I hope there's comparison chart for cost per computation/memory of cloud services, based on benchmarking.

It seems random with 4 directions works well more than 3.

http://imgur.com/u0Yws7T Here is what I ran so far with random 3 directions. V shape emerges.

I beat this with first try. I feel like I could almost always win with my strategy... http://imgur.com/HtC2mOh

I missed #2. I wonder which case assigning sort order(ASC or DESC) to columns in index gives performance advantage.