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 range(i,a,b) for(int i = (a); i < (b); i++)
#define rep(i,b) for(int i = 0; i < (b); i++)
#define all(a) (a).begin(), (a).end()
#define show(x)  cerr << #x << " = " << (x) << endl;
using namespace std;

template<typename T>
ostream& operator << (ostream& os, vector<T>& v){
	rep(i,v.size()){ os << v[i] << (i == v.size() - 1 ? "" : " "); } return os;
}
template<typename T>
istream& operator >> (istream& is, vector<T>& v){
	for(T& x: v){ is >> x; } return is;
}

typedef complex<double> Point;
typedef Point Vector;
//線分を表す構造体
struct Segment{
	Point p1, p2;
	Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
};
//直線を表す構造体
typedef Segment Line;
//多角形を表す構造体
typedef vector<Point> Polygon;

namespace std{
	bool operator < (const Point &a, const Point &b){
		return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
	}
	bool operator == (const Point &a, const Point &b){
		return a.real() == b.real() && a.imag() == b.imag();
	}
}

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

// 許容する誤差
#define EPS (1e-10)
#define INF (1e10)

// ベクトルaの絶対値を求める
//double length = abs(a);

// 2点a,b間の距離を求める
//double distance = abs(a-b);

/*
// ベクトルaの単位ベクトルを求める
Point b = a / abs(a);

// ベクトルaの法線ベクトルn1,n2を求める
Point n1 = a * Point(0, 1);
Point n2 = a * Point(0, -1);
*/

int ccw(Point, Point, Point);

// 2つのスカラーが等しいかどうか
bool EQ(double a, double b){
	show(a - b);
	return (abs(a - b) < EPS);
}

// 2つのベクトルが等しいかどうか
bool EQV(Vector a, Vector b){
	return ( EQ(a.real(), b.real()) && EQ(a.imag(), b.imag()) );
}

// 内積 (dot product) : a・b = |a||b|cosΘ
double dot(Point a, Point b) {
	return (a.real() * b.real() + a.imag() * b.imag());
}

// 外積 (cross product) : a×b = |a||b|sinΘ
double cross(Point a, Point b) {
	return (a.real() * b.imag() - a.imag() * b.real());
}

// 2直線の直交判定 : a⊥b <=> dot(a, b) = 0
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
	return EQ( dot(a1-a2, b1-b2), 0.0 );
}
bool isOrthogonal(Line s1, Line s2) {
	return isOrthogonal(s1.p1, s1.p2, s2.p1, s2.p2);
}

// 2直線の平行判定 : a//b <=> cross(a, b) = 0
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
	return EQ( cross(a1-a2, b1-b2), 0.0 );
}
bool isParallel(Line s1, Line s2) {
	return isParallel(s1.p1, s1.p2, s2.p1, s2.p2);
}

// 点cが直線a,b上にあるかないか
bool isPointOnLine(Point a, Point b, Point c) {
	return EQ( cross(b-a, c-a), 0.0 );
}
bool isPointOnLine(Line s, Point c) {
	return isPointOnLine(s.p1, s.p2, c);
}

// 点a,bを通る直線と点cとの距離
double distanceLPoint(Point a, Point b, Point c) {
	return abs(cross(b-a, c-a)) / abs(b-a);
}
double distanceLPoint(Line s, Point c) {
	return distanceLPoint(s.p1, s.p2, c);
}

// 点a,bを端点とする線分と点cとの距離
double distanceLsPoint(Point a, Point b, Point c) {
	if ( dot(b-a, c-a) < EPS ) return abs(c-a);
	if ( dot(a-b, c-b) < EPS ) return abs(c-b);
	return abs(cross(b-a, c-a)) / abs(b-a);
}
double distanceLsPoint(Segment s, Point c) {
	return distanceLsPoint(s.p1, s.p2, c);
}

// a1,a2を端点とする線分とb1,b2を端点とする線分の交差判定
// 端点が重なる場合も、線分が交差しているとみなす
bool isIntersectedLs(Point a1, Point a2, Point b1, Point b2) {
	return ( ccw(a1, a2, b1) * ccw(a1, a2, b2) <= 0 &&
			ccw(b1, b2, a1) * ccw(b1, b2, a2) <= 0 );
}
bool isIntersectedLs(Segment s1, Segment s2) {
	return isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2);
}

