Problem: For given two circles $c1$ and $c2$, print the coordinates of the cross points of them.

Constraints

* The given circle have at least one cross point and have different center coordinates.
* $-10,000 \leq c1x, c1y, c2x, c2y \leq 10,000$
* $1 \leq c1r, c2r \leq 10,000$

Input

The input is given in the following format.

$c1x\; c1y\; c1r$
$c2x\; c2y\; c2r$


$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle. $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle. All input values are given in integers.

Output

Print the coordinates ($x1$, $y1$) and ($x2$, $y2$) of the cross points $p1$ and $p2$ respectively in the following rules.

* If there is one cross point, print two coordinates with the same values.
* Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.



The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

0 0 2
2 0 2


Output

1.00000000 -1.73205080 1.00000000 1.73205080


Input

0 0 2
0 3 1


Output

0.00000000 2.00000000 0.00000000 2.00000000

Solution (in CPP):

Solution:
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
using namespace std;
//using ll=long long;
const double EPS = 1e-10;
inline bool equals(double a, double b) { return fabs(a - b) < EPS; }
const double PI = 3.141592653589793238;
class Point {
public:
	double x, y;
	Point(double x, double y) :x(x), y(y) {}
	Point() {}
	Point operator +(const Point &p) const{ return Point(x + p.x, y + p.y); };
	Point operator -(const Point &p) const{ return Point(x - p.x, y - p.y); }
	Point operator *(double k) { return Point(x*k, y*k); }
	Point operator /(double k) { return Point(x / k, y / k); }
	void show() { printf("%.10lf %.10lf", x, y); }
};

using Vector = Point;
inline double norm(Vector a) {
	return a.x*a.x + a.y*a.y;
}
double absv(Vector a) {
	return sqrt(norm(a));
}
inline double dot(Vector a, Vector b) {
	return a.x*b.x + a.y*b.y;
}
inline double cross(Vector a, Vector b) {
	return a.x*b.y - a.y*b.x;
}
struct Segment {
	Point p1, p2;
};

using Line = Segment;
class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) :c(c), r(r) {}
};
using Polygon = vector<Point>; 
Point project(Segment s, Point p) {
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / norm(base);
	return s.p1 + base*r;
}
Point reflect(Segment s, Point p) {
	return p + (project(s, p) - p)*2.0;
}
double getDistanceLP(Line, Point);
double getDistance(Point, Point);
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

int ccw(Point p0, Point p1, Point p2) {
	Vector a = p1 - p0;
	Vector b = p2 - p0;
	if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
	if (cross(a, b) < -EPS) return CLOCKWISE;
	if (dot(a, b) < -EPS) return ONLINE_BACK;
	if (norm(a) < norm(b)) return ONLINE_FRONT;
	return ON_SEGMENT;
}
bool intersect(Point p1, Point p2, Point p3, Point p4) {
	return (ccw(p1, p2, p3)*ccw(p1, p2, p4) <= 0 and ccw(p3, p4, p1)*ccw(p3, p4, p2) <= 0);
}

bool intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
bool intersect(Circle c1, Circle c2) {
	return c1.r + c2.r >= getDistance(c1.c, c2.c);
}

bool intersect(Circle c, Line l) {
	double d = getDistanceLP(l, c.c);
	return d <= c.r;
}

double getDistance(Point a, Point b) {
	return absv(a - b);
}

double getDistanceLP(Line l, Point p) {
	return abs(cross(l.p2 - l.p1, p - l.p1) / absv(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return absv(p - s.p1);
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return absv(p - s.p2);
	return getDistanceLP(s, p);
}

double getDistance(Segment s1,Segment s2){
	if (intersect(s1, s2)) return 0.0;
	return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)), min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPoint(Segment s1, Segment s2) {
	Vector base = s2.p2 - s2.p1;
	double d1 = abs(cross(base, s1.p1 - s2.p1));
	double d2 = abs(cross(base, s1.p2 - s2.p1));
	return s1.p1 + (s1.p2 - s1.p1)*(d1 / (d1 + d2));
}
pair<Point, Point> getCrossPoints(Circle c, Line l) {
	assert(intersect(c, l));
	Point pr = project(l, c.c);
	Vector lv = l.p2 - l.p1;
	Vector le = lv / absv(lv);
	double base = sqrt(c.r*c.r - norm(c.c - pr));
	return make_pair(pr + le*base, pr - le*base);
}
double arg(Vector p) {
	return atan2(p.y, p.x);
}
Vector polar(double a, double r) {
	return Point(a * cos(r), a * sin(r));
}

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
	assert(intersect(c1, c2));
	double d = getDistance(c1.c, c2.c);
	double a = acos((c1.r*c1.r + d*d - c2.r*c2.r) / (2 * c1.r*d));
	double t = arg(c2.c - c1.c);
	return make_pair(c1.c + polar(c1.r, a + t), c1.c + polar(c1.r, t - a));
}

int main() {
	int cx, cy, r;
	cin >> cx >> cy >> r;
	Circle c1 = Circle(Point(cx, cy), r);
	cin >> cx >> cy >> r;
	Circle c2 = Circle(Point(cx, cy), r);
	pair<Point, Point> ans = getCrossPoints(c1,c2);
		if (ans.first.x < ans.second.x) {
			ans.first.show();
			cout << " ";
			ans.second.show();
			cout << endl;
		}
		else {
			if (equals(ans.first.x - ans.second.x, 0.0)) {
				if (ans.first.y < ans.second.y) {
					ans.first.show();
					cout << " ";
					ans.second.show();
					cout << endl;
				}
				else {
					ans.second.show();
					cout << " ";
					ans.first.show();
					cout << endl;
				}
			}
			else {
				ans.second.show();
				cout << " ";
				ans.first.show();
				cout << endl;
			}
		}
}