Clock optimal solver

As there're only 18 possible moves in WCA notation (instead of all 30 moves of the clock puzzle), we can easily solve the clock by brute-force search + Gaussian Elimination.
The average solution length of the optimal solver is about 10.8 moves, which is 2 moves less than randomly generated moves (14 * (1 - 1/12) = 12.83). 
If we do nothing, about a half of the gaussian elimination procedures are redundant. If we filter all redundant combinations, we will have to generate a very large table and put it in the source code or generate it when initialization. 
As a tradeoff, I only filtered redundant combinations caused by the combinations of 8 moves, which is able to filter most of the redundant combinations.