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;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define INF 1<<30
#define LINF 1LL<<60

typedef long double ld;
typedef complex<ld> Point;
const ld eps = 1e-9, pi = acos(-1.0);
namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}
Point input_point() { ld x, y; cin >> x >> y; return Point(x, y); } // ????????\???
bool eq(ld a, ld b) { return (abs(a - b) < eps); } // ????????????????????????
ld dot(Point a, Point b) { return real(conj(a) * b); } // ??????
ld cross(Point a, Point b) { return imag(conj(a) * b); } // ??????

														 // ??´????????????
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
	Point operator[](const int _num) {
		if (_num == 0)return a;
		else if (_num == 1)return b;
		else assert(false);
	}
};

// ????????????
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// ??????????¶?
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);
}

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

/* ???????????? */
// ??´?????¨??´??????????????????
bool isis_ll(Line l, Line m) { return !eq(cross(l.b - l.a, m.b - m.a), 0); }
// ??´?????¨?????????????????????
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}
// ????????¨?????????????????????
bool isis_ss(Line s, Line t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}
// ????????´????????????
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 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);
}

// ??´?????¨???????????¢
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) });
}

/* ??? */
// ?????¨????????????
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	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;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) 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) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		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 l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}
// ?????¨????????\???
vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}
// ?????¨????????\???
vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> ret;
	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);
		ret = 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> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), nret.begin(), nret.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;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}


int main(void) {
	cin.tie(0); ios::sync_with_stdio(false);
	Circle c1, c2;
	c1.p = input_point(); cin >> c1.r;
	c2.p = input_point(); cin >> c2.r;

	auto ls = tangent_cc(c1, c2);
	vector<Point> ps;
	for (auto l : ls) {
		auto t_ps = is_lc(c1, l);
		ps.push_back(t_ps[0]);
	}
	sort(ps.begin(), ps.end());
	cout << fixed << setprecision(10);
	for (auto p : ps) {
		cout << p.real() << " " << p.imag() << endl;
	}
	return 0;
}