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1) hash all states (8^4 = 4096) into 4 separate arrays
- nara1 August 20, 20142) mark a different solution state (all Ns, Es, Ss, Ws) in each of the four arrays
3) start a loop
4) for each array, going backward from the solution as the root, build one level adjacency (to include all MOVEs)
5) if the input state is visited, return loop count
6) continue loop
Optimize by excluding states already visited when building adjacency sets