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<iostream>
#include<vector>
#include<iomanip>
#include<cmath>
#include<algorithm>
#include<cassert>
using namespace std;

#define double long double

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

struct Point;
typedef Point Vector;
typedef vector<Point> Polygon;
struct Circle;
struct Segment;
typedef Segment Line;
double norm(Point a);
double abs(Point a);
double dot(Vector a, Vector b);
double cross(Vector a, Vector b);
double getDistance(Point a, Point b);
double getDistanceLP(Line l, Point p);
double getDistanceSP(Segment s, Point p);
double getDistance(Segment s1, Segment s2);
bool isOrthogonal(Vector a, Vector b);
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2);
bool isOrthogonal(Segment s1, Segment s2);
bool isParallel(Vector a, Vector b);
bool isParallel(Point a1, Point a2, Point b1, Point b2);
bool isParallel(Segment s1, Segment s2);
int ccw(Point p0, Point p1, Point p2);
bool intersect(Point p1, Point p2, Point p3, Point p4);
bool intersect(Segment s1, Segment s2);
bool intersect(Circle c, Line l); // 誤差の検証をしていない
bool intersect(Circle c1, Circle c2); // 誤差の検証をしていない

Point project(Segment s, Point p);
Point reflect(Segment s, Point p);
Point getCrossPoint(Segment s1, Segment s2);
pair<Point,Point> getCrossPoints(Circle c, Line l);
pair<Point,Point> getCrossPoints(Circle c1, Circle c2); // 誤差の検証をしていない
pair<Point,Point> getContactPoints(Circle c, Point p); // 接点 点は円の外部

double area(Polygon g); // convexでなくてもよい. absを消せば符号付き面積
bool isConvex(Polygon g); // O(n^2) 線形時間アルゴリズムが存在するらしい
int contains(Polygon g, Point p);

double arg(Vector p);   // 偏角
Vector polar(double a, double r); // 極座標系->ベクトル

Polygon andrewScan(Polygon g); // 凸包の辺上の点も含めたければ!=CLOCKWISEを==COUNTER_CLOCKWISEに
double convexDiameter(Polygon g); // gはconvex 

struct Line2d;  // 直線を2つのPointではなくax+by+c=0の形で表したいときに
void tangents(Point p, double r1, double r2, vector<Line2d> &v);    // https://cp-algorithms.com/geometry/tangents-to-two-circles.html
vector<Line2d> commonTangents(Circle c1, Circle c2);

struct Point{
    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); }

    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 fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
    }
};

typedef Point Vector;
typedef vector<Point> Polygon;

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

struct Segment{
    Point p1, p2;
    Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};

typedef Segment Line;


double norm(Point a){
    return a.x * a.x + a.y * a.y;
}

double abs(Point a){
    return sqrt(norm(a));
}

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 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);
}

double getDistance(Segment s1, Segment s2){
    if(intersect(s1, s2))   return 0.0;
    return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2), 
                getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)});
}


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);
}
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);
}


static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;   // p2->p0->p1
static const int ONLINE_FRONT = -2; // p0->p1->p2
static const int ON_SEGMENT = 0;    // p0->p2->p1
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(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(Segment s1, Segment s2){
    return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
bool intersect(Circle c, Line l){
    return getDistanceLP(l, c.c) < c.r+EPS;
}
bool intersect(Circle c1, Circle c2){
    return abs(c1.r-c2.r) <= getDistance(c1.c, c2.c) && getDistance(c1.c, c2.c) < c1.r+c2.r+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;
}

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;
}

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(fabs(c.r * c.r - norm(pr - c.c)));
    return make_pair(pr + e*base, pr - e*base);
}

pair<Point,Point> 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);
    return make_pair(c1.c + polar(c1.r, t+a), c1.c + polar(c1.r, t-a));
}

pair<Point,Point> getContactPoints(Circle c, Point p){
    assert(c.r < getDistance(c.c, p));
    double d = getDistance(c.c, p);
    return getCrossPoints(c, Circle(p, sqrt(d*d-c.r*c.r)));
}

double area(Polygon g){
    if(g.size() < 3)    return 0;
    int n = g.size();
    Point o(0.0, 0.0);
    double s = 0.0;
    for(int i = 0; i < n; i++)  s += cross(g[i]-o, g[(i+1)%n]-o);
    return abs(s) / 2.0;
}

bool isConvex(Polygon g){
    bool ret = true;
    int n = g.size();
    for(int i = 0; i < n; i++){
        for(int j = i+1; j < n; j++){
            if(cross(g[i]-g[(i+n-1)%n], g[j]-g[(i+n-1)%n]) < -EPS || cross(g[(i+1)%n]-g[i], g[j]-g[i]) < -EPS){
                ret = false;
            }
        }
    }
    return ret;
}

