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<math.h>
#include<float.h>
#include<cstdio>
#include<vector>
using namespace std;
#define EPS (1e-10)
#define equals(a,b) fabs((a)-(b))<DBL_EPSILON*fmax(1,fmax(fabs(a),fabs(b)))
//点のクラス
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(Point p){return p.x*p.x+p.y*p.y;}
        double abs(Point p){return sqrt(norm(p));}    
        bool operator < (const Point &p)const{
            return x!=p.x?x<p.x:y<p.y;
        }
        bool operator == (const Point &p)const{
            return equals(x,p.x)&&equals(y,p.y);
        }
};
typedef Point Vector;
struct Segment{ Point p1,p2; };
typedef Segment Line;
double norm(Vector v){return v.x*v.x+v.y*v.y;} 
double abs(Vector v){return sqrt(norm(v));}    
//円
class Circle{
    public:
        Point c;
        double r;
        Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};
//多角形
typedef vector<Point> Polygon;
//内積
double dot(Vector a,Vector b){ return a.x*b.x+a.y*b.y; }
//外戚
double cross(Vector a,Vector b){ return a.x*b.y-a.y*b.x; }
//直交
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 equals(dot(s1.p1-s1.p2,s2.p1-s2.p2),0.0); }
//平行
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 equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0); }
//射影
Point project(Segment s,Point p){ //射影　p377
    Vector base=s.p2-s.p1;
    double r=dot(p-s.p1,base)/norm(base);
    return s.p1+base*r;
}
//反射　p379
Point reflect(Segment s,Point p){return p+(project(s,p)-p)*2.0;}
//ベクトルa,bの位置関係
int ccw(Point p0,Point p1,Point p2){
    Vector a=p1-p0;
    Vector b=p2-p0;
    if(cross(a,b)>EPS) return 1;//p0,p1,p2が反時計回り
    if(cross(a,b)<-EPS) return -1;//p0,p1,p2が時計回り
    if(dot(a,b)<-EPS) return 2;//p1,p0,p2の順で一直線
    if(norm(a)<norm(b)) return -2;//p0,p1,p2の順で一直線
    return 0; //p0,p2,p1の順で一直線
}
//交差判定　p389
bool intersect(Point p1,Point p2,Point p3,Point p4){
    return ( ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0&&
            ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);//p1,p2,p3,p4の順で一直線になるのを除く
}
bool intersect(Segment s1,Segment s2){
    return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}
//交点の座標　p392
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;
}
//距離p380
double getDistance(Point a,Point b){ return abs(a-b);} //点aと点b
double getDistanceLP(Line l,Point p){//直線lと点p
    return abs(cross(l.p2-l.p1,p-l.p1)/abs(l.p2-l.p1));
}
double getDistanceSP(Segment s,Point p){//線分sと点p
    if(dot(s.p2-s.p1,p-s.p1)<0.0)return abs(p-s.p1);
    if(dot(s.p1-s.p2,p-s.p2)<0.0)return abs(p-s.p2);
    return getDistanceLP(s,p);
}
double getDistance(Segment s1,Segment s2){ //線分s1と線分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)));
}
//円　交点
pair<Point,Point> getCrossPoints(Circle c,Line l){
    //asert(intersect(c,l));   交点を持つことの確認
    Vector pr =project(l,c.c);
    Vector e=(l.p2-l.p1)/abs(l.p2-l.p1);
    double base=sqrt(c.r*c.r-norm(pr-c.c));
    return make_pair(pr+e*base,pr-e*base);
}
//２つの円の交点
double arg(Vector p){ return atan2(p.y,p.x); }
Vector polar(double a,double r){ return Point(cos(r)*a,sin(r)*a);}
pair<Point,Point> getCrossPoints(Circle c1,Circle c2){
    //assert(intersect(c1,c2));
    double d=abs(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,t+a),c1.c+polar(c1.r,t-a));
}
int main(){ 
    Circle c1,c2;
    cin>>c1.c.x>>c1.c.y>>c1.r;
    cin>>c2.c.x>>c2.c.y>>c2.r;
    pair<Point,Point> pp;
    pp=getCrossPoints(c1,c2);
    if(pp.first.x>pp.second.x)
        swap(pp.first,pp.second);
    else if(pp.first.x==pp.second.x&&pp.first.y>pp.second.y)
        swap(pp.first,pp.second);

    printf("%.10f %.10f %.10f %.10f\n",pp.first.x,pp.first.y,pp.second.x,pp.second.y);    
    return 0;
}