// 端点が重なっているかを検出する
bool isContainSamePoints(Segment s1, Segment s2){
	if(abs(s1.p1 - s2.p1) < EPS) return true;
	if(abs(s1.p1 - s2.p2) < EPS) return true;
	if(abs(s1.p2 - s2.p1) < EPS) return true;
	if(abs(s1.p2 - s2.p2) < EPS) return true;
	return false;
}

// a1,a2を端点とする線分とb1,b2を端点とする線分の交点計算
Point intersectionLs(Point a1, Point a2, Point b1, Point b2) {
	Vector base = b2 - b1;
	double d1 = abs(cross(base, a1 - b1));
	double d2 = abs(cross(base, a2 - b1));
	double t = d1 / (d1 + d2);

	return Point(a1 + (a2 - a1) * t);
}
Point intersectionLs(Segment s1, Segment s2) {
	return intersectionLs(s1.p1, s1.p2, s2.p1, s2.p2);
}

// a1,a2を通る直線とb1,b2を通る直線の交差判定
bool isIntersectedL(Point a1, Point a2, Point b1, Point b2) {
	return !EQ( cross(a1-a2, b1-b2), 0.0 );
}
bool isIntersectedL(Line l1, Line l2) {
	return isIntersectedL(l1.p1, l1.p2, l2.p1, l2.p2);
}

// a1,a2を通る直線とb1,b2を通る直線の交点計算
Point intersectionL(Point a1, Point a2, Point b1, Point b2) {
	Point a = a2 - a1; Point b = b2 - b1;
	return a1 + a * cross(b, b1-a1) / cross(b, a);
}
Point intersectionL(Line l1, Line l2) {
	return intersectionL(l1.p1, l1.p2, l2.p1, l2.p2);
}

// 線分s1と線分s2の距離
double distanceLL(Segment s1, Segment s2){
	if(isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2) ) return 0.0;
	return min(
			min(distanceLsPoint(s1.p1, s1.p2, s2.p1),
				distanceLsPoint(s1.p1, s1.p2, s2.p2)),
			min(distanceLsPoint(s2.p1, s2.p2, s1.p1),
				distanceLsPoint(s2.p1, s2.p2, s1.p2)) );
}
double distanceLL(Point p0, Point p1, Point p2, Point p3){
	Segment s1 = Segment{p0, p1}, s2 = Segment{p2, p3};
	return distanceLL(s1, s2);
}

// 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) / norm(base);
	return Point(s.p1 + base * r);
}

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

//点pをangle分だけ時計回りに回転
Point rotation(Point p, double angle){
	double x, y;
	x = p.real() * cos(angle) - p.imag() * sin(angle);
	y = p.real() * sin(angle) + p.imag() * cos(angle);
	return Point(x, y);
}

//円cと線分lの交点
pair<Point, Point> getCrossPoints(Circle c, Line l){
	Vector pr = project(l, c.p);
	Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
	double base = sqrt(c.r * c.r - norm(pr - c.p));
	return make_pair(pr + e * base, pr - e * base);
}

//円c1と円c2の交点
double arg(Vector p) { return atan2(p.imag(), p.real()); }
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.p - c2.p);
	double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
	double t = arg(c2.p - c1.p);
	return make_pair(Point(c1.p + polar(c1.r, t + a)), Point(c1.p + polar(c1.r, t - a)));
}

//点の内包
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;
	rep(i,n){
		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.imag() > b.imag() ) swap(a, b);
		if( a.imag() < EPS && EPS < b.imag() && cross(a, b) > EPS ) x = not x;
	}
	return ( x ? IN : OUT );
}

//弧度法から度数法の変換
double radianToDegree(double rad){
	return 180 * rad / M_PI;
}

//度数法から変弧度法の換
double degreeToRadian(double deg){
	return M_PI * deg / 180;
}

//2つのベクトルからなる角度を求める
double angleOf2Vector(Vector a, Vector b){
	return acos( dot(a,b) / (abs(a) * abs(b)) );
}

