Rimi learned a new thing about integers, which is - any positive integer greater than 1 can be divided by its divisors. She is playing with this property now in the form of a game.
She first selects a number N. She then randomly chooses a divisor of N (1 to N) and divides N by the number to obtain a new N. She repeats this procedure until N becomes 1. What is the expected number of turns required for Rimi to end the game - meaning N becomes 1?
Input
Input starts with an integer T (≤ 10000), denoting the number of test cases.
Each case begins with an integer N (1 ≤ N ≤ 105).
Output
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
| Sample Input | Sample Output |
|---|---|
3 1 2 50 | Case 1: 0 Case 2: 2.0 Case 3: 3.0333333333 |