Circumscribed Circle of a Triangle

Write a program which prints the central coordinate ($cx$,$cy$) and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) on the plane surface.

Input

The input is given in the following format

$x_1$ $y_1$
$x_2$ $y_2$
$x_3$ $y_3$

All the input are integers.

Constraints

• $-10000 \leq x_i, y_i \leq 10000$
• The three points are not on the same straight line

Output

Print $cx$, $cy$ and $r$ separated by a single space in a line. The output val ues should be in a decimal fraction with an error less than 0.000001.

Sample Input 1

1 -2
3 2
-2 0

Sample Output 1

0.62500000000000000000 0.68750000000000000000 2.71353666826155124291

Sample Input 2

0 3
4 0
0 0

Sample Output 2

2.00000000000000000000 1.50000000000000000000 2.50000000000000000000

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