<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:
        left, right = int(left), int(right)
        count = 0

        def is_palindrome(num):
            return str(num) == str(num)[::-1]

        def generate_palindromes(limit):
            palindromes = []
            for i in range(1, 10):
                palindromes.append(i)
            for length in range(2, 19):
                half_length = (length + 1) // 2
                for i in range(10 ** (half_length - 1), 10 ** half_length):
                    s = str(i)
                    if length % 2 == 0:
                        palindrome = int(s + s[::-1])
                    else:
                        palindrome = int(s + s[:-1][::-1])
                    if palindrome > limit:
                        return palindromes
                    palindromes.append(palindrome)
            return palindromes

        palindromes = generate_palindromes(int(right) ** 0.5 + 1)
        for palindrome in palindromes:
            square = palindrome ** 2
            if left <= square <= right and is_palindrome(square):
                count += 1

        return count

# Example usage:
solution = Solution()
print(solution.superpalindromesInRange("4", "1000"))  # Output: 4
print(solution.superpalindromesInRange("1", "2"))     # Output: 1
21000