35. The sides of a square are sequentially numbered with the numbers $1,2,3,4$. For an arbitrary point $A$ and side $k$, denote by $A_{k}$ the point symmetric to the projection of $A$ onto the line $k$ relative to the point $A$. Find all points $A$ such that each of the points $A_{1}, A_{12}, A_{123}, A_{1234}, A_{12341}, \ldots$ lies inside our square.
74.35. Let's introduce coordinates in the square such that the origin is at the vertex belonging to sides 1 and 2. Then there is a unique point $A$ with the required property. This is the point with coordinates $(1 / 3 ; 1 / 3)$. Hint. Note that the operations $A \rightarrow A_{2}, A \rightarrow A_{4}$ do not affect one, while the operations $A \rightarrow A_{1}, A \rightarrow A_{3}$ affect the other coordinate.