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

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 Input

Output for Sample Input

3

1

2

50

Case 1: 0

Case 2: 2.00

Case 3: 3.0333333333

Problem Setter: Jane Alam Jan

dp[i]表示把i变成1的期望次数

/*************************************************************************
    > File Name: c.cpp
    > Author: ALex
    > Mail: zchao1995@gmail.com 
    > Created Time: 2015年04月29日 星期三 19时40分52秒
 ************************************************************************/

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