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<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<ctime>
using namespace std;

typedef long long ll;

bool debug = false;
const int NIL = -1;
const int INF = 1000000000;
const int NUM = 100010;
const double eps = 1e-12;
const double PI = 3.1415926535898;
clock_t START, END;

int X, Y, E;

//basic defitition
int dcmp(double x) { if (fabs(x) < eps)return 0; else return x < 0 ? -1 : 1; }
struct Point {
	double x, y;
	Point(double x = 0, double y = 0) :x(x), y(y) {}
	bool operator < (const Point& rhs) const {
		if (dcmp(x - rhs.x) == 0)
			return y < rhs.y;
		return x < rhs.x;
	}
};
typedef Point Vector;
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Point A, Point B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x * p, A.y * p); }
Vector operator / (Vector A, double p) { return Vector(A.x / p, A.y / p); }
bool operator == (const Point& a, const Point& b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; }
// basic operator
double Dot(Vector A, Vector B) { return A.x * B.x + A.y * B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; }
double Area2(Point A, Point B, Point C) { return Cross(B - A, C - A); }
Vector Rotate(Vector A, double rad) { return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); }
Vector Normal(Vector A) { double L = Length(A); return Vector(-A.y / L, A.x / L); } //A is not zero vector
//point and line
Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
	Vector u = P - Q;
	double t = Cross(w, u) / Cross(v, w);
	return P + v * t;
}//two lines only have one intersection and Cross(v,w) is not zero
double DistanceToLine(Point P, Point A, Point B) {
	Vector v1 = B - A, v2 = P - A;
	return fabs(Cross(v1, v2)) / Length(v1);
}
double DistanceToSegment(Point P, Point A, Point B) {
	if (A == B) return Length(P - A);
	Vector v1 = B - A, v2 = P - A, v3 = P - B;
	if (dcmp(Dot(v1, v2)) < 0) return Length(v2);
	else if (dcmp(Dot(v1, v3)) > 0) return Length(v3);
	else return fabs(Cross(v1, v2)) / Length(v1);
}
Point GetLineProjection(Point P, Point A, Point B) {
	Vector v = B - A;
	return A = v * (Dot(v, P - A) / Dot(v, v));
}
bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
	double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1), c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
	return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}
bool OnSegment(Point p, Point a1, Point a2) {
	return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) <= 0;
}
double angle(Vector v) { return atan2(v.y, v.x); }
//polygon
double ConvexPolygonArea(Point* p, int n) {
	double area = 0;
	for (int i = 1; i < n - 1; i++)
		area = Cross(p[i] - p[0], p[i + 1] - p[0]);
	return area / 2;
}
//circle
struct Circle {
	Point c;
	double r;
	Circle(Point c, double r) :c(c), r(r) {}
	Point point(double a) { return Point(c.x + cos(a) * r, c.y + sin(a) * r); }
};
int getCircleCircleIntersection(Circle C1, Circle C2, vector<Point>& sol) {
	double d = Length(C1.c - C2.c);
	if (dcmp(d) == 0) {
		if (dcmp(C1.r - C2.r) == 0) return -1;
		return 0;
	}
	if (dcmp(C1.r + C2.r - d) < 0) return 0;
	if (dcmp(fabs(C1.r - C2.r) - d) > 0) return 0;
	double a = angle(C2.c - C1.c);
	double da = acos((C1.r * C1.r + d * d - C2.r * C2.r) / (2 * C1.r * d));
	Point p1 = C1.point(a - da), p2 = C1.point(a + da);
	sol.push_back(p1);
	if (p1 == p2) return 1;
	sol.push_back(p2);
	return 2;
}
int getTangents(Circle A, Circle B, Point* a, Point* b) {
	int cnt = 0;
	if (A.r < B.r) {
		swap(A, B);
		swap(a, b);
	}
	double d2 = (A.c.x - B.c.x) * (A.c.x - B.c.x) + (A.c.y - B.c.y) * (A.c.y - B.c.y);
	double rdiff = A.r - B.r;
	double rsum = A.r + B.r;
	if (dcmp(d2 - rdiff * rdiff) == -1)
		return 0;
	double base = atan2(B.c.y - A.c.y, B.c.x - A.c.x);
	if (d2 == 0 && A.r == B.r) return -1;
	if (dcmp(d2 - rdiff * rdiff) == 0) {
		a[cnt] = A.point(base);
		b[cnt++] = B.point(base);
		return 1;
	}
	double ang = acos((A.r - B.r) / sqrt(d2));
	a[cnt] = A.point(base + ang);
	b[cnt++] = B.point(base + ang);
	a[cnt] = A.point(base - ang);
	b[cnt++] = B.point(base - ang);
	if (dcmp(d2 - rsum * rsum) == 0) {
		a[cnt] = A.point(base);
		b[cnt++] = B.point(PI + base);
	}
	else if (dcmp(d2 - rsum * rsum) == 1) {
		double ang = acos((A.r + B.r) / sqrt(d2));
		a[cnt] = A.point(base + ang);
		b[cnt++] = B.point(PI + base + ang);
		a[cnt] = A.point(base - ang);
		b[cnt++] = B.point(PI + base - ang);
	}
	return cnt;
}

int main(void)
{
	if (debug) {
		START = clock();
		freopen("in29.txt", "r", stdin);
		freopen("out.txt", "w", stdout);
	}
	int ans;
	Point O, a[5], b[5];
	double r;
	scanf("%lf%lf%lf", &O.x, &O.y, &r);
	Circle C1(O, r);
	scanf("%lf%lf%lf", &O.x, &O.y, &r);
	Circle C2(O, r);
	ans = getTangents(C1, C2, a, b);
	sort(a, a + ans);
	for (int i = 0; i < ans; i++)
		printf("%.10lf %.10lf\n", a[i].x, a[i].y);
	if (debug) {
		END = clock();
		double endtime = (double)(END - START) / 1000;
		printf("total time = %lf s", endtime);
	}
	return 0;
}