Escher Symmetry

Escher Symmetry

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M. C. Escher was a Dutch graphic artist who created incredible illustrations which were inspired by mathematics. For example, he filled the canvas with self-similar objects, whose contours fit into themselves, creating very impressive geometric symmetries.

See a very simple example of this idea in the following figure, which shows an object that is an orthogonal profile defined by a sequence of natural numbers representing the sequence of heights. We can take a copy of the object, rotate it 180 degrees and fit it perfectly into the original object, forming a rectangle.


In more general terms, if a sequence of N natural numbers representing the sequence of heights is A1, A2, A3, ..., AN-2, AN-1, AN, the profile defined will be called an Escher profile if we have A1+AN equal to A2+AN-1 equal to A3+AN-2, and so on. In this problem, you will be given the sequence of heights that define the profile and your program must decide whether the profile is Escher or not.

Input: List of integers (int)

Output: Boolean value (bool).


assert is_figure([1, 2, 1, 2]) == True
assert is_figure([1, 3, 2, 1, 3]) == True
assert is_figure([1, 2, 2, 1]) == False
assert is_figure([4, 4, 4, 4, 4, 4, 4, 4, 4]) == True
Invalid hot key. Each hot key should be unique and valid
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