Panex puzzle 8 layers

Panex puzzle, designed by Toshio Akanuma. It features 3 tracks connected at the top, left and right filled with stacks of pieces, originally 10 high. Your goal is to swap all the stacks. The catch: Every piece can only slide downward as far as its' original position, i.e. The third piece from the top can only slide 3 positions down, making it highly difficult.

This version has stacks only 8 pieces high, which has an optimal solution 5556 steps long.