idx in range(length_string):
#                 for idx2 in range(idx+1,length_string):
#                     substring = string[idx:idx2+1]
#                     palindrome = isPalindrome(substring)
#                     if palindrome:
#                         count += 1
#             return count
        
#         length_s = len(s)
#         output = countPalindromicSubstrings(s) + length_s
#         return output

class Solution:
    def countSubstrings(self, s: str) -> int:
        def isPalindrome(substring):
            return substring == substring[::-1]

        def helper(start, end, memo):
            if start >= end:
                return 0
            if (start, end) in memo:
                return memo[(start, end)]

            count = 0
            if isPalindrome(s[start:end]):
                count = 1

            count += helper(start + 1, end, memo) + helper(start, end - 1, memo) - helper(start + 1, end - 1, memo)
            memo[(start, end)] = count
            return count

        memo = {}
        return helper(0, len(s), memo)
        
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