<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 {
    private:
    int solve(int i,int j,string s,vector<vector<int>> &memo){
        while(i < j) if(s[i++] != s[j--]) return false;
        return true;
    }
public:
    int countSubstrings(string s) {
        int cnt = s.size();
        int n = s.size();
        vector<vector<int>> memo(n,vector<int>(n,-1));
        for(int i=0; i<s.size(); i++){
            for(int j=i+1; j<s.size(); j++){
                if(s[i] == s[j]) {
                if(memo[i][j] != -1) cnt += memo[i][j];
                else cnt += solve(i,j,s,memo); 
                } 
            }
        }
        return cnt;
    }
};
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