$12\mathrm{.}2.$ Ski instructor's problem. A ski instructor needs to assign $n$ pairs of skis to $n$ novice skiers. The skis are available in lengths $l_1{l}_2$cdots$l_n,$ and the skiers have heights $h_1{h}_2$cdots$h_n.$ The lengths of the skis assigned to a skier should be proportional to his height: Assume that the constant of proportionality is $.$ The instructor wishes to assign the skis to skiers so that the total absolute difference between the actual ski lengths and the ideal ski lengths is as small as possible. Show that if for each $i,$ she assigns the $i$ th skier to the $i$ th pair of skis, her assignment is optimal.