<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:
    def superpalindromesInRange(self, left: str, right: str) -> int:
        def is_palindrome(s: str) -> bool:
            return s == s[::-1]
        
        def generate_palindromes(limit: int) -> list:
            palindromes = []
            # Generate palindromes by expanding from half-length segments
            for length in range(1, 11):  # up to 10-digit palindromes
                half_length = (length + 1) // 2
                start = 10**(half_length - 1)
                end = 10**half_length
                for half in range(start, end):
                    half_str = str(half)
                    if length % 2 == 0:
                        pal = int(half_str + half_str[::-1])
                    else:
                        pal = int(half_str + half_str[-2::-1])
                    if pal <= limit:
                        palindromes.append(pal)
                    else:
                        break
            return palindromes
        
        left_int = int(left)
        right_int = int(right)
        
        limit = int(right_int**0.5) + 1
        palindromes = generate_palindromes(limit)
        
        count = 0
        for pal in palindromes:
            square = pal * pal
            if square > right_int:
                break
            if square >= left_int and is_palindrome(str(square)):
                count += 1
        
        return count

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