Pseudoperfect numbers P82891

The proper divisors of a number $n$ are all the positive divisors of $n$ that are smaller than $n$. For instance, the proper divisors of 20 are 1, 2, 4, 5, and 10. In this problem, we will say that a number is pseudoperfect if it can be obtained by adding up some of (or all) its proper divisors. For instance, 20 is pseudoperfect, because $1 + 4 + 5 + 10 = 20$.

Write a program that, for every given number $n$,

• if $n$ has more than 15 proper divisors, prints how many it has;

• if $n$ has 15 or less proper divisors, tells if $n$ is pseudoperfect or not.

Input

Input consists of several strictly positive natural numbers.

Output

For every given $n$, print its number of proper divisors, if this is larger than 15. Otherwise, tell if $n$ is pseudoperfect or not. Follow the format of the example.