//ベクトルの位置検出
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;

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( abs(a) < abs(b) ) return ONLINE_FRONT;

	return ON_SEGMENT;
}

//凸包
Polygon convexHull( Polygon s ){
	Polygon u;
	if( s.size() < 3 ) return s;
	sort(s.begin(), s.end());

	range(i,0,s.size()){
		//== COUNTER_CLOCKWISEだと内角は180以下（一直線上に並んでいても、頂点として数える）
		//!= CLOCKWISEだと内角は180未満（一直線上の頂点は数えない）
		for(int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], s[i]) == COUNTER_CLOCKWISE; n--){
			u.pop_back();
		}
		u.emplace_back(s[i]);
	}

	for(int i = s.size() - 2; i >= 0; i--){
		//ここも == と != を変更する
		for(int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], s[i]) == COUNTER_CLOCKWISE; n--){
			u.pop_back();
		}
		u.emplace_back(s[i]);
	}

	reverse(u.begin(), u.end());
	u.pop_back();

	//最も下にある点の中で最も右にある点から反時計回りに並び替え
	/*
	   int i = 0;
	   while(i < u.size() - 1){
	   if(u[i].imag() > u[i + 1].imag()){
	   u.emplace_back(u[i]);
	   u.erase(u.begin());
	   continue;
	   }else if(u[i].imag() == u[i + 1].imag() && u[i].real() > u[i + 1].real()){
	   u.emplace_back(u[i]);
	   u.erase(u.begin());
	   continue;
	   }
	   break;
	   }
	   */

	return u;
}

//キャリパー法を用いて凸多角形の直径を求める
double diameterOfConvexPolygon(Polygon p){
	Polygon s = convexHull(p);
	int n = s.size();

	if(n == 2) return abs(s[1] - s[0]);

	int i = 0, j = 0;
	rep(k,n){
		if(not (s[i] < s[k])) i = k;
		if(s[j] < s[k]) j = k;
	}

	double ret = 0.0;
	int is = i, js = j;

	while(i != js || j != is){
		ret = max(ret, abs(s[i] - s[j]));
		if(cross(s[(i + 1) % n] - s[i], s[(j + 1) % n] - s[j]) < 0){
			i = (i + 1) % n;
		}else{
			j = (j + 1) % n;
		}
	}
	return ret;
}

//凸多角形の切り取りに使う関数。これがなんなのかはまだ知らない。
Point getCrossPointLL(Line a, Line b){
	double A = cross(a.p2 - a.p1, b.p2 - b.p1);
	double B = cross(a.p2 - a.p1, a.p2 - b.p1);
	if(abs(A) < EPS && abs(B) < EPS) return b.p1;
	return b.p1 + (b.p2 - b.p1) * (B / A);
}

Polygon convexCut(Polygon p, Line l) {
	Polygon q;
	rep(i,p.size()){
		Point a = p[i], b = p[(i + 1) % p.size()];
		if (ccw(l.p1, l.p2, a) != -1) q.emplace_back(a);
		if (ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) < 0){
			q.emplace_back(getCrossPointLL(Line{a, b}, l));
		}
	}
	return q;
}

//三角形の面積
double AreaOfTriangle(Point a, Point b, Point c){
	double w, x, y, z;
	w = b.real()-a.real();
	x = b.imag()-a.imag();
	y = c.real()-a.real();
	z = c.imag()-a.imag();
	return abs((w * z - x * y) / 2);
}

//多角形の面積
double areaOfPolygon(Polygon g){
	int n = g.size();
	double ret = 0.0;
	rep(i,n) ret += cross(g[i], g[ (i + 1) % n ]);
	return abs(ret) / 2.0;
}

//凸多角形かどうかの判定
bool isConvex(Polygon g){
	int n = g.size();
	rep(i,n){
		if(ccw(g[i], g[(i + 1) % n], g[(i + 2) % n]) == CLOCKWISE) return false;
	}
	return true;
}

//凹多角形を線分lで切断した際の多角形の数
int dividedPolygonNumber(Polygon p, Line l){
	int cnt = 0;
	rep(i,p.size()){
		if(isIntersectedLs(p[i], p[(i + 1) % p.size()], l.p1, l.p2)) cnt++;
	}
	return cnt / 2 + 1;
}

