Happy Number

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 S_i = 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 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.

#10591Happy Number

Input

Output