Clipboard
Bart Simpson, from the animated series "The Simpsons," has been assigned a punishment for skipping classes: he must send an email to the school principal. In this email, Bart is required to type the phrase "I will not skip school anymore" N times. The principal believes that this exercise will deter Bart from skipping school in the future. Naive principal!
Instead of typing the phrase N times, Bart cleverly writes it once and then uses the clipboard to replicate it. In one operation, Bart can either copy the entire current content of the email to the clipboard or paste the text from the clipboard into the email.
Your task is to write a program that, given the number of times the phrase must appear in the email, determines the minimum number of clipboard operations Bart needs to perform to achieve the required number of phrases.
Input
The input consists of a single number N, which represents the number of times the phrase "I will not skip school anymore" must appear in the email. The number N is a natural number and does not exceed 2∙10^9.
Output
Output a single integer, which is the minimum number of clipboard operations needed for the email to contain exactly N phrases.
Explanation. After Bart writes the first phrase, he can perform the following clipboard operations:
Copy the current content of the email (1 phrase).
Paste the copied text (the email now has 2 phrases).
Paste the copied text (the email now has 3 phrases).
Paste the copied text (the email now has 4 phrases).
Copy the current content of the email (4 phrases).
Paste the copied text (the email now has 8 phrases).
Paste the copied text (the email now contains the required 12 phrases).