Minimum Sum LCM |

**LCM** (Least Common Multiple) of a set of integers is defined as
the minimum number, which is a multiple of all integers of that set. It is
interesting to note that any positive integer can be expressed as the **LCM** of a set of positive integers. For example **12** can be expressed as the **LCM** of **1**, **12** or **12**, **12** or **3**, **4** or **4**, **6** or **1**, **2**, **3**, **4** etc.

In this problem, you will be given a positive
integer *N*. You have to find out a set of at least two positive integers
whose **LCM** is *N*. As infinite such sequences are possible,
you have to pick the sequence whose summation of elements is minimum. We will
be quite happy if you just print the summation of the elements of this set. So,
for *N* = 12, you should print **4+3 = 7** as **LCM** of **4** and **3**
is **12** and **7** is the minimum possible summation.

The input file contains at most **100** test cases. Each test case consists of a positive integer *N* (
1*N*2^{31} - 1).

Input is terminated by a case where *N* = 0. This case should not be processed. There can be at most **100** test cases.

Output of each test case should consist of a line starting
with ``Case #: `' where # is the test case number. It should be
followed by the summation as specified in the problem statement. Look at the output for sample input for details.

12 10 5 0

Case 1: 7 Case 2: 7 Case 3: 6

Problem setter: Md. Kamruzzaman

Special Thanks: Shahriar Manzoor

Miguel Revilla 2004-12-10