<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 {
    vector<pair<int, int>> axises;

public:
    int countSubstrings(string s) {
        for (int i = 0; i < s.size(); ++i) {
            axises.emplace_back(i, i);
        }

        for (int i = 0; i < s.size() - 1; ++i) {
            if (s[i] == s[i + 1]) {
                axises.emplace_back(i, i + 1);
            }
        }

        int total = axises.size();

        bool updated = true;
        while (updated) {
            vector<pair<int, int>> new_axis;
            for (auto [i, j] : axises) {
                check(s, i, j, new_axis);
            }
            updated = !new_axis.empty();
            total += new_axis.size();
            axises.swap(new_axis);
        }
        return total;
    }

    void check(const string& s, int i, int j,
               vector<pair<int, int>>& new_axis) {
        if (i - 1 < 0 || j + 1 >= s.size()) {
            return;
        }

        if (s[i - 1] == s[j + 1]) {
            new_axis.emplace_back(i - 1, j + 1);
        }
    }
};
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