A string is called a palindrome string if the reverse of the string is same as the original string.

A string $$$S$$$ is called an extended palindrome string if the string becomes a palindrome after chucking it in chunks of length $$$d$$$, where $$$d$$$ is either 1 or a prime divisor of $$$|S|$$$, where $$$|S|$$$ is the length of the string. For example, 'abcxyzabc' is not a palindrome but an extended palindrome as it can be broken as {abc}{xyz}{abc} into chunks of length 3.

The degree of a string is defined as the minimum possible chunk length that can make the string an extended palindrome.

Given a string $$$S$$$, find its degree.