Distinct Prime Factor Sorter

Given a list of integers, sort them based on the number of distinct prime factors each number has (descending). If two numbers have the same number of distinct prime factors, sort them based on the value of their largest prime factor (descending). If they are still tied, sort them by the original number in ascending order. Example: Input: '10 12 15' - 10: factors {2, 5}. Count: 2, Max: 5. - 12: factors {2, 3}. Count: 2, Max: 3. - 15: factors {3, 5}. Count: 2, Max: 5. Sorted: 10 (2,5), 15 (2,5), 12 (2,3) Output: '10 15 12'