<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 __init__(self):
        self.count = 0
        self.s = None
        self.myset = set()
        self.sset = set()


    def isPalindrome(self, head, tail):
        if tuple([head, tail]) in self.myset:
            return True
        if head >= tail:
            return True

        ans = self.s[head] == self.s[tail] and self.isPalindrome(head+1, tail-1)
        if ans:
            self.myset.add(tuple([head, tail]))
            return True
        else:
            return False

        while head <= tail:
            if self.s[head:tail+1] in self.myset:
                return True
            if self.s[head] != self.s[tail]:
                return False
            head += 1
            tail -= 1
            
        return True


    def countSubstrings(self, s: str) -> int:
        self.s = s
        for head in range(len(s)):
            for tail in range(head, len(s)):
                if s[head:tail+1] in self.sset:
                    self.count += 1
                elif self.isPalindrome(head, tail):
                    self.sset.add(s[head:tail+1])
                    self.count += 1

        return self.count

54243