906. Super Palindromes

Hard

50 Points

Math

String

Enumeration

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].

Examples

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.