//多角形が点対象となる点の座標
Point pointSymmetry(Polygon g){
	int size = g.size() / 2;
	if(g.size() % 2) return Point{INF,INF};

	set<Point> s;
	rep(i,size){
		rep(j,size){
			if(i == j) continue;
			s.insert(intersectionLs(g[i], g[i + size], g[j], g[j + size]));
		}
	}
	if(s.size() > 1) return Point{INF,INF};
	return *s.begin();
}

//角abcの二等分線を求める
Line requireBisectorOfAngle(Point a, Point b, Point c){
	a-=b;
	c-=b;
	//cout << a << ' ' << c << endl;

	double angle = angleOf2Vector(a, c);
	angle /= 2;

	if(ccw(Point{0,0}, a, c) == COUNTER_CLOCKWISE){
		return Line{b, rotation(a, angle) + b};
	}else{
		return Line{b, rotation(a, -angle) + b};
	}
	assert(false);
}

//三角形の内接円を求める
Circle requireIncircle(Point p[3]){
	Line bisector1 = requireBisectorOfAngle(p[0], p[1], p[2]);
	Line bisector2 = requireBisectorOfAngle(p[0], p[2], p[1]);
	//cout << bisector1.p1 << ' ' << bisector1.p2 << endl;
	//cout << bisector2.p1 << ' ' << bisector2.p2 << endl;
	Point center = intersectionL(bisector1, bisector2);
	//show(center)
	double r = distanceLPoint(p[0], p[1], center);
	//show(r)
	return Circle{center, r};
}

// 円と点の接線を求める
Line getTangentPointointCp(Circle c, Point p) {
	auto pow = [](double a) -> double {return a * a; };
	double x = p.real() - c.p.real(), y = p.imag() - c.p.imag();

	double sqt = sqrt((pow(x) + pow(y)) - pow(c.r));
	double denominator = pow(x) + pow(y);

	double x1 = c.r * (x * c.r + y * sqt) / denominator + c.p.real();
	double y1 = c.r * (y * c.r - x * sqt) / denominator + c.p.imag();
	double x2 = c.r * (x * c.r - y * sqt) / denominator + c.p.real();
	double y2 = c.r * (y * c.r + x * sqt) / denominator + c.p.imag();

	return Line(Point(x1, y1), Point(x2, y2));
}

// 円と円の接線を求める
vector<Line> getTangentPointointCc(Circle a, Circle b) {
	auto pow = [](double a) -> double {return a * a; };

	Circle c(Point(b.p.real() - a.p.real(), b.p.imag() - a.p.imag()), b.r);

	vector<Line> res;

	auto f = [&](double R) {
		double left = a.r + R;
		double right = sqrt((pow(c.p.real()) + pow(c.p.imag())) - pow(a.r + R));
		double denominator = pow(c.p.real()) + pow(c.p.imag());

		double x1 = a.r * (c.p.real() * left + c.p.imag() * right) / denominator + a.p.real();
		double y1 = a.r * (c.p.imag() * left - c.p.real() * right) / denominator + a.p.imag();

		double x2 = a.r * (c.p.real() * left - c.p.imag() * right) / denominator + a.p.real();
		double y2 = a.r * (c.p.imag() * left + c.p.real() * right) / denominator + a.p.imag();

		Line l = Line(Point(x1, y1), Point(x2, y2));
		if (not std::isnan(l.p1.real())) res.emplace_back(l);
	};

	f(c.r);		// 内接線
	f(-c.r);	// 外接線

	return res;
}

int main(){
	Circle c[2];
	rep(i,2){
		double cx, cy, r;
		cin >> cx >> cy >> r;
		c[i] = Circle(Point(cx, cy), r);
	}
	
	vector<Line> l = getTangentPointointCc(c[0], c[1]);
	set<Point> p;
	rep(i,l.size()){
		p.emplace(l[i].p1);
		p.emplace(l[i].p2);
	}

	cout << fixed << setprecision(10);
	for(auto i : p){
		cout << i.real() << ' ' << i.imag() << endl;
	}
}