Sliders

The goal in this puzzle is to order the numbers sequentially in their natural order starting with 0 in the left upper corner and proceeding right and down. One should do this by sliding either whole columns or whole rows. But there is a caveat. In the original position rows and columns rotate not just slide. This means, for example, that the first element becomes the last when a row is rotated left. This is very much akin to the Rubik's Cube but played on the flat surface of a torus. There are two additional surfaces on which the game can be played - Klein bottle and Projective plane. The difference is in how points on the sides of the square are identified with each other. Two small squares on the left and right from the game board indicate the selected surface.

Explanation

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