You have 8 circles of equal size and you want to pack them inside a square. You want to minimize the size of the square. The following figure illustrates the minimum way of packing 8 circles inside a square:
The Problem: Given the radius, r, find the area of the minimum square into which 8 circles of that radius can be packed.
The first input line contains a positive integer, n, indicating the number of test cases. Each test case consists of a positive real number (between 0.001 and 1000, inclusive) in a single line denoting the radius, r.
For each test case, output the area of the minimum square where 8 circles of radius r can be packed. Print 5 digits after the decimal. Your output is considered correct if it is within ±0.00001 of the judge’s output.