Problem C |
Happy Number |
Time Limit |
1 Second |
Let the sum of the square of the digits of a positive integer S_{0} be represented by S_{1}_{.} In a similar way, let the sum of the squares of the digits of S_{1} be represented by S_{2} and so on. If S_{i} = 1 for some i ³ 1, then the original integer S_{0} 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 10^{9}.
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
Special
thanks to Muhammad Abul Hasan