Server Time: Sun Oct 25, 2020 10:18 am
Welcome ( logout
C - Race to 1 Again
PDF (English) Ranklist
Time Limit: 2 second(s) Memory Limit: 32 MB

Rimi learned a new thing about integers, which is - any positive integer greater than 1 can be divided by its divisors. So, he is now playing with this property. He selects a number N. And he calls this D.

In each turn he randomly chooses a divisor of D (1 to D). Then he divides D by the number to obtain new D. He repeats this procedure until D becomes 1. What is the expected number of moves required for N to become 1.


Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each case begins with an integer N (1 ≤ N ≤ 105).


For each case of input you have to print the case number and the expected value. Errors less than 10-6 will be ignored.

Sample Input

Output for Sample Input





Case 1: 0

Case 2: 2.00

Case 3: 3.0333333333


Problem Setter: Jane Alam Jan
Developed and Maintained by
Copyright © 2012
LightOJ, Jane Alam Jan