Statement

After playing petanque with his friends and beating them all the time, Benewski has decided to meditate for a little and quickly became interested in architecture and, most importantly, in shapes. More exactly, he started drawing shapes made of straight line segments and decided to use them for his drawings. Over time, his drawings became more and more complex, and he is now wondering, given one of his drawings, how many times a specific pattern appears in it. A pattern is given by the coordinates of its segments that represent it. For a pattern to appear in a drawing, one should find the exact segments of the pattern up to translation in it. More exactly, a pattern occurs in the drawing if there exist numbers (dx, dy) such that, when shifting the pattern up by dx units on the X axis and up by dy units on the Y axis, one finds a subset of the segments of the drawing...