4 tokens are placed in the plane. If the tokens are now at the vertices of a convex quadrilateral $P$, then the following move could be performed: choose one of the tokens and shift it in the direction perpendicular to the diagonal of $P$ not containing this token; while shifting tokens it is prohibited to get three collinear tokens. Suppose that initially tokens were at the vertices of a rectangle $\Pi$, and after a number of moves tokens were at the vertices of one another rectangle $\Pi'$ such that $\Pi'$ is similar to $\Pi$ but not equal to $\Pi $. Prove that $\Pi$ is a square.