Control C301C P57882

Given a natural number $n \ge 1$, being $s(n)$ the sum of its divisors not counting itself. A number $n \ge 3$ is called popiropis if $n = s(n-2) + s(n) + s(n+2)$. A number $n \ge 3$ is called $k$-popiropis if $n*k = s(n-2) + s(n) + s(n+2)$ for an integer $k \ge 2$.

For instance, the number 133 is popiropis, because $s(131) = 1$, $s(133) = 27$ and $s(135) = 105$. Besides, 132 is 3-popiropis, because $s(130) + s(132) + s(134) = 396 = 132*3$.

Your task is to write a program that, for each natural number given, print if it is popiropis, if is $k$-popiropis (and which is the value of $k$), or if it is nothing.

Input

The input is a sequence of natural numbers $n \ge 3$.

Output

Your program must print a line for each $n$, indicating which class is: popiropis, $k$-popiropis, or nothing.

Observation

Your program must implement and use the function

    int sum_divisors(int n);

that, given a natural number |n| different than 0, returns the sum of its divisors (not counting itself).