A distant planetary system has a single sun and $$$N-1$$$ planets. Each planet is identified by a distinct integer from $$$2$$$ to $$$N$$$. In planet $$$b$$$, numbers are represented using base $$$b$$$.
A palindromic number is a number that remains the same when its digits are written both forward and backward. In this context, leading zeroes are not considered when determining if a number is palindromic.
The same number can be palindromic in one planet's base but not in another. For instance, in base $$$10$$$, the number $$$33$$$ is palindromic. It is also palindromic in base $$$2$$$ and base $$$32$$$ but not in bases such as $$$3$$$ or $$$33$$$, since $$$33_{10}=100001_2=1020_3=11_{32}=10_{33}$$$.
The inhabitants of this planetary system have a peculiar fondness for palindromic numbers and want to know which planets make the number $$$N$$$ a palindromic number when represented in their base. Your task is to help them with this cosmic challenge.
The input consists of a single line that contains an integer $$$N$$$ ($$$2 \le N \le 10^{12}$$$) indicating the number to be checked for palindromic representation. $$$N$$$ is given in base $$$10$$$.
Output a single line with an increasing list of integers in the interval $$$[2, N]$$$, indicating the planets in which $$$N$$$ is a palindromic number when expressed in the base of the planet's identifier. Output these integers in base $$$10$$$. If $$$N$$$ is not palindromic in any of the planets, output the character "*" (asterisk) instead.
33
2 10 32
3
2
2
*
