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 ≤ 10^{5}).
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 |
3 1 2 50 |
Case 1: 0 Case 2: 2.00 Case 3: 3.0333333333 |
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