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

Source: aizu | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
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))
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)