Almost Perfect

A positive integer $p$
is called a *perfect number* if all the
proper divisors of $p$ sum
to $p$ exactly. Integer
$d$ is a proper divisor of
$p$ if $1 \le d \le p-1$ and $p$ is evenly divisible by
$d$. For example, the
number $28$ is a perfect
number, since its proper divisors (which are $1$, $2$, $4$, $7$ and $14$) add up to $28$.

Perfect numbers are rare; only $10$ of them are known. Perhaps the
definition of perfection is a little too strict. Instead, we
will consider numbers that we’ll call *almost
perfect*. Positive integer $p$ is almost perfect if the proper
divisors of $p$ sum to a
value that differs from $p$ by no more than two.

Input consists of a sequence of up to $500$ integers, one per line. Each integer is in the range $2$ to $10^9$ (inclusive). Input ends at end of file.

For each input value, output the same value and then one of the following: “perfect” (if the number is perfect), “almost perfect” (if it is almost perfect but not perfect), or “not perfect” (otherwise).

Sample Input 1 | Sample Output 1 |
---|---|

6 65 650 |
6 perfect 65 not perfect 650 almost perfect |