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This problem may at first glance appear pretty difficult, but the key point is to note that all the different hieroglyphic shapes contain a different number of “holes”. This makes the problem one of the easiest: find the connected regions of the picture and then, for every black region R, count how many different white regions are adjacent to R (making sure to pad the entire picture with a white frame to make the outer region one single region).

A different, more fancy solution, is to use the Euler characteristic to compute the genus of each black region.