Suppose we have two identical cardboard polygons. We placed one polygon upon the other one and aligned. Then we pierced polygons with a pin at a point. Then we turned one of the polygons around this pin by $25^{\circ}300^{\prime}$ . It turned out that the polygons coincided (aligned again). What is the minimal possible number of sides of the polygons? 

Let's think step by step and output the final answer within \boxed{}.
user