Problem Link  Prime Distinctness in Number theory
Problem Statement:
Given a positive integer N, the objective is to determine whether integer N is prime or not. If N is prime or 1, the function should return 1. Otherwise, if N is not prime, the task is to calculate and return the count of distinct prime factors of N.
Approach:

Understanding the Problem: Check if a positive integer N is prime and, if not, count the distinct prime factors.

Prime Checking and Factorization:
 If the input number is
1
or2
, it directly outputs1
since both are not considered to have prime factors.  Use a method to calculate the prime factors of n. An unordered set is used to store distinct prime factors. Sets automatically handle duplicates, ensuring only unique prime factors are counted.
 Finding Prime Factors:Iterates from 2 to √n to find prime factors. If n is divisible by i, it divides n and stores i in the set. If n is still greater than 1 after the loop, it is a prime factor itself.
 Finally, the size of the set gives the count of distinct prime factors.
Complexity:
 Time Complexity:
O(√N)
For calculating the prime numbers.  Space Complexity:
O(√N)
At the worst case the set can store up to√N
number of prime factors.