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 <cstring>
#include <string>
#include <vector>
#include <algorithm>
#include <tuple>
#include <queue>
#include <set>
#include <cstdio>
#include <climits>
#include <cmath>
#include <array>
#include <functional>
#include <sstream>
#include <list>
#include <iomanip>
#include <set>
const int MOD=1000000007;
const int INF=1000000000;
using namespace std;
typedef long long ll;
typedef vector<int> vi;
const double eps=1e-10;
const int inf=1e9;
typedef pair<int,int> P;
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,double y): 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 * (double k)
  {
    return Point(x*k,y*k);
  }
  Point operator / (double k)
  {
    return Point(x/k,y/k);
  }
  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;
  }
  double abs(){return sqrt(norm());}
  double norm(){return x*x+y*y;}
};
typedef Point Vector;
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;
}
double norm(Point a)
{
  return a.x*a.x + a.y*a.y;
}
double abs(Vector a)
{
  return sqrt(norm(a));
}
struct Segment
{
  Point p1,p2;
  Segment(Point p1,Point p2): p1(p1),p2(p2){}
};
typedef Segment Line;

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

typedef vector<Point> Polygon;


bool isorthogonal(Vector a,Vector b)
{
  return fabs(dot(a,b)-0.0)<eps;
}

bool isparallel(Vector a,Vector b)
{
  return fabs(cross(a,b)-0.0)<eps;
}
Point project(Segment s,Point p)
{
  Vector base=s.p2-s.p1;
  double r=dot(p-s.p1,base) / norm(base);
  return  s.p1 + base*r;
}
Point reflect(Segment s,Point p)
{
  return p+ (project(s,p)-p)*2.0;
}
double getdistance(Point a,Point b)
{
  return abs(a-b);
}
double getdistanceLP(Line l,Point p)
{
  return abs(cross(l.p2-l.p1,p-l.p1) / abs(l.p2-l.p1));
}
double getdistanceSP(Segment 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)
{
  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)
{
  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);
}
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;
}

double getdistanceSS(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)));
}

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 - norm(pr-c.c));
  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(cos(r)*a,sin(r)*a);}
pair <Point,Point> getcrosspoints(Circle c1,Circle 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(int argc,char const* argv[])
{
  double cx0,cy0,r0,cx1,cy1,r1;
  cin >> cx0 >> cy0 >> r0;
  Point mid0=Point(cx0,cy0);
  Circle c0=Circle(mid0,r0);
  cin >> cx1 >> cy1 >> r1;
  Point mid1=Point(cx1,cy1);
  Circle c1=Circle(mid1,r1);
  pair<Point,Point> ans=getcrosspoints(c0,c1);
  if(ans.second<ans.first)
    {
      cout << fixed << setprecision(12) << ans.second.x << ' ' << ans.second.y << ' ' << ans.first.x << ' ' << ans.first.y << endl;
    }
  else
    {
      cout << fixed << setprecision(12) << ans.first.x << ' ' << ans.first.y << ' ' << ans.second.x << ' ' << ans.second.y << endl;
    }
}