Problem C

Happy Number

Time Limit

1 Second

 

Let the sum of the square of the digits of a positive integer S0 be represented by S1. In a similar way, let the sum of the squares of the digits of S1 be represented by S2 and so on. If Si = 1 for some i 1, then the original integer S0 is said to be Happy number. A number, which is not happy, is called Unhappy number. For example 7 is a Happy number since 7 -> 49 -> 97 -> 130 -> 10 -> 1 and 4 is an Unhappy number since 4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4.

 

Input

The input consists of several test cases, the number of which you are given in the first line of the input. Each test case consists of one line containing a single positive integer N smaller than 109.

 

Output

For each test case, you must print one of the following messages:

 

Case #p: N is a Happy number.

Case #p: N is an Unhappy number.

 

Here p stands for the case number (starting from 1). You should print the first message if the number N is a happy number. Otherwise, print the second line.

 

Sample Input

Output for Sample Input

3

7

4

13

Case #1: 7 is a Happy number.

Case #2: 4 is an Unhappy number.

Case #3: 13 is a Happy number.

 

Problemsetter: Mohammed Shamsul Alam

International Islamic University Chittagong

Special thanks to Muhammad Abul Hasan