Palindrome Number#2194
A palindrome is a string that reads the same forwards and backwards. For example, the string abba is a palindrome, while the string abc is not.
Your task is to determine in which numeral systems, with bases from to , the representation of the given number is a palindrome.
In numeral systems with bases greater than , letters of the Latin alphabet are used as digits: a, b, , z. For example, \textbf{a_{11}} = \textbf{10_{10}}, \textbf{z_{36}} = \textbf{35_{10}}.
The input contains a single integer , given in decimal (1 \leq n \leq 10^9).
If there is exactly one base where the representation of is a palindrome, print unique on the first line. If there are multiple such bases, print multiple on the first line. If no such base exists, print none on the first line.
If there is at least one suitable base, print all such bases in increasing order, separated by spaces, on the second line.
Example 1