Elegant Permuted Sum
By Sohel Hafiz 
Bangladesh*
By Sohel Hafiz Bangladesh*
You will be given n integers A1A2A3...An. Find a permutation of these n integers so that summation of the absolute differences between adjacent elements is maximized.
Suppose n = 4 and the given integers are 4 2 1 5. The permutation 2 5 1 4 yields the maximum summation. For this permutation sum = abs(2-5) + abs(5-1) + abs(1-4) = 3+4+3 = 10.
Of all the 24 permutations, you won’t get any summation whose value exceeds 10. We will call this value, 10, the elegant permuted sum.
The first line of input is an integer T (T < 100) that represents the number of test cases. Each case consists of a line that starts with n (1 < n < 51) followed by n non-negative integers separated by a single space. None of the elements of the given permutation will exceed 1000.
For each case, show the case number followed by the elegant permuted summation.
| Input Sample | Output Sample |
|
3 |
Case 1: 10 |