The Luckiest number
Time Limit: 1000ms
Memory Limit: 65536kb
DescriptionChinese people think of '8' as the lucky digit. Bob also likes digit '8'. Moreover, Bob has his own lucky number L. Now he wants to construct his luckiest number which is the minimum among all positive integers that are a multiple of L and consist of only digit '8'.
InputThe input consists of multiple test cases. Each test case contains exactly one line containing L(1 ≤ L ≤ 2,000,000,000).
The last test case is followed by a line containing a zero.
OutputFor each test case, print a line containing the test case number(beginning with 1) followed by a integer which is the length of Bob's luckiest number. If Bob can't construct his luckiest number, print a zero.
8 11 16 0
Case 1: 1 Case 2: 2 Case 3: 0
Source2008 Asia Regional, Hefei, Preliminary