You are given a tower consisting of identical cubes, each of which has the same colors on the vertical sides in the same clockwise order as in Figure 1. The goal is for all cubes to be aligned in that all colors are the same vertically. A tower with such an alignment is called tidy.
Figure 1. The vertical sides of each cube consist of the colors red, green, blue, and yellow in clockwise order.
Two kinds of operations are allowed: rotate a cube and then all cubes above it rotate as well or rotate a cube c1 and hold a cube c2 above c1 so that neither cube c2 nor the cubes above c2 rotate but all cubes starting with c1 and up to the cube just below c2 rotate.
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