Multi-base happiness (small)

Replace an integer $N$ by the sum of the squares of its digits. A happy number is a number that reaches 1 when you repeat this process. Starting from 82:

8*8 + 2*2       = 64 + 4    = 68,  repeat:
6*6 + 8*8       = 36 + 64   = 100, repeat:
1*1 + 0*0 + 0*0 = 1 + 0 + 0 = 1 (happy!)

The process reached 1, so 82 is a happy number.

Being happy in base $b$ means writing the number in base $b$, adding the squares of those digits, and repeating until 1 appears. The same number can be happy in one base and not happy in another. The decimal number 82 is written 10001 in base 3, and in base 3 it is not happy.

Some of the bases got together (yes, they are organized) and hired you for a job: find the smallest integer greater than 1 that is happy in all of the given bases.

The first line contains the number of test cases $T$. Each of the next $T$ lines holds one test case: a space separated list of distinct bases in increasing order.

Limits

• $1 \le T \le 42$
• each line lists 2 or 3 bases
• every base $b$ in the input satisfies $2 \le b \le 10$

For each test case, print one line:

Case #X: K

where $X$ is the test case number starting from 1, and $K$ is the decimal form of the smallest integer greater than 1 that is happy in all of the given bases.