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:
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cassert>

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

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;

class Point {
public:
	double x, y;
	Point(double x = 0, double y = 0) : x(x), y(y) {}

	Point operator + (Point p) { return Point(x + p.x, y + p.y); }
	Point operator - (Point p) { return Point(x - p.x, y - p.y); }
	Point operator * (double a) { return Point(a*x, a*y); }
	Point operator / (double a) { return Point(x / a, y / a); }

	double norm() { return x*x + y*y; }
	double abs() { return sqrt(norm()); }

	bool operator < (const Point &p) const {
		return x != p.x ? x < p.x : y < p.y;
	}

	bool operator == (const Point &p) const {
		return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
	}
};

typedef Point Vector;

struct Segment {
	Point p1, p2;
	Segment() {}
};

typedef Segment Line;

class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
};


double norm(Vector a) {
	return a.norm();
}

double abs(Vector a) {
	return a.abs();
}

double dot(Vector a, Vector b) {
	return a.x*b.x + a.y*b.y;
}

double cross(Vector a, Vector b) {
	return a.x*b.y - a.y*b.x;
}

bool isOrthogonal(Vector a, Vector b) {
	return equals(dot(a, b), 0.0);
}

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
	return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
	return isOrthogonal(s1.p1, s1.p2, s2.p1, s2.p2);
}

bool isParallel(Vector a, Vector b) {
	return equals(cross(a, b), 0.0);
}

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
	return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(Segment s1, Segment s2) {
	return isParallel(s1.p1, s1.p2, s2.p1, s2.p2);
}

Point project(Segment s, Point p) {
	double alpha = dot(p - s.p2, s.p1 - s.p2) / (s.p1 - s.p2).norm();
	return s.p2 + (s.p1 - s.p2)*alpha;
}

Point reflect(Segment s, Point p) {
	return project(s, p)*2.0 - p;
}

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 (a.norm() < b.norm()) return ONLINE_FRONT;
	return ON_SEGMENT;
}

bool intersect(Point p1, Point p2, Point p3, Point p4) {
	int p1p2p3, p1p2p4, p3p4p1, p3p4p2;
	p1p2p3 = ccw(p1, p2, p3);
	p1p2p4 = ccw(p1, p2, p4);
	p3p4p1 = ccw(p3, p4, p1);
	p3p4p2 = ccw(p3, p4, p2);

	if (p1p2p3 == ON_SEGMENT) return true;
	if (p1p2p4 == ON_SEGMENT) return true;
	if (p3p4p1 == ON_SEGMENT) return true;
	if (p3p4p2 == ON_SEGMENT) return true;
	if (p1p2p3 == ONLINE_FRONT && p1p2p4 == ONLINE_BACK) return true;
	if (p1p2p3 == ONLINE_BACK && p1p2p4 == ONLINE_FRONT) return true;
	if (p1p2p3 == COUNTER_CLOCKWISE && p1p2p4 == CLOCKWISE && p3p4p1 == CLOCKWISE && p3p4p2 == COUNTER_CLOCKWISE) return true;
	if (p1p2p3 == CLOCKWISE && p1p2p4 == COUNTER_CLOCKWISE && p3p4p1 == COUNTER_CLOCKWISE && p3p4p2 == CLOCKWISE) return true;
	return false;
}

bool intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

bool intersect(Circle c, Line l) {
	return (project(l, c.c) - c.c).norm() <= c.r*c.r;
}

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

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

double getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();
	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));
	double t = d1 / (d1 + d2);
	return s1.p1 + (s1.p2 - s1.p1)*t;

}

pair<Point, Point> getCrossPoints(Circle c, Line l) {
	assert(intersect(c, l));
	Vector pr = project(l, c.c);
	Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
	double base = sqrt(c.r*c.r - (pr - c.c).norm());
	return make_pair(pr + e*base, pr - e*base);
}

Vector rotate90(Vector v) {
	Vector w;
	w.x = -v.y; w.y = v.x;
	return w;
}

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
	Vector v = c1.c - c2.c;
	Vector w = rotate90(v);
	double d = v.abs();
	double x = 0.5*(c2.r*c2.r - c1.r*c1.r + d*d) / d;
	double y = sqrt(c2.r*c2.r - x*x);
	Vector v1, v2;
	v1 = c2.c + v*(x / d);
	v2 = w*(y / w.abs());
	return make_pair(v1 + v2, v1 - v2);
}

int main() {
	Circle C1, C2;
	double cx, cy, r;
	cin >> cx >> cy >> r;
	C1.c.x = cx; C1.c.y = cy; C1.r = r;
	cin >> cx >> cy >> r;
	C2.c.x = cx; C2.c.y = cy; C2.r = r;

	pair<Point, Point> crossPoints;

	crossPoints = getCrossPoints(C1, C2);
	double x1 = crossPoints.first.x;
	double y1 = crossPoints.first.y;
	double x2 = crossPoints.second.x;
	double y2 = crossPoints.second.y;

	cout << fixed << setprecision(15);

	if (x1 < x2) {
		cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
	}
	else if (x1 > x2) {
		cout << x2 << " " << y2 << " " << x1 << " " << y1 << endl;
	}
	else {
		if (y1 < y2) {
			cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
		}
		else if (y1 > y2) {
			cout << x2 << " " << y2 << " " << x1 << " " << y1 << endl;
		}
		else {
			cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
		}
	}

	return 0;
}