Hard Way

Description:

Input:

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. Description of the test cases follows.

Each test case contains three lines, each of them contains two integers $$$x_i$$$, $$$y_i$$$ ($$$0 \le x_i, y_i \le 10^9$$$) — coordinates of the vertices of the downtown's border.

Output:

For each test case print a single number — the answer to the problem.

Your answer will be considered correct if its absolute or relative error does not exceed $$$10^{-9}$$$. Formally let your answer be $$$a$$$, jury answer be $$$b$$$. Your answer will be considered correct if $$$\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-9}$$$.

Sample Input:

5
8 10
10 4
6 2
4 6
0 1
4 2
14 1
11 2
13 2
0 0
4 0
2 4
0 1
1 1
0 0

Sample Output:

0.0000000
0
2.0000
0.00
1

Note:

In the picture, the downtowns of the first three test cases are illustrated. Triangles are enumerated according to the indices of test cases they belong to.

In the first two test cases, all points on the borders of the downtowns are safe, thus the answers are $$$0$$$.

In the following picture unsafe points for the third test case are marked with black color:

In the fourth test case, all points on the border of the downtown are safe.