Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

#define rep(i, a, b) for (int i = a, i##end = b; i <= i##end; ++i)
#define per(i, a, b) for (int i = a, i##end = b; i >= i##end; --i)
#define rep0(i, a) for (int i = 0, i##end = a; i < i##end; ++i)
#define per0(i, a) for (int i = (int)a-1; ~i; --i)
#define max(a, b) ((a) > (b) ? (a) : (b))
#define min(a, b) ((a) < (b) ? (a) : (b))
#define chkmax(a, b) a = max(a, b)
#define chkmin(a, b) a = min(a, b)
#define x first
#define y second
#define enter putchar('\n')

typedef long long ll;
typedef double DB;

const DB eps = 1e-12;
const DB PI = acos(-1);

int sgn(DB x) { return fabs(x) < eps ? 0 : (x > 0 ? 1 : -1); }

struct Point {
	DB x, y;
	Point(DB x = 0, DB y = 0) : x(x), y(y) {}
	Point operator + (Point a) { return Point(x + a.x, y + a.y); }
	Point operator - (Point a) { return Point(x - a.x, y - a.y); }
	Point operator - () { return Point(-x, -y); }
	friend Point operator * (DB k, Point a) { return Point(k * a.x, k * a.y); }
	Point operator / (DB k) { return Point(x / k, y / k); }
	DB operator % (Point a) { return x * a.x + y * a.y; }
	DB operator / (Point a) { return x * a.y - y * a.x; }
	operator DB() { return sqrt(x*x + y*y); }
	bool operator < (const Point &a) const { int d1 = sgn(x-a.x), d2 = sgn(y-a.y); return d1 < 0 || (d1 == 0 && d2 < 0); }
};

struct Circle { Point P; DB r; };

Point Proj(Point P, Point P1, Point P2) {
	Point v = P2-P1; DB t = (P-P1)%v / (v%v);
	return P1 + t*v;
}

Point GetLineInter(Point P1, Point P2, Point Q1, Point Q2) {
	Point v = P2-P1, w = Q2-Q1; DB t = (Q1-P1)/w / (v/w);
	return P1 + t*v;
}

int Direct1(Point P, Point P1, Point P2) { return sgn((P1-P)%(P2-P)); }
int Direct2(Point P, Point P1, Point P2) { return sgn((P1-P)/(P2-P)); }

Point A, B, C;

Circle GetInnerCir(Point A, Point B, Point C) {
	Point v1 = B-A, v2 = C-A, v3 = C-B;
	v1 = v1/DB(v1), v2 = v2/DB(v2), v3 = v3/DB(v3);
	Point P = GetLineInter(A, A + (v1+v2), B, B + (v3-v1));
	return (Circle){P, DB(P-Proj(P, A, B))};
}

Circle GetOuterCir(Point A, Point B, Point C) {
	Point M = 0.5*(A+B), N = 0.5*(A+C), v = B-A, w = C-A;
	Point P = GetLineInter(M, M + Point(v.y, -v.x), N, N + Point(w.y, -w.x));
	return (Circle){P, DB(P-A)};
}

int main() {
	scanf("%lf%lf%lf%lf%lf%lf", &A.x, &A.y, &B.x, &B.y, &C.x, &C.y);
	Circle X = GetOuterCir(A, B, C);
	printf("%.10lf %.10lf %.10lf\n", X.P.x, X.P.y, X.r);
	return 0;
}