SP118 RHOMBS - Rhombs

An unbounded triangular grid is a plane covered by equilateral triangles:  Two neighboring triangles in the grid form a rhomb. There are 3 types of such rhombs:  A grid polygon is a simple polygon which sides consist entirely of sides of triangles in the grid. We say that a grid polygon is rhombastic if it can be partitioned into internally disjoint rhombs of types A, B and C. As an example let's consider the following grid hexagon:  This hexagon can be partitioned into 4 rhombs of type A, 4 rhombs of type B and 4 rhombs of type C:  For a given rhombastic grid polygon P compute the numbers of rhombs of types A, B and C in some correct partition. ### Task Write a program that: - reads a description of a rhombastic grid polygon from the standard input, - computes the numbers of rhombs of types A, B and C in some correct partition of the polygon, - writes the results to the standard output.

The input begins with the integer t, the number of test cases. Then t test cases follow. For each test case the first line of the input contains an integer n (3

For each test case the first and only line of the output contains three integers separated by single spaces denoting the number of rhombs of type A, B and C respectively, in some partition of the input polygon.