Problem E
In-Circle
Input: Standard Input

Output: Standard Output

 

In-circle of a triangle is the circle that touches all the three sides of the triangle internally. The center of the in-circle of a triangle happens to be the common intersection point of the three bisectors of the internal angles. In this problem you will not be asked to find the in-circle of a triangle, but will be asked to do the opposite!!


You can see in the figure above that the in-circle of triangle ABC touches the sides AB, BC and CA at point P, Q and R respectively and P, Q and R divides AB, BC and CA in ratio m1:n1, m2:n2 and m3:n3 respectively. Given these ratios and the value of the radius of in-circle, you have to find the area of triangle ABC.

 


Input

First line of the input file contains an integer N (0<N<50001), which denotes how many input sets are to follow. The description of each set is given below.

 

Each set consists of four lines. The first line contains a floating-point number r (1<r<5000), which denotes the radius of the in-circle. Each of the next three lines contains two floating-point numbers, which denote the values of m1, n1, m2, n2, m3 and n3 (1<m1, n1, m2, n2, m3, n3<50000) respectively.

                                                           

Output

For each set of input produce one line of output. This line contains a floating-point number that denotes the area of the triangle ABC. This floating-point number should contain four digits after the decimal point. Errors less than 5*10-3 will be ignored. Use double-precision floating-point number for calculation.

 

Sample Input                               Output for Sample Input

2

140.9500536497

15.3010457320 550.3704847907

464.9681681852 65.9737378230

55.0132446384 10.7791711946

208.2835101182

145.7725891419 8.8264176452

7.6610997600 436.1911036207

483.6031801012 140.2797089713

400156.4075

908824.1322

Problemsetter: Shahriar Manzoor

Special Thanks: Mohammad Mahmudur Rahman