p02307 Circumscribed Circle of a Triangle_28814
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
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)

1 -2
3 2
-2 0 0 3
4 0
0 0 1 -2
1 2
-2 0 0 3
4 -1
0 0 1 -2
1 2
-2 -1 1 3
4 -1
0 0 1 -3
1 2
-2 -1 2 3
4 -1
0 0 1 -3
1 2
-4 -1 3 3
4 -1
0 0 1 -3
1 3
-4 -1 1 3
4 -1
1 0 1 -6
1 3
-4 -1 1 3
4 0
1 0 1 -6
2 3
-4 -1 0 3
4 0
1 0 1 -6
2 1
-4 -1 0 3
4 0
1 1 1 -6
1 1
-4 -1 0 3
4 -1
1 0 1 -6
1 1
-2 -1 0 1
4 0
1 0 1 -10
1 1
-2 -1 1 1
4 0
1 0 1 -10
1 1
-2 -2 1 1
4 0
1 -1 1 -10
1 1
-3 -2 1 -13
1 1
-3 -2 1 -6
1 1
-3 -2 1 -12
1 1
-3 -2 1 -12
1 1
-1 -2 1 -12
1 1
-1 -3 1 -12
1 1
-1 0 1 -12
1 1
-2 0 1 -12
1 1
-2 -1 1 -12
1 1
-2 -2 1 -12
1 1
-4 -4 0 -12
1 1
-4 -4 2 -12
1 1
-4 -4 2 -12
0 1
-4 -4 4 -10
1 1
-4 -4 4 -10
1 1
-7 -4 4 -10
0 1
-7 -4 4 -10
2 1
-7 -4 4 -18
2 1
-7 -4 4 -18
2 0
-7 -4 7 -18
2 0
-7 -4 7 -18
2 0
-7 -7 7 -18
0 0
-7 -7 7 -18
0 0
-9 -7 7 -18
0 0
-9 -13 7 -2
0 0
-9 -13 7 -2
1 0
-9 -13 7 -3
1 0
-9 -13 7 -3
1 0
-9 -23 7 -3
1 0
-13 -23 7 -5
1 0
-9 -23 7 -1
1 0
-9 -23 7 -1
1 0
-9 -45 7 -1
1 0
-8 -45 7 -1
2 0
-8 -45 11 -1
2 0
-8 -45 11 -1
2 0
-4 -45 9 -1
2 0
-4 -45 9 -1
3 0
-4 -45 9 -1
5 0
-4 -45 9 -1
5 0
-4 -6 9 -2
5 0
-4 -6 9 -2
5 0
-4 -9 9 -2
5 0
-4 -1 9 -2
5 0
-6 -1 9 -4
5 0
-6 -1 9 -4
5 -1
-6 -1 9 -2
5 -1
-6 -1 9 -3
5 -1
-6 -1 9 -3
1 -1
-6 -1 9 -3
0 -1
-6 -1 8 -3
0 -1
-6 -1 8 -3
0 -2
-6 -1 8 -2
0 -2
-6 -1 8 -2
1 -2
-6 -1 8 -2
1 -1
-6 -1 1 -2
0 2
-2 0 0 3
4 0
0 1 1 3
4 -2
0 0 1 -2
0 2
-2 -1 1 0
4 -1
0 0 2 3
8 -1
0 0 1 -6
1 2
-4 -1 3 3
6 -1
0 0 1 3
4 -2
1 0 0 -7
1 3
-4 -1 1 3
4 0
2 0 2 -6
2 3
-4 -1 0 3
4 0
-1 1 1 -11
2 1
-4 -1 0 6
4 0
0 1 1 -2
1 2
-4 -1 0 3
4 -2
1 0 0 1
4 0
2 0 1 -4
1 1
-2 -1 1 1
2 0
1 0
0.62500000000000000000 0.68750000000000000000 2.71353666826155124291 2.00000000000000000000 1.50000000000000000000 2.50000000000000000000 0.166667 0.000000 2.166667 2.500000 1.500000 2.915476 -0.000000 0.000000 2.236068 2.346154 0.884615 2.507386 0.500000 -0.500000 2.549510 2.285714 0.642857 2.374396 -0.900000 -0.500000 3.140064 2.300000 0.700000 2.404163 -0.700000 0.000000 3.448188 3.166667 1.500000 2.635231 0.500000 -1.500000 4.527693 2.500000 1.500000 2.121320 0.600000 -1.400000 4.617359 2.500000 2.166667 2.635231 -0.250000 -2.250000 3.952847 3.500000 3.500000 3.535534 -0.500000 -2.500000 3.807887 3.500000 2.500000 3.535534 1.166667 -2.500000 