<p>Let&#39;s say a positive integer is a <strong>super-palindrome</strong> if it is a palindrome, and it is also the square of a palindrome.</p>

<p>Given two positive integers <code>left</code> and <code>right</code> represented as strings, return <em>the number of <strong>super-palindromes</strong> integers in the inclusive range</em> <code>[left, right]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> left = &quot;4&quot;, right = &quot;1000&quot;
<strong>Output:</strong> 4
<strong>Explanation</strong>: 4, 9, 121, and 484 are superpalindromes.
Note that 676 is not a superpalindrome: 26 * 26 = 676, but 26 is not a palindrome.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> left = &quot;1&quot;, right = &quot;2&quot;
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= left.length, right.length &lt;= 18</code></li>
	<li><code>left</code> and <code>right</code> consist of only digits.</li>
	<li><code>left</code> and <code>right</code> cannot have leading zeros.</li>
	<li><code>left</code> and <code>right</code> represent integers in the range <code>[1, 10<sup>18</sup> - 1]</code>.</li>
	<li><code>left</code> is less than or equal to <code>right</code>.</li>
</ul>

class Solution {
 public:
  int superpalindromesInRange(string left, string right) {
    int ans = 0;
    const long l = stoll(left);
    const long r = stoll(right);

    for (long i = sqrt(l); i * i <= r;) {
      const long palindrome = nextPalindrome(i);
      const long squared = palindrome * palindrome;
      if (squared <= r && isPalindrome(squared))
        ++ans;
      i = palindrome + 1;
    }

    return ans;
  }

 private:
  long nextPalindrome(int num) {
    const string s = to_string(num);
    const int n = s.length();
    string half = s.substr(0, (n + 1) / 2);
    string reversedHalf = reversed(half.substr(0, n / 2));
    const long candidate = stoll(half + reversedHalf);
    if (candidate >= num)
      return candidate;
    half = to_string(stoll(half) + 1);
    reversedHalf = reversed(half.substr(0, n / 2));
    return stoll(half + reversedHalf);
  }

  string reversed(const string& s) {
    return {s.rbegin(), s.rend()};
  }

  bool isPalindrome(long num) {
    const string s = to_string(num);
    int l = 0;
    int r = s.length() - 1;
    while (l < r)
      if (s[l++] != s[r--])
        return false;
    return true;
  }
};
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