Perfect or Amicable?

Given a positive number x, if all the positive divisors of x (excluding x) add up to x, then x is said to be a perfect number.

For example, the set of positive divisors of 6 excluding 6 itself is (1, 2, 3). The sum of this set is 6. Therefore, 6 is a perfect number.

Given a positive number x, if all the positive divisors of x add up to a second number y, and all the positive divisors of y add up to x, then x and y are said to be a pair of amicable numbers.

Create a function that takes a number and returns "Perfect" if the number is perfect, "Amicable" if the number is part of an amicable pair, or "Neither".

Examples

num_type(6) ➞ "Perfect"

num_type(2924) ➞ "Amicable"

num_type(5010) ➞ "Neither"

Notes

N/A