<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 answer;
  long long low, high;
  
  bool isPolin(string s){
    long long n = stoll(s);
    n *= n;
    if(n < low || n > high) return false;
    
    s = to_string(n);
    int l = 0, r = s.size() - 1;
        
    while(l < r)
      if(s[l++] != s[r--]) return false;
            
    return true;
  }
 
  void helper(int l, int r, string &s){
    if(l > r) return;
    
    for(int i = 0; i != 9; i++){
      if(l == 0 && i == 0) continue;
        s[r] = s[l] = '0' + i;
        if(r - l < 2 && isPolin(s)) answer++;
        helper(l + 1, r - 1, s);
        s[r] = s[l] = '0';
      }
    }

  int superpalindromesInRange(string L, string R) {
    answer = 0, low = stoll(L), high = stoll(R);
    string s;
    
    int limit = (R.size() + 1)>>1;
      for(int length = L.size()>>1; length <= limit; length++){
        s.resize(length,'0');
        helper(0, length - 1, s);
      }
    
    return answer;
  }
};
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