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>
using namespace std;

using ld = long double;
const ld eps = 1e-8, pi = acos(-1.0);

bool eq(ld a, ld b) {
	return abs(a - b) < eps;
}

using Point = complex<ld>;
class Line {
public:
	Point a, b;
};
ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

int ccw(Point a, Point b, Point c) {
	b -= a, c -= a;
	if (cross(b, c) > eps) return 1;
	if (cross(b, c) < -eps) return -1;
	if (dot(b, c) < 0) return 2;
	if (norm(b) < norm(c)) return -2;
	return 0;
}

bool isis_ll(Line l, Line m) {
	return abs(cross(l.b - l.a, m.b - m.a)) > eps;
}

bool isis_ls(Line l, Line s) {
	return (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

bool isis_lp(Line l, Point p) {
	return abs(cross(l.b - p, l.a - p)) < eps;
}

bool isis_sp(Line s, Point p) {
	return abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps;
}

Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

bool isis_ss(Line s, Line t) {
	if (isis_ll(s, t)) return isis_ls(s, t) && isis_ls(t, s);
	return isis_sp(s, t.a) || isis_sp(s, t.b) || isis_sp(t, s.a);
}

ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


class Circle {
public:
	Point p;
	ld r;
};

int nct(Circle c1, Circle c2) {
	ld d = abs(c1.p - c2.p);
	ld r1 = max(c1.r, c2.r), r2 = min(c1.r, c2.r);
	if (d > r1 + r2 + eps) return 4;
	if (eq(d, r1 + r2)) return 3;
	if (d > r1 - r2 + eps) return 2;
	if (eq(d, r1 - r2)) return 1;
	return 0;
}

vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	assert(d != 0.0);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	if (dfr < 0.0) return res;
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

vector<Point> is_lc(Circle c, Line l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d > c.r + eps) return res;
	ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d);
	Point nor = (l.a - l.b) / abs(l.a - l.b);
	res.push_back(proj(l, c.p) + len * nor);
	res.push_back(proj(l, c.p) - len * nor);
	return res;
}

vector<Point> is_sc(Circle c, Line s) {
	vector<Point> v = is_lc(c, s), res;
	for (size_t k = 0; k < v.size(); k++) {
		if (ccw(s.a, v[k], s.b) == -2) {
			res.push_back(v[k]);
		}
	}
	return res;
}

vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> res;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) return res;
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	res.push_back((Line) { p, p + v1 });
	if (l < eps) return res;
	res.push_back((Line) { p, p + v2 });
	return res;
}

vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> res;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		res = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nres = tangent_cp(c1, out);
		res.insert(res.end(), nres.begin(), nres.end());
	}
	else {
		Point v = c2.p - c1.p; v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		res.push_back((Line) { q1, q1 + v });
		res.push_back((Line) { q2, q2 + v });
	}
	return res;
}


int main()
{
	ld x1, x2, y1, y2, r1, r2;
	cout << fixed << setprecision(9);
	cin >> x1 >> y1 >> r1 >> x2 >> y2 >> r2;
	Circle c1 = { (Point) { x1, y1 }, r1 };
	Circle c2 = { (Point) { x2, y2 }, r2 };
	auto t = tangent_cc(c1, c2);
	vector<Point> res;
	for (auto &l : t) {
		res.push_back(proj(l, c1.p));
	}
	sort(res.begin(), res.end(), [](const Point& l, const Point& r) { return l.real() < r.real() ? true : l.real() == r.real() && l.imag() < r.imag() ? true : false; });
	for (auto &p : res) {
		cout << p.real() << ' ' << p.imag() << endl;
	}
	return 0;
}