A polygon (not necessarily convex) on the coordinate plane is called plump if it satisfies the following conditions:
∙ coordinates of vertices are integers;
∙ each side forms an angle of 0∘, 90∘, or 45∘ with the abscissa axis;
∙ internal angles belong to the interval [90∘,270∘].
Prove that if a square of each side length of a plump polygon is even, then such a polygon can be cut into several convex plump polygons.(A. Yuran) combinatoricsanalytic geometry