Problem: Find common tangent lines of two circles $c1$ and $c2$.

Constraints

* $-1,000 \leq c1x, c1y, c2x, c2y \leq 1,000$
* $1 \leq c1r, c2r \leq 1,000$
* $c1$ and $c2$ are different

Input

Center coordinates ($cix$, $ciy$) and radii $cir$ of two circles $c1$ are $c2$ are given in the following format.

$c1x \; c1y \; c1r$
$c2x \; c2y \; c2r$

All input values are given in integers.

Output

Print coordinates of the tangent points on circle $c1$ based on the following rules.

* 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 0.00001.

Examples

Input

1 1 1
6 2 2


Output

0.6153846154 1.9230769231
1.0000000000 0.0000000000
1.4183420913 1.9082895434
1.7355040625 0.3224796874


Input

1 2 1
4 2 2


Output

0.6666666667 1.0571909584
0.6666666667 2.9428090416
2.0000000000 2.0000000000


Input

1 2 1
3 2 2


Output

0.5000000000 1.1339745962
0.5000000000 2.8660254038


Input

0 0 1
1 0 2


Output

-1.0000000000 0.0000000000


Input

0 0 1
0 0 2


Output

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define f first
#define s second
#define mp make_pair
#define pi M_PI
#define inf 1<<30
#define eps (1e-11)
#define equals(a,b) (fabs((a)-(b))<eps)
using namespace std;

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 k){ return Point(x*k,y*k);}
  Point operator/(double k){ return Point(x/k,y/k);}
  bool operator<(Point p)const{ return (!equals(x,p.x) ? x<p.x : y<p.y);}
  bool operator==(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;
typedef vector<Point> Polygon;

class Segment{
public:
  Point p1,p2;
  Segment(Point p1=Point(),Point p2=Point()):p1(p1),p2(p2){}
};
typedef Segment Line;

class Circle{
public:
  Point c;
  double r;
  Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};

double norm(Vector a){ return (a.x*a.x+a.y*a.y);}
double abs(Vector a){ return sqrt(norm(a));}

// base????????????a???r?????????counter_clock_wise????????¢
Point rotate(Point base,Point a,double r){
  Point b=a-base;
  a.x=b.x*cos((r/180)*M_PI)-b.y*sin((r/180)*M_PI);
  a.y=b.x*sin((r/180)*M_PI)+b.y*cos((r/180)*M_PI);
  a=a+base;
  return a;
}

// ??¢???????????? return 4
// ?????\?????? return 3
// ????????? return 2
// ?????\?????? return 1
// ?????? return 0
int intersect(Circle a,Circle b){
  double dis=abs(a.c-b.c),sumr=a.r+b.r,minr=min(a.r,b.r),maxr=max(a.r,b.r);
  if((sumr-dis)<-eps)return 4;
  if(equals(sumr,dis))return 3;
  if((maxr-(dis+minr))<-eps)return 2;
  if(equals(dis+minr,maxr))return 1;
  return 0;
}

vector<Line> getCommonTangent(Circle a,Circle b){
  vector<Line> vp;
  int intersection=intersect(a,b);
  if(intersection==0)return vp;
  if(intersection==1){
    Vector v=b.c-a.c;
    if(b.r<a.r)v=(v*a.r)/abs(v);
    else v=(v*a.r*(-1))/abs(v);
    vp.push_back(Line(a.c+v,a.c+v));
    return vp;
  }
  if(intersection==3){
    Vector v=b.c-a.c;
    v=v*a.r/abs(v);
    vp.push_back(Line(a.c+v,a.c+v));
  }
  double d=abs(b.c-a.c),c,s;
  Vector v=(b.c-a.c)/d,v1=v*a.r,v2=v*b.r;
  Point p1,p2;

  c=sqrt(d*d-(a.r-b.r)*(a.r-b.r));
  s=(180*asin(c/d))/pi;

  if(a.r<b.r){
    vp.push_back(Line(rotate(a.c,a.c+v1,180-s),rotate(b.c,b.c-v2,360-s)));
    vp.push_back(Line(rotate(a.c,a.c+v1,180+s),rotate(b.c,b.c-v2,s)));
  }
  else {
    vp.push_back(Line(rotate(a.c,a.c+v1,s),rotate(b.c,b.c-v2,180+s)));
    vp.push_back(Line(rotate(a.c,a.c+v1,360-s),rotate(b.c,b.c-v2,180-s)));
  }
  if(intersection==2 || intersection==3)return vp;
  
  c=sqrt(d*d-(a.r+b.r)*(a.r+b.r));
  s=(180*asin(c/d))/pi;
  
  vp.push_back(Line(rotate(a.c,a.c+v1,s),rotate(b.c,b.c-v2,s)));
  vp.push_back(Line(rotate(a.c,a.c+v1,360-s),rotate(b.c,b.c-v2,360-s)));
  
  return vp;
}
  
vector<Point> solve(Circle a,Circle b){
  vector<Point> vp;
  vector<Line> vl=getCommonTangent(a,b);
  for(int i=0;i<vl.size();i++)vp.push_back(vl[i].p1);
  sort(vp.begin(),vp.end());
  return vp;
}

int main()
{
  Circle c1,c2;

  cin>>c1.c.x>>c1.c.y>>c1.r;
  cin>>c2.c.x>>c2.c.y>>c2.r;

  vector<Point> v=solve(c1,c2);
  for(int i=0;i<v.size();i++)printf("%.10f %.10f\n",v[i].x,v[i].y);
  return 0;
}