Cutting a set of rectangles into two identical shapes

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I am trying to cut this (in the link above) figure into two identical parts (while rotating a part of the figure you should get the other one). There is actually 6x4 matrix in which a11 and a53 are blank. The figure must be cut only by following the edges. If anyone knows what is the trick here I would be very grateful as I have no idea what pattern must be fallowed in order to generate all combinations...