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)
//点を表す構造体
class Point {
  public:
  double x,y;
  Point(double x=0,double y=0): x(x),y(y){}

  //各種演算
  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 abs() { return sqrt(norm()); }
  double norm() { return x*x+y*y; }

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

  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;
  }
};

//ベクトルを表す構造体
typedef Point Vector;

//線分を表す構造体
struct Segment{
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  Point p1,p2;
};

//直線を表す構造体
typedef Segment Line;

//円を表すクラス
class Circle{
  public:
  //円の中心
  Point c;
  //半径
  double r;
  Circle(Point c=Point(),double r=0.0): c(c),r(r) {}
};

//多角形の表現
typedef vector<Point> Polygon;

//ベクトルaとbの内積
double dot(Vector a,Vector b){
  return a.x*b.x+a.y*b.y;
}

//ベクトルaとbの外積
double cross(Vector a,Vector b){
  return a.x*b.y-a.y*b.x;
}

//ベクトルaとbの直交判定
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.p2-s1.p1,s2.p2-s2.p1),0.0);
}

//ベクトルaとbの平行判定
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);
}

//線分sに対する点pの射影
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;
}

//線分sを対称軸とした点pの線対称の点
Point reflect(Segment s,Point p){
  return p+(project(s,p)-p)*2.0;
}


//反時計回りCCW
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;
//反時計回りCCW
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;
}

//線分p1p2と線分p3p4の交差判定
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);
}


//点aと点bの距離
double getDistace(Point a,Point b){
  return (a-b).abs();
}
//直線lと点pの距離
double getDistaceLP(Line l,Point p){
  return abs(cross(l.p2-l.p1,p-l.p1)/(l.p2-l.p1).abs());
} 
//線分sと点pの距離
double getDistaceSP(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 getDistaceLP(s,p);
}
//線分s1と線分s2の距離
double getDistace(Segment s1,Segment s2){
  if(intersect(s1,s2)) return 0.0;
  return min(min(getDistaceSP(s1,s2.p1),getDistaceSP(s1,s2.p2))
  ,min(getDistaceSP(s2,s1.p1),getDistaceSP(s2,s1.p2)));
}

//線分s1と線分s2の交点
Point getCrossPoint(Segment s1,Segment s2){
  Vector base=s1.p2-s1.p1;
  double d1=abs(cross(base,s2.p2-s2.p1));
  double d2=abs(cross(base,s1.p2-s2.p1));
  if(equals(fabs(d1),0.0) && equals(fabs(d2),0.0)) return s2.p1;
  return s2.p1+(s2.p2-s2.p1)*d2/d1;
}

//円cと線分lの交点
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);
}

//円と円の交点
double arg(Vector p) { return atan2(p.y,p.x); }
Vector polar(double a,double r) {return Point(cos(r)*a,sin(r)*a); }
//円c1と円c2の交点
pair<Point,Point> getCrossPoints(Circle c1,Circle 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(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  int c1x,c1y,c1r,c2x,c2y,c2r;
  cin>>c1x>>c1y>>c1r>>c2x>>c2y>>c2r;
  Circle c1(Point(c1x,c1y),c1r),c2(Point(c2x,c2y),c2r);
  auto p=getCrossPoints(c1,c2);
  Point p2,p3;
  tie(p2,p3)=p;
  if(p2>p3){
    swap(p2,p3);
  }
  cout<<fixed<<setprecision(15)<<p2.x<<' '<<p2.y<<' '<<p3.x<<' '<<p3.y<<'\n';
  return(0);
}