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<iomanip>
#include<cmath>
#include<vector>
#include<algorithm>
#include<cassert>
#include<set>
#include<limits>

using namespace std;

const double EPS = 1e-8;
template<typename T> bool equals(T a, T b){ return (fabs(a - b)) < EPS;};

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;

static const int NOTCROSS = 4;
static const int CIRCUMSCRIBED = 3; 
static const int INTERSECT = 2;
static const int INSCRIBED = 1;
static const int INCLUDE = 0;

const double PI = acos(-1);

class Point{
public:
	double x, y;
	
	Point(double x = 0, double y = 0): x(x), y(y) {}
	Point(const Point &p) { x = p.x; y = p.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 * (const double &a) { return Point(x * a, y * a); }
	Point operator / (const double &a) { return Point(x / a, y / a); }
	
	Point & operator = (const Point& p) {x = p.x; y = p.y; return *this;};
	Point & operator += (const Point& p) {x += p.x; y += p.y; return *this;};
	Point & operator -= (const Point& p) {x -= p.x; y -= p.y; return *this;};
	Point & operator *= (const Point& p) {x *= p.x; y *= p.y; return *this;};
	Point & operator /= (const Point& p) {x /= p.x; y /= p.y; return *this;};
	
	bool operator < (const Point &p) const {
		return x != p.x ? x < p.x : y < p.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;
	}
	
	double abs() { return sqrt(norm()); };
	double norm() { return x * x + y * y;};
};

typedef Point Vector;


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

double abs(Vector 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;
}

struct Segment{
	Point p1, p2;
};

typedef Segment Line;

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

typedef vector<Point> Polygon;



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 isPrallel(Segment s1, Segment s2){
	return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

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;
}

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);
}

int intersect(Circle c1, Circle c2){
	double dis = abs(c1.c - c2.c);
	
	if(dis > c1.r + c2.r + EPS) return NOTCROSS;
	if(fabs(dis - c1.r - c2.r) < EPS) return CIRCUMSCRIBED;
	if(dis > fabs(c1.r - c2.r) + EPS) return INTERSECT;
	if(fabs(dis - fabs(c1.r - c2.r)) < EPS) return INSCRIBED;
	return INCLUDE;
}

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(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)), min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrosPoint(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;
}

bool intersect(Circle c, Line l){
	return getDistanceLP(l, c.c) < c.r + EPS;
}

pair<Point, Point> getCrossPoint(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> getCrosPoint(Circle c1, Circle c2){
	Point res1, res2;
	int ins = intersect(c1, c2);
	if(ins == NOTCROSS || ins == INCLUDE) {
		assert(false); // 0
	}
	if(ins == INSCRIBED && equals(c1.r, c2.r)){
		assert(false); // infinity
	}
	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);
	res1 = c1.c + polar(c1.r, t + a);
	res2 = c1.c + polar(c1.r, t - a);
	return make_pair(res1, res2);
}


double getArea(Circle c){
	return c.r*c.r*PI;
}

double getArea(Polygon& p){
	double area = 0;
	
	for(int i = 0; i < p.size(); i++){
		area += (p[i].x * p[(i + 1) % p.size()].y - p[(i + 1) % p.size()].x * p[i].y);
	}
	
	return fabs(area)/2;
}

bool isConvex(Polygon& p){
	int b = 0;
	
	for(int i = 0; i < p.size(); i++){
		int j = (i + 1) % p.size(), k = (i + 2) % p.size();
		int c = ccw(p[i], p[j], p[k]);
		if(c == ON_SEGMENT || c == ONLINE_BACK || c == ONLINE_FRONT) continue;
		if(c*b < 0) return false;
		if(!b) b = c;
	}
	
	return 1;
}

/*
IN 2, ON 1, 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 1;
		if(a.y > b.y) swap(a, b);
		if(a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
	}
	return (x ? 2 : 0);
}

Polygon andrewScan(Polygon s){
	Polygon u, l;
	if(s.size() < 3) return s;
	sort(s.begin(), s.end());
	u.push_back(s[0]);
	u.push_back(s[1]);
	l.push_back(s[s.size() - 1]);
	l.push_back(s[s.size() - 2]);
	
	for(int i = 2; i < s.size(); i++){
		// for(int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], s[i]) != CLOCKWISE; n--){ //凸包の辺上の点を含めない
		for(int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], s[i]) == COUNTER_CLOCKWISE; n--){ //凸包の辺上の点を含める
			u.pop_back();
		}
		u.push_back(s[i]);
	}
	
	for(int i = s.size() - 3; i >= 0; i--){
		// for(int n = l.size(); n >= 2 && ccw(l[n-2], l[n-1], s[i]) != CLOCKWISE; n--){ //凸包の辺上の点を含めない
		for(int n = l.size(); n >= 2 && ccw(l[n-2], l[n-1], s[i]) == COUNTER_CLOCKWISE; n--){ //凸包の辺上の点を含める
			l.pop_back();
		}
		l.push_back(s[i]);
	}
	
	reverse(l.begin(), l.end());
	for(int i = u.size() - 2; i >= 1; i--) l.push_back(u[i]);
	
	return l;
}


class EndPoint {
public:
	Point p;
	int seg, st;
	EndPoint() {}
	EndPoint(Point p, int seg, int st): p(p), seg(seg), st(st) {}
	
	bool operator < (const EndPoint &ep) const {
		if(p.y == ep.p.y) {
			return st < ep.st;
		} else return p.y < ep.p.y;
	}
};


