<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:
        ret = [set(), set((i, i) for i in range(len(s)))]
        if len(s) > 1:
            mem = set()
            for lhs, rhs in ret[1]:
                if 0 <= lhs - 1 and s[lhs - 1] == s[lhs]:
                    mem.add((lhs - 1, lhs))
                if rhs + 1 < len(s) and s[rhs] == s[rhs + 1]:
                    mem.add((rhs, rhs + 1))
            ret.append(mem)
        if len(s) > 2:
            for seg in range(3, len(s) + 1):
                mem = set()
                for lhs, rhs in ret[seg - 2]:
                    if 0 <= lhs - 1 and rhs + 1 < len(s) and s[lhs - 1] == s[rhs + 1]:
                        mem.add((lhs - 1, rhs + 1))
                ret.append(mem)
        return sum(len(mem) for mem in ret)

96296