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 <bits/stdc++.h>
using namespace std;

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

class Point{
    public:
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
    Point operator+(const Point &p){
        return Point(x+p.x,y+p.y);
    }
    Point operator-(const Point &p){
        return Point(x-p.x,y-p.y);
    }
    Point operator*(const double &a){
        return Point(a*x,a*y);
    }
    Point operator/(const double &a){
        return Point(x/a,y/a);
    }
    double abs(){
        return sqrt(norm());
    }
    double norm(){
        return x*x+y*y;
    }
    bool operator<(const Point &p){
        return x!=p.x?x<p.x:y<p.y;
    }
    bool operator==(const Point &p){
        return fabs(x-p.x)<EPS&&fabs(y-p.y)<EPS;
    }
};
typedef Point Vector;
struct Segment{
    Point p1,p2;
    Segment(){}
    Segment(Point p1,Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;

class Circle{
    public:
    Point c;
    double r;
    Circle(Point c=Point(),double r=0):c(c),r(r){}
};

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(Segment s1,Segment s2){
    return equals(dot(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

bool isParallel(Segment s1,Segment s2){
    return equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

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

Point reflect(Segment s,Point p){
    return p+(project(s,p)-p)*2;
}

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){
        return (p-s.p1).abs();
    }
    if(dot(s.p1-s.p2,p-s.p2)<0){
        return (p-s.p2).abs();
    }
    return getDistanceLP(s,p);
}

int ccw(Point p0,Point p1,Point p2){
    Vector a=p1-p0;
    Vector b=p2-p0;
    if(cross(a,b)>EPS) return 1;
    if(cross(a,b)<-EPS) return -1;
    if(dot(a,b)<-EPS) return 2;
    if(a.norm()<b.norm()) return -2;
    return 0;
}

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);
}

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

double getDistance(Segment s1,Segment s2){
    if(intersect(s1,s2)) return 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;
}

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

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

bool intersect(Circle c1,Circle c2){
    int x=(c1.c-c2.c).abs();
    return (abs(c1.r-c2.r)<=x&&x<=(c1.r+c2.r));
}

pair<Point,Point> getCrossPoints(Circle c1,Circle c2){
    assert(intersect(c1,c2));
    double d=(c1.c-c2.c).abs();
    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(){
    double c1x,c1y,c1r,c2x,c2y,c2r;
    cin>>c1x>>c1y>>c1r>>c2x>>c2y>>c2r;
    Point c1(c1x,c1y),c2(c2x,c2y);
    Circle cc1(c1,c1r),cc2(c2,c2r);
    auto points=getCrossPoints(cc1,cc2);
    if(points.first<points.second){
        printf("%.7lf %.7lf %.7lf %.7lf\n",
            points.first.x,points.first.y,
            points.second.x,points.second.y);
    }
    else{
        printf("%.7lf %.7lf %.7lf %.7lf\n",
            points.second.x,points.second.y,
            points.first.x,points.first.y);
    }
}