Medians
By Shahriar Manzoor 
Bangladesh
By Shahriar Manzoor Bangladesh
Given the length of three medians of a triangle you will have to find out the area of the triangle. Unless you are weak in geometry you should know that median of a triangle is formed by connecting any vertex of a triangle and the mid-point of its opposite edge. So a triangle has three medians.
The input file contains aproximately 1000 lines of input. Each line contains three numbers which denote the length of the medians of a triangle. All the values in the input will be less than 100. Input is terminated by end of file.
For each line of input you should produce one line of output. This line should contain the area of the triangle for the corresponding input. If it is not possible to form a triangle with the given medians, the area of the triangle should be set as -1. The areas should be rounded up to three digits after the decimal point.
| Sample Input | Sample Output |
|
3 3 3 |
5.196 |