Pandemic Restrictions

Description:

Input:

The first line contains the two integers $$$x_1, y_1$$$ ($$$-10^4 \le x_1, y_1 \le 10^4$$$) — the coordinates of the house of your friend Fabio.

The second line contains the two integers $$$x_2, y_2$$$ ($$$-10^4 \le x_2, y_2 \le 10^4$$$) — the coordinates of the house of your friend Flavio.

The third line contains the two integers $$$x_3, y_3$$$ ($$$-10^4 \le x_3, y_3 \le 10^4$$$) — the coordinates of the house of your friend Francesco.

It is guaranteed that your three friends live in different places (i.e., the three points $$$(x_1, y_1)$$$, $$$(x_2, y_2)$$$, $$$(x_3, y_3)$$$ are guaranteed to be distinct).

Output:

Print the minimum value of $$$r$$$ which allows you to find a residence place satisfying the above conditions. Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-4}$$$.

Formally, let your answer be $$$a$$$, and the jury's answer be $$$b$$$. Your answer is accepted if and only if $$$\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-4}$$$.

Sample Input:

0 0
5 0
3 3

Sample Output:

5.0686143166

Sample Input:

-1 0
0 0
1 0

Sample Output:

2.0000000000

Note:

In the first sample, Fabio, Flavio and Francesco live at the points with coordinates $$$(0,0)$$$, $$$(5,0)$$$ and $$$(3,3)$$$ respectively. The optimal place of residence, represented by a green house in the picture below, is at the point with coordinates $$$(2.3842..., 0.4151...)$$$.

For instance, it is possible for you to meet Flavio and Francesco at the point depicted below, so that the sum of the lengths travelled by the three attendees is at most (and in fact equal to) $$$r=5.0686...$$$.

In the second sample, any point on the segment $$$\{(x,0):\ -1 \leq x \leq 1 \}$$$ is an optimal place of residence.