Description:
Monocarp tries to get home from work. He is currently at the point $$$O = (0, 0)$$$ of a two-dimensional plane; his house is at the point $$$P = (P_x, P_y)$$$.
Unfortunately, it is late in the evening, so it is very dark. Monocarp is afraid of the darkness. He would like to go home along a path illuminated by something.
Thankfully, there are two lanterns, located in the points $$$A = (A_x, A_y)$$$ and $$$B = (B_x, B_y)$$$. You can choose any non-negative number $$$w$$$ and set the power of both lanterns to $$$w$$$. If a lantern's power is set to $$$w$$$, it illuminates a circle of radius $$$w$$$ centered at the lantern location (including the borders of the circle).
You have to choose the minimum non-negative value $$$w$$$ for the power of the lanterns in such a way that there is a path from the point $$$O$$$ to the point $$$P$$$ which is completely illuminated. You may assume that the lanterns don't interfere with Monocarp's movement.
The picture for the first two test cases
Input Format:
The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
Each test case consists of three lines:
- the first line contains two integers $$$P_x$$$ and $$$P_y$$$ ($$$-10^3 \le P_x, P_y \le 10^3$$$) — the location of Monocarp's house;
- the second line contains two integers $$$A_x$$$ and $$$A_y$$$ ($$$-10^3 \le A_x, A_y \le 10^3$$$) — the location of the first lantern;
- the third line contains two integers $$$B_x$$$ and $$$B_y$$$ ($$$-10^3 \le B_x, B_y \le 10^3$$$) — the location of the second lantern.
Additional constraint on the input:
- in each test case, the points $$$O$$$, $$$P$$$, $$$A$$$ and $$$B$$$ are different from each other.
Output Format:
For each test case, print the answer on a separate line — one real number equal to the minimum value of $$$w$$$ such that there is a completely illuminated path from the point $$$O$$$ to the point $$$P$$$.
Your answer will be considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$ — formally, if your answer is $$$a$$$, and the jury's answer is $$$b$$$, your answer will be accepted if $$$\dfrac{|a - b|}{\max(1, b)} \le 10^{-6}$$$.
Note:
None