3.503966 2.500000 2.500000 2.915476 2.500000 -4.500000 5.700877 2.500000 0.500000 1.581139 3.500000 -4.500000 6.041523 2.333333 -0.000000 1.666667 2.000000 -4.500000 5.590170 3.125000 -6.000000 7.315437 0.500000 -2.500000 3.535534 2.750000 -5.500000 6.731456 7.500000 -5.500000 9.192388 9.000000 -5.500000 10.307764 3.000000 -5.500000 6.800735 1.500000 -5.500000 6.519202 3.166667 -5.500000 6.851602 4.500000 -5.500000 7.382412 2.500000 -5.500000 6.670832 2.666667 -5.666667 6.871843 2.428571 -5.428571 6.585389 2.677419 -5.241935 6.791931 1.714286 -4.714286 5.758756 -0.597087 -5.344660 6.542584 -0.664948 -5.469072 6.503157 -0.481651 -5.133028 6.616088 1.477901 -8.660221 9.674319 0.723529 -9.252941 9.340573 1.038462 -9.961538 10.007837 2.261421 -9.621827 9.625378 2.420000 -9.420000 9.725883 0.642180 -10.111374 10.131747 0.689723 -10.092885 10.116425 0.866972 -10.215596 10.252319 0.908163 -10.275510 10.275921 -0.027778 -9.555556 9.610670 -1.535714 -12.571429 12.824612 -2.166667 -13.833333 14.191155 -3.632979 -11.659574 12.546321 1.750000 -14.000000 14.020075 0.178571 -23.428571 23.442967 0.209677 -23.241935 23.255369 -0.031915 -23.159574 23.248539 3.885542 -24.030120 24.103982 3.981752 -23.164234 23.248851 2.294393 -22.939252 22.941141 2.261733 -22.929603 22.941485 1.452381 -22.690476 22.966134 4.772727 -9.409091 9.411835 3.642857 -7.714286 7.832754 3.666667 -7.666667 7.781745 1.727273 -11.545455 12.000344 0.692308 -13.615385 14.280578 0.250000 -8.750000 9.956154 -0.500000 -12.500000 12.747549 -0.500000 -31.500000 30.991934 -0.500000 -17.000000 16.918924 -2.500000 -32.000000 31.196955 -3.000000 -35.750000 34.879256 -3.000000 -30.000000 29.154759 25.500000 169.500000 173.385409 4.000000 40.500000 42.687820 4.500000 47.500000 49.623583 -2.500000 -50.500000 49.623583 0.100000 -0.100000 2.102380 2.375000 2.000000 2.576941 2.857143 0.714286 2.945075 -0.045455 -0.136364 2.136847 0.500000 -6.500000 6.519202 4.000000 -0.500000 4.031129 -0.000000 -2.000000 4.123106 3.071429 -0.071429 3.072259 4.166667 1.500000 3.503966 0.934783 -2.043478 5.043900 3.000000 2.000000 2.236068 0.666667 -1.500000 4.693376 1.590909 0.954545 2.591308 0.642857 -4.928571 6.081924 2.750000 3.500000 3.716517 -1.200000 0.000000 2.973214 5.214286 3.071429 5.214775 3.000000 4.500000 4.609772 0.500000 -1.500000 2.549510 1.500000 0.500000 0.707107