Perfect Number Check

A number $n$ is a perfect number if it equals the sum of all its divisors except itself.

For example, $6 = 1 + 2 + 3$, so $6$ is perfect.

Write a program that decides whether $n$ is a perfect number.

The input holds several test cases, one integer $n$ per line ($2 < n < 100{,}000$).

The last line of the input is $-1$, and that line is not processed. The number of test cases is not given in advance.

Print one line per test case.

If $n$ is perfect, print it as n = d1 + d2 + ... + dk, where $d_1 < d_2 < \cdots < d_k$ are the divisors of $n$ other than $n$ itself, in ascending order. Put one space on each side of the equals sign and of every plus sign.

If $n$ is not perfect, print n is NOT perfect.