You are given a positive integer n.

Repeatedly replace n with the sum of its prime factors. Continue this replacement process until the value of n stops changing.

Return the smallest value that n takes on throughout this process.

Note: If a prime factor divides n multiple times, it must be included in the sum as many times as it divides n.

Constraints:

• $2 \leq$ n $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.