int manhattanIntersection(vector<Segment> S){
	const int BOTTOM = 0;
	const int LEFT = 1;
	const int RIGHT = 2;
	const int TOP = 3;
	int n = S.size();
	vector<EndPoint> EP(2*n);
	
	
	for(int i = 0, k = 0; i < n; i++){
		if(S[i].p1.y == S[i].p2.y){
			if(S[i].p1.x > S[i].p2.x) swap(S[i].p1, S[i].p2);
		} else if(S[i].p1.y > S[i].p2.y) swap(S[i].p1, S[i].p2);
		
		if(S[i].p1.y == S[i].p2.y){
			EP[k++] = EndPoint(S[i].p1, i, LEFT);
			EP[k++] = EndPoint(S[i].p2, i, RIGHT);
		} else {
			EP[k++] = EndPoint(S[i].p1, i, BOTTOM);
			EP[k++] = EndPoint(S[i].p2, i, TOP);
		}
	}
	
	sort(EP.begin(), EP.end());
	
	set<int> BT;
	const int INF = (1<<30);
	BT.insert(INF);
	int cnt = 0;
	
	for(int i = 0; i < 2*n; i++){
		if(EP[i].st == TOP){
			BT.erase(EP[i].p.x);
		} else if(EP[i].st== BOTTOM) {
			BT.insert(EP[i].p.x);
		} else if(EP[i].st == LEFT) {
			set<int>::iterator b = BT.lower_bound(S[EP[i].seg].p1.x);
			set<int>::iterator e = BT.upper_bound(S[EP[i].seg].p2.x);
			cnt += distance(b, e);
		}
	}
	
	return cnt;	
}


bool compare_y(Point a, Point b){
	return a.y < b.y;
}

// aはx座標の昇順で渡すこと
double closest_pair(Point *a, int n){
	if(n <= 1) return numeric_limits<double>::max();
	int m = n / 2;
	double x = a[m].x;
	double d = min(closest_pair(a, m), closest_pair(a + m, n - m));
	inplace_merge(a, a + m, a + n, compare_y);
	
	vector<Point> b;
	
	for(int i = 0; i < n; i++){
		if(fabs(a[i].x - x) >= d - EPS) continue;
		
		for(int j = 0; j < b.size(); j++){
			Point e(a[i].x - b[b.size() - j - 1].x, a[i].y - b[b.size() - j - 1].y);
			if(e.y >= d) break;
			d = min(d, e.abs());
		}
		b.push_back(a[i]);
	}
	
	return d;
}

Vector rotation(Vector v, double arg){
	double theta = acos((v.x)/abs(v));
	if(v.y < -EPS) theta *= -1;
	return Vector(cos(arg + theta), sin(arg + theta)) * abs(v);
}

pair<Point,Point> getTangent(Circle c, Point p){
	double d = getDistance(c.c, p);
	double dr = sqrt(d*d - c.r*c.r);
	double arg = acos(dr/d);
	Vector base(c.c - p);
	return make_pair(rotation(base, arg) * (dr/d) + p, rotation(base, -arg) * (dr/d) + p);
}

// c1とc2の共通接線とc1の接点
vector<Point> getTangent(Circle c1, Circle c2){
	vector<Point> res;
	int in = intersect(c1, c2);
	
	if(in == INCLUDE){
		res.resize(0);
	} else if(in == INSCRIBED){
		if(c2.r > c1.r) swap(c1, c2);
		Vector e = (c2.c - c1.c) / abs(c1.c - c2.c);
		res.resize(1);
		res[0] = e * c1.r + c1.c;
	} else if(in == INTERSECT){
		Vector v = (c2.c - c1.c), e;
		double theta = acos((c1.r - c2.r) / getDistance(c1.c, c2.c));
		e = v / abs(v);
		res.resize(2);
		res[0] = rotation(e,  theta) * c1.r + c1.c;
		res[1] = rotation(e, -theta) * c1.r + c1.c;
	} else if(in == CIRCUMSCRIBED){
		Vector v = (c2.c - c1.c), e;
		double theta = acos((c1.r - c2.r) / getDistance(c1.c, c2.c));
		e = v / abs(v);
		res.resize(3);
		res[0] = rotation(e,  theta) * c1.r + c1.c;
		res[1] = rotation(e, -theta) * c1.r + c1.c;
		res[2] = e * c1.r + c1.c;
	} else if(in == NOTCROSS){
		Vector v = (c2.c - c1.c), e;
		Point p = v * c1.r / (c1.r + c2.r) + c1.c;
		pair<Point, Point> pp = getTangent(c1, p);
		double theta = acos((c1.r - c2.r) / getDistance(c1.c, c2.c));
		e = v / abs(v);
		res.resize(4);
		res[0] = rotation(e,  theta) * c1.r + c1.c;
		res[1] = rotation(e, -theta) * c1.r + c1.c;
		res[2] = pp.first;
		res[3] = pp.second;
	}
	
	
	
	return res;
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout<<fixed<<setprecision(10);
	
	vector<Point> ans;
	Circle c, c2;
	
	cin>>c.c.x>>c.c.y>>c.r;
	cin>>c2.c.x>>c2.c.y>>c2.r;
	
	ans = getTangent(c, c2);
	
	sort(ans.begin(), ans.end());
	
	for(int i = 0; i < ans.size(); i++){
		cout<<ans[i].x<<" "<<ans[i].y<<endl;
	}
	
	return 0;
}