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>
#define r(i,n) for(int i=0;i<n;i++)
using namespace std;
#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b))<EPS)
//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;
/////////////////////////////////////////
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);}

  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;
  }
};
struct Circle{
  Point c;
  double r;
};
typedef Point vect;
struct seg{Point p1,p2;};
//????????´????????????
double norm(Point p){return p.x*p.x+p.y*p.y;}
//??¶???????????????absolute  ?????????????????¶?????????
double abs(Point p){return sqrt(norm(p));}
//?????????????????????????????????
double dot(Point a,Point b){
  return a.x*b.x+a.y*b.y;
}
//?????? ????????????????????????
double cross(Point a,Point b){
  return a.x*b.y-a.y*b.x;
}
//??´?????????????????¨?????\?????????????????????
bool C90(seg s1,seg s2){
  return equals(dot(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}
//????????????????????¨?????\??????????????????????????????????????????
bool C0(seg s1,seg s2){
  return equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}
//?°???± ??????????????´???????????????
Point project(seg s,Point p){
  Point base = s.p2-s.p1;
  double r=dot(p-s.p1,base) / norm(base);
  return s.p1+base*r;
}
//????°??????????????????????
Point reflection(seg s,Point p){
  return  p+(project(s,p)-p)*2.0;
}
//2???????????¢   ???????????????
double getDistancePP(Point a,Point b){
  return abs(a-b);
}
//??´??????????????¢(????°?)???????????????
double getDistanceLP(seg l,Point p){
  return abs(cross(l.p2-l.p1,p-l.p1)/abs(l.p2-l.p1));
}
//?????????????????¢??????????????????
double getDistanceSP(seg s,Point 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);
}
//????¨?????????????????¨??????????????????????????????????
int CCW(Point p0,Point p1,Point p2){
  Point a=p1-p0;
  Point 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&&CCW(p3,p4,p1)*CCW(p3,p4,p2)<=0);
}
bool intersect(seg s1,seg s2){
  return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}
//2??????????§???¢?????\??????????????????...????????????????????????
bool squareintersect(seg s1,seg s2){
  if(s1.p2.x<s2.p1.x||s2.p2.x<s1.p1.x)return 0;
  if(s1.p2.y<s2.p1.y||s2.p2.y<s1.p1.y)return 0;
  return 1;
}
//??????????????¢?????????????????????????????§??¨???????????????
double getDistance(seg s1,seg 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(seg s1,seg s2){
  Point 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;
}
//???????£????????????¢??????????????¢??????????????????????????\????????????????????§???????????£???????????????????????????????????§?????????????????????
int intersectCC(Circle a,Circle b){
  double dist=abs(a.c-b.c);
  if(dist>a.r+b.r+EPS)return 4;
  if(dist>a.r+b.r-EPS)return 3;
  if(dist>abs(a.r-b.r)+EPS)return 2;
  if(dist>abs(a.r-b.r)-EPS)return 1;
  return 0;
}
//?????¨??´???????????????2?????? (LINE)
seg getCrossPoint(Circle c,seg l){
  //assert(intersect(cc,l));
  Point pr=project(l,c.c);
  Point e=(l.p2-l.p1)/abs(l.p2-l.p1);
  double base =sqrt(c.r*c.r-norm(pr-c.c));
  seg pp;pp.p1=(pr+e*base);pp.p2=(pr-e*base);
  return pp;
}
//?????¨??´??????Line??????????????°
int getCircleLine(Circle c,seg l){
  seg a=getCrossPoint(c,l);
  if(isnan(a.p1.x)&&isnan(a.p2.y))return 0;
  else if(a.p1.x==a.p2.x&&a.p1.y==a.p2.y)return 1;
  else return 2;
}
//??????
Point gaishin(Point a, Point b, Point c){
  double a1,a2,b1,b2,c1,c2;
  a1=2*(b.x-a.x);b1=2*(b.y-a.y);c1=a.x*a.x-b.x*b.x+a.y*a.y-b.y*b.y;
  a2=2*(c.x-a.x);b2=2*(c.y-a.y);c2=a.x*a.x-c.x*c.x+a.y*a.y-c.y*c.y;
  Point p;p.x=(b1*c2-b2*c1)/(a1*b2-a2*b1);p.y=(c1*a2-c2*a1)/(a1*b2-a2*b1);
  return p;
}
//2??????????????????
double arg(Point p){return atan2(p.y,p.x);}
Point polar(double a,double r){return Point(cos(r)*a,sin(r)*a);}
seg 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);
  seg s;s.p2=c1.c+polar(c1.r,t+a);s.p1=c1.c+polar(c1.r,t-a);
  return s;
}
//????´???°2D///////////A???)///////////
typedef complex<double> comp;
typedef vector<comp> cvec;
//????´???????
double dot(comp a,comp b){return real(b*conj(a));}
//????´???????
double cross(comp a,comp b){return imag(b*conj(a));}
double Area(cvec &a){
  double b=0;int n=a.size();
  for(int i=0;i<n;i++)
    b+=cross(a[i],a[(i+1==n?0:i+1)]);
  return abs(b/2.0);
}
////how to use(exp)/////////////////////
//  double a,b; cvec t; cin>>n;       //
// while(n--){                        //
//    cin>>a>>b;                      //
//    t.push_back(comp(a,b));         //
//  }printf("%.11f\n",Area(t));       //
////////////////////////////////////////
//    ???????????°??¨??????
seg scan(){seg a;scanf("%lf%lf%lf%lf",&a.p1.x,&a.p1.y,&a.p2.x,&a.p2.y);return a;}
void prin(seg a){printf("%.10f %.10f %.10f %.10f\n",a.p1.x,a.p1.y,a.p2.x,a.p2.y);}
//
/////------Library END-------//////////////////////////////////////
int main(){
  Circle c1,c2;
  cin>>c1.c.x>>c1.c.y>>c1.r;
  cin>>c2.c.x>>c2.c.y>>c2.r;
  seg a=getCrossPoints(c1,c2);
  if(intersectCC(c1,c2)!=3){if(a.p1.x>a.p2.x){
    Point t;
    t=a.p1;
    a.p1=a.p2;
    a.p2=t;
  }
  else if(a.p1.x==a.p2.x&&a.p1.y>a.p2.y){
    Point t;
    t=a.p1;
    a.p1=a.p2;
    a.p2=t;
  }
  prin(a);}
  else printf("%.10f %.10f %.10f %.10f\n",a.p1.x,a.p1.y,a.p1.x,a.p1.y);
}