44. In the Land of Fools, there are $N^{2}$ cities arranged in a square, with the distance between adjacent cities being 10 km. The cities are connected by a road system consisting of straight segments parallel to the sides of the square. What is the minimum length of such a road system, given that it is possible to travel from any city to any other city?
83.44. Answer. $10\left(N^{2}-1\right)$. Hint. Consider an arbitrary segment of such a system that starts and ends not in a city. Suppose that on one side it is adjacent to $a$ segments, and on the other $b$, with $a \geqslant b$. Moving it in the first direction, we will not increase the length of the system. Its movement can end either by overlapping with some other segment - then the length of the road system will decrease, or by turning into a longer segment, which can also be moved in some direction (of course, if neither of its ends is a city). Acting in this way, we can achieve that the transformed road system will have a length no greater than the original system, but at the same time all its roads will start and end in cities.