Statement

As building a house is a hard process, you should seriously consider asking an engineer pieces of advice and plans. Despite this, Luca ignored Marco's warnings and decided to try building his house himself. Following the well-known proverb "you cannot build the roof without the floor", he started from building the floor. He was so happy with the newly purchased tiles that he placed all the 100 × 100 tiles, forming a square, even before raising the walls! What a terrible mistake! Now he has to break and throw away some of his tiles in order to raise the planned walls, keeping only those completely inside the house. The original plan of the house has the shape of a polygon and luckily all the vertexes of this polygon coincide with a corner of a tile. How many tiles will survive the raising of the walls?