Finding maximum differences in an array of real numbers .

Question

This is an algorithm design question which often appears in exams in a course that I take in the university . Suppose I have an array $A\in\mathbb{R}$ of size $n$ . I am required to find the $\frac{n}{\log n}$ largest differences $|a_i-a_j|$ for every $\,\,i\neq j\,\,$ ($i,j\in [1,n]$) . I must do this in linear time , that is my algorithm should run in $\, O(n)$ .
Now the initial idea for the solution would be to use the Select algorithm to find the $\frac{n}{\log n}$ and $n-\frac{n}{\log n}$ order statistics , then scan the array again and split it to groups $A_1$ in which every member is smaller than the $\frac{n}{\log n}$ order statistic, and $A_2$ in which every member is greater than the $n-\frac{n}{\log n}$ order statistic . Each such group is of size $\frac{n}{\log n}$ so sorting them will take linear time (I won't go into the calculation of this).
Now here's my problem . As mentioned I'm at the stage where I have 2 arrays containing $\frac{n}{\log n}$ smallest and $\frac{n}{\log n}$ greatest elements of array $A$ sorted in two arrays . I can't think of an algorithm to find the greatest $\frac{n}{\log n}$ differences other than knowing that the min value of $A_1$ and the max value of $A_2$ will form the first greatest difference .Help?