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, ..., A_N-2, A_N-1, A_N, the profile defined will be called an Escher profile if we have A₁+A_N equal to A₂+A_N-1 equal to A₃+A_N-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