p02307 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.

Constraints

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

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.

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.

Examples

Input

1 -2
3 2
-2 0


Output

0.62500000000000000000 0.68750000000000000000 2.71353666826155124291


Input

0 3
4 0
0 0


Output

2.00000000000000000000 1.50000000000000000000 2.50000000000000000000
```python
from decimal import Decimal

x1, y1 = map(str, input().split())
x2, y2 = map(str, input().split())
x3, y3 = map(str, input().split())
x1, y1 = Decimal(x1), Decimal(y1)
x2, y2 = Decimal(x2), Decimal(y2)
x3, y3 = Decimal(x3), Decimal(y3)

#3辺の長さ
a = (((x1-x2)**Decimal('2'))+((y1-y2)**Decimal('2')))**Decimal('0.5')
b = (((x3-x2)**Decimal('2'))+((y3-y2)**Decimal('2')))**Decimal('0.5')
c = (((x1-x3)**Decimal('2'))+((y1-y3)**Decimal('2')))**Decimal('0.5')
s = ((a+b+c)/Decimal('2'))

r = (a*b*c)/(((s*(s-a)*(s-b)*(s-c))**Decimal('0.5'))*Decimal('4'))
xa, ya = (x1+x2)/2, (y1+y2)/2
xb, yb = (x3+x2)/2, (y3+y2)/2

if (y3-y2) != 0 and (y2-y1) != 0:
    a1, b1 = -(x3-x2)/(y3-y2), ((x3-x2)*xb+(y3-y2)*yb)/(y3-y2)
    a2, b2 = -(x2-x1)/(y2-y1), ((x2-x1)*xa+(y2-y1)*ya)/(y2-y1)
    cx = (b2-b1)/(a1-a2)
    cy = a1 * cx + b1

if y3-y2 == 0:
    cx = xb
    a2, b2 = -(x2-x1)/(y2-y1), ((x2-x1)*xa+(y2-y1)*ya)/(y2-y1)
    cy = a2 * cx + b2

if y2-y1 == 0:
    cx = xa
    a1, b1 = -(x3-x2)/(y3-y2), ((x3-x2)*xb+(y3-y2)*yb)/(y3-y2)
    cy = a1 * cx + b1

print(cx, cy, r)

```