Digital Division

In this challenge, you have to verify if a number is exactly divisible by a combination of its digits. There are three possible conditions to test:

• The given number is exactly divisible by each of its digits excluding the zeros.
• The given number is exactly divisible by the sum of its digits.
• The given number is exactly divisible by the product of its digits.

Given an integer n, implement a function that returns:

• If every test is true, a string "Perfect".
• If some test is true, the number of true tests (1 or 2).
• If every test is false, a string "Indivisible".

Examples

digital_division(21) ➞ 1
# Exactly divisible only by the sum of its digits (2 + 1 = 3).

digital_division(128) ➞ 2
# Exactly divisible by each of its digits.
# Exactly divisible by the product of its digits (1 * 2 * 8 = 16).

digital_division(100) ➞ 2
# Exactly divisible by each of its digits (excluding zeros).
# Exactly divisible by the sum of its digits (1 + 0 + 0 = 1).

digital_division(12) ➞ "Perfect"
# Exactly divisible by each of its digits.
# Exactly divisible by 3 (sum of digits = 1 + 2).
# Exactly divisible by 2 (product of digits = 1 * 2).

digital_division(31) ➞ "Indivisible"
# Every testing condition is false.

Notes

• Remember to exclude any 0-digit when testing if the given n is divisible by each of its digits (see example #3).
• A number containing at least a 0-digit can't be exactly divided by the product of its digits (division by 0).
• Trivially, every single-digit positive number greater than 0 is Perfect
• Any given number will be a positive integer greater than 0.