<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 L, string R) {
        int res = 0;
        long left = stol(L), right = stol(R);
        helper("", left, right, res);
        for (char c = '0'; c <= '9'; ++c) {
            helper(string(1, c), left, right, res);
        }
        return res;
    }
    void helper(string cur, long& left, long& right, int& res) {
        if (cur.size() > 9) return;
        if (!cur.empty() && cur[0] != '0') {
            long num = stol(cur);
            num *= num;
            if (num > right) return;
            if (num >= left && isPalindrome(to_string(num))) ++res;
         }
         for (char c = '0'; c <= '9'; ++c) {
            helper(string(1, c) + cur + string(1, c), left, right, res);
        }
    }
    bool isPalindrome(string str) {
        int left = 0, right = (int)str.size() - 1;
        while (left < right) {
            if (str[left++] != str[right--]) return false;
        }
        return true;
    }
};
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