<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 {
public:


    bool palindrome(const int& l, const int& r, const string& s, map<pair<int,int>, bool>& cache)
    {
        if(r - l == 0)
            return true;
        
        if(s[l] != s[r])
            return false;

        if(r - l == 1) // two chars and equal
            return true;

        pair<int,int> indexes = {l,r};
        if(cache.count(indexes) > 0)
            return cache[indexes];

    
        cache[indexes] = palindrome(l+1, r-1, s, cache); 
        return cache[indexes];
    }

    int countSubstrings(string s) {
        
        int count = 0;

        map<pair<int,int>, bool> palindromeCache;
        for(int l = 0; l < s.size(); l++)
        {
            for(int r = l; r < s.size(); r++)
            {
                if(palindrome(l,r,s, palindromeCache))
                    count++;
            }
        }

        return count;
    }
};
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