Minimum Steps to Reduce N to 1

You are given an integer N. Your task is to determine the minimum number of steps required to reduce N to 1. In each step, you are allowed to divide N by any prime divisor greater than 1 that evenly divides N.

This is equivalent to finding the total count of prime factors (with multiplicity) in the prime factorization of N. Formally, if the prime factorization of N is \( N = p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k} \), then the minimum number of steps required is \( e_1 + e_2 + \cdots + e_k \).

Note: It is guaranteed that N > 1 for all test cases.

inputFormat

The input consists of a single integer N on a single line, representing the number you need to reduce to 1.

outputFormat

Output a single integer representing the minimum number of steps required to reduce N to 1 using the allowed operations.

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