<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 isPalindrome(std::string& str, int start, int end)
{
    while(start <= end)
    {
        if(str[start++] != str[end--])
        {
            return false;
        }
    }
    return true;
}

int allPossiblePalindrome(std::string& str, int start, int end, std::vector<std::vector<bool>> &mem)
{
    if(mem[start][end] ==  true)
    {
        return 0;
    }
    if(start == end)
    {
        mem[start][end] = true;
        return 0;
    }
    int count = 0;
    if(isPalindrome(str, start, end))
    {
        count = 1;
    }
    mem[start][end] = true;
    count+= allPossiblePalindrome(str, start+1, end, mem) + allPossiblePalindrome(str, start, end -1, mem);

    return count;
}
    int countSubstrings(string s) {
            int l = s.length();
    std::vector<std::vector<bool>> mem;
    for(int i = 0; i<l;i++){
        std::vector<bool> v;
        mem.push_back(v);
        for(int j = 0; j<l; j++)
        {
            mem[i].push_back(false);
        }
    }
        return allPossiblePalindrome(s, 0, s.length()-1, mem) + s.length();
    }
};
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