Question 57
There are $n$ stone piles, each consisting of $2018$ stones. The weight of each stone is equal to one of the numbers $1, 2, \ldots, 25$, and the total weights of any two piles are different. It is given that if we choose any two piles and remove the heaviest and the lightest stones from each of these two piles, then the pile which was the heavier one becomes the lighter one. Determine the maximal possible value of $n$.