RU-ALLRUSSIAN 2016 Problem 96

A square is partitioned in $n^2\geq 4$ rectanles using $2(n-1)$ lines, $n-1$ of which,are parallel to the one side of the square, $n-1$ are parallel to the other side.Prove that we can choose $2n$ rectangles of the partition,such that,for each two of them,we can place the one inside the other (possibly with rotation).