Given an integer N, replace it by the sum of the squares of its digits. A happy number is a number where, if you apply this process repeatedly, it eventually results in the number 1. For example, if you start with 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! :)
Since this process resulted in 1, 82 is a happy number.
Notice that a number might be happy in some bases, but not happy in others. For instance, the base 10 number 82 is not a happy number when written in base 3 (as 10001).
You are one of the world's top number detectives. Some of the bases got together (yes, they are organized!) and hired you for an important task: find out what's the smallest integer number that's greater than 1 and is happy in all the given bases.
The first line of input gives the number of cases T. T test cases follow. Each case consists of a single line. Each line contains a space separated list of distinct integers, representing the bases. The list of bases is always in increasing order.
For each test case, output:
Case #X: Kwhere X is the test case number, starting from 1, and K is the decimal representation of the smallest integer (greater than 1) which is happy in all of the given bases.
2 ≤ all possible input bases ≤ 10
1 ≤ T ≤ 42
2 ≤ number of bases on each test case ≤ 3
1 ≤ T ≤ 500
2 ≤ number of bases on each test case ≤ 9
Please remember that you must submit all code used to solve the problem.