Let's say a positive integer is a super-palindrome if it is a palindrome, and it is also the square of a palindrome.

Given two positive integers left and right represented as strings, return the number of super-palindromes integers in the inclusive range [left, right].

 

Example 1:

Input: left = "4", right = "1000"
Output: 4
Explanation: 4, 9, 121, and 484 are superpalindromes.
Note that 676 is not a superpalindrome: 26 * 26 = 676, but 26 is not a palindrome.

Example 2:

Input: left = "1", right = "2"
Output: 1

 

Constraints:

• 1 <= left.length, right.length <= 18
• left and right consist of only digits.
• left and right cannot have leading zeros.
• left and right represent integers in the range [1, 1018 - 1].
• left is less than or equal to right.