CF1886B.Fear of the Dark

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

Monocarp 尝试从公司回家。他当前位于二维平面上的点 $O = (0, 0)$；他的家位于点 $P = (P_x, P_y)$。

不幸的是，此时已近深夜，四周一片漆黑。Monocarp 害怕黑暗，因此希望沿着一条被光源完全照亮的路径回家。

幸运的是，存在两盏灯笼，分别位于点 $A = (A_x, A_y)$ 和 $B = (B_x, B_y)$。你可以选择任意一个非负实数 $w$，并将两盏灯笼的功率均设为 $w$。若一盏灯笼的功率设为 $w$，则它会照亮以该灯笼位置为中心、半径为 $w$ 的圆形区域（包含圆周边界）。

你需要确定最小的非负值 $w$，使得存在一条从点 $O$ 到点 $P$ 的、全程均被照亮的路径。你可以假设灯笼不会妨碍 Monocarp 的移动。

前两个测试用例的示意图

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.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$），表示测试用例的数量。

每个测试用例由三行组成：

• 第一行包含两个整数 $P_x$ 和 $P_y$（$-10^3 \le P_x, P_y \le 10^3$），表示 Monocarp 家的位置；
• 第二行包含两个整数 $A_x$ 和 $A_y$（$-10^3 \le A_x, A_y \le 10^3$），表示第一盏灯笼的位置；
• 第三行包含两个整数 $B_x$ 和 $B_y$（$-10^3 \le B_x, B_y \le 10^3$），表示第二盏灯笼的位置。

输入的附加约束：

• 在每个测试用例中，点 $O$、$P$、$A$ 和 $B$ 互不相同。

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 $\dfrac{|a - b|}{\max(1, b)} \le 10^{-6}$.

对于每个测试用例，在单独一行中输出答案——即满足存在一条从点 $O$ 到点 $P$ 的完全被照亮路径的最小 $w$ 值（一个实数）。

若你的答案的绝对误差或相对误差不超过 $10^{-6}$，则该答案视为正确。形式化地说，若你的答案为 $a$，评测机的标准答案为 $b$，则当 $\dfrac{|a - b|}{\max(1, b)} \le 10^{-6}$ 时，你的答案将被接受。