# Control C301C P57882

Statement

thehtml

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

Public test cases
• Input

```131
132
133
134
```

Output

```131: nothing
132: 3-popiropis
133: popiropis
134: nothing
```
• Input

```3
80
273
38222
44642
1000000
1629073
8802908
```

Output

```3: nothing
80: 3-popiropis
273: popiropis
38222: 4-popiropis
44642: 4-popiropis
1000000: nothing
1629073: popiropis
8802908: 3-popiropis
```
• Information
Author
Professorat de P1
Language
English
Translator
Carlos Molina
Original language
Catalan
Other languages
Catalan
Official solutions
C++
User solutions
C++