Not Quite Perfect

A perfect number is a number that is equal to the sum of all its proper (non-self) divisors. Take 6 for example:

6 = 1 + 2 + 3

A number that is equal to the sum of all its proper divisors -- provided that one of them is negative -- is not quite perfect, but admirable.

To illustrate. The proper divisors of 12 are 1, 2, 3, 4, 6, totalling 16. However, if 2 is negative, the total would be 12, the number itself. 12 is therefore an admirable number.

12 = 1 - 2 + 3 + 4 + 6

Create a function that takes a number n as input.

1. If n is perfect, return "Perfect".
2. If n is admirable, return the proper divisor that must be rendered negative to make the sum of the proper divisors equal to n.
3. If n is neither perfect nor admirable, return "Neither".

Examples

admirable(6) ➞ "Perfect"

admirable(12) ➞ 2

admirable(18) ➞ "Neither"

Notes

N/A