static const int IN = 2;
static const int ON = 1;
static const int OUT = 0;
int contains(Polygon g, Point p){
    int n = g.size();
    bool x = false;
    for(int i = 0; i < n; i++){
        Point a = g[i] - p, b = g[(i+1)%n] - p;
        if(abs(cross(a, b)) < EPS && dot(a, b) < EPS)   return ON;
        if(a.y > b.y)   swap(a, b);
        if(a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
    }
    return x ? IN : OUT;
}


double arg(Vector p){
    return atan2(p.y, p.x);
}

Vector polar(double a, double r){
    return Point(a * cos(r), a * sin(r));
}


Polygon andrewScan(Polygon g){
    Polygon u, l;
    if(g.size() < 3)    return g;
    sort(g.begin(), g.end());
    u.push_back(g[0]);
    u.push_back(g[1]);
    l.push_back(g[g.size()-1]);
    l.push_back(g[g.size()-2]);

    // upper
    for(int i = 2; i < g.size(); i++){
        for(int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], g[i]) != CLOCKWISE; n--){
            u.pop_back();
        }
        u.push_back(g[i]);
    }

    // lower
    for(int i = g.size()-3; i >= 0; i--){
        for(int n = l.size(); n >= 2 && ccw(l[n-2], l[n-1], g[i]) != CLOCKWISE; n--){
            l.pop_back();
        }
        l.push_back(g[i]);
    }

    reverse(l.begin(), l.end());
    for(int i = u.size()-2; i >= 1; i--)    l.push_back(u[i]);

    return l;
}

double convexDiameter(Polygon g){
    double d = 0.0;
    int n = g.size();
    int is = 0, js = 0;
    for(int i = 1; i < n; i++){
        if(g[i].y > g[is].y)    is = i;
        if(g[i].y < g[js].y)    js = i;
    }
    d = getDistance(g[is], g[js]);

    int i = is, j = js, maxi = is, maxj = js;
    do{
        if(cross(g[(i+1)%n]-g[i], g[(j+1)%n]-g[j]) >= 0.0)  j = (j+1)%n;
        else    i = (i+1)%n;
        if(getDistance(g[i], g[j]) > d){
            d = getDistance(g[i], g[j]);
            maxi = i, maxj = j;
        }
    }while(i != is || j != js);

    return d; // farthest pair is (maxi, maxj).
}


struct Line2d{
    double a, b, c;
    double eval(double x){
        // fail when b is zero (= the line is orthogonal to x axis)
        return (-a*x-c)/b;   
    }
};

void tangents(Point p, double r1, double r2, vector<Line2d> &v){
    double r = r2-r1;
    double z = p.x*p.x + p.y*p.y;
    double d = z - r*r;
    if(d < -EPS)    return; // discriminant < 0 means there's no answer
    d = sqrt(d);
    Line2d l;
    l.a = (p.x*r + p.y*d) / z;
    l.b = (p.y*r - p.x*d) / z;
    l.c = r1;
    v.push_back(l);
}

vector<Line2d> commonTangents(Circle c1, Circle c2){
    if(c1.r > c2.r) swap(c1, c2);
    vector<Line2d> ans;
    if(c1.c == c2.c && c1.r == c2.r)            return ans;
    if(getDistance(c1.c, c2.c) < c2.r-c1.r)     return ans;
    for(int i : {-1, 1}){
        for(int j : {-1, 1}){
            tangents(c2.c-c1.c, c1.r*i, c2.r*j, ans);
        }
    }
    for(int i = 0; i < ans.size(); i++){
        ans[i].c -= ans[i].a*c1.c.x + ans[i].b*c1.c.y;
    }
    return ans;
}

int main(){
    double a, b, c, d, e, f;
    cin >> a >> b >> c >> d >> e >> f;
    Circle c1(Point(a,b), c);
    Circle c2(Point(d,e), f);
    vector<Line2d> ans = commonTangents(c1, c2);
    vector<Point> res;
    for(Line2d x : ans){
        Line l({0,0}, {0,0});
        if(x.b != 0)    l = Line(Point(0, x.eval(0)), Point(1, x.eval(1)));
        else            l = Line(Point(-x.c/x.a, 0), Point(-x.c/x.a, 1));
        res.push_back(getCrossPoints(c1, l).first);
    }
    sort(res.begin(), res.end());
    res.erase(unique(res.begin(),res.end()),res.end());
    cout << fixed << setprecision(12);
    for(Point p : res)  cout << p.x << " " << p.y << endl;
    return 0;
}