Let be an integer. Find the maximal integer such that there exists a polygon with vertices (convex or not, but not self-intersecting!) having internal angles.
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Let $n \geq 5$ be an integer. Find the maximal integer $k$ such that there exists a polygon with $n$ vertices (convex or not, but not self-intersecting!) having $k$ internal $90^{\circ}$ angles.
Izvor: Međunarodna matematička olimpijada, shortlist 2003
Školjka 
be an integer. Find the maximal integer 
such that there exists a polygon with 
vertices (convex or not, but not self-intersecting!) having 
angles.