Factorization 3

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

Let $n = p_{1}^{a_{1}} p_{2}^{a_{2}} ... p_{k}^{a_{k}} (p_{1} < p_{2} < ... < p_{k})$ be a factorization of positive integer $n$ .

Find the value of $a_{1} + a_{2} + ... + a_{k}$ .

Input

One positive integer $n (1 < n \leq 1 0^{9})$ .

Find the factorization of $n$ and print the value of $a_{1} + a_{2} + ... + a_{k}$ .

For example, $72 = 2^{3} \cdot 3^{2}$ . The answer is $a_{1} + a_{2} = 3 + 2 = 5$ .

Input #1

Answer #1

Submissions 276

Acceptance rate 50%