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;
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define rep(i, a, b) for(int i = (a); i < (b); ++i)
#define per(i, a, b) for(int i = (b) - 1; i >= (a); --i)
#define sz(a) (int)a.size()
#define de(x) cout << #x << " = " << x << endl
#define dd(x) cout << #x << " = " << x << " "
#define endl "\n"
#define all(a) a.begin(), a.end()
#define pw(a) (1ll << (a))
typedef long long ll;
typedef pair<int, int> pii;
typedef double db;
typedef vector<int> vi;

const db eps = 1e-8;

int sign(db x) {
	return (x > eps) - (x < -eps);
}

struct P {
	db x, y;
	P() {}
	P(db x, db y) : x(x), y(y) {}
	void read() {
		cin >> x >> y;
	}
	P operator + (const P &c) const {
		return P(x + c.x, y + c.y);
	}
	P operator - (const P &c) const {
		return P(x - c.x, y - c.y);
	}
	P operator * (const db &c) const {
		return P(x * c, y * c);
	}
	P operator / (const db &c) const {
		return P(x / c, y / c);
	}
	db len2() {
		return x * x + y * y;
	}
	db len() {
		return sqrt(x * x + y * y);
	}
	P turn90() {
		return P(-y, x);
	}
	bool operator < (const P &c) const {
		int o = sign(x - c.x);
		return o ? o < 0 : sign(y - c.y) < 0;
	}
};
struct L {
	P a, b;
	L() {}
	L(P a, P b) : a(a), b(b) {}
	void read() {
		a.read();
		b.read();
	}
};
struct C {
	P o;
	db r;
	C() {}
	C(P o, db r) : o(o), r(r) {}
	void read() { 
		o.read();
		cin >> r;
	}
};
db det(P a, P b) {
	return a.x * b.y - a.y * b.x;
}
db dot(P a, P b) {
	return a.x * b.x + a.y * b.y;
}
P isLL(const L &l1, const L &l2) {
	db s1 =  det(l2.b - l2.a, l1.a - l2.a);
	db s2 = -det(l2.b - l2.a, l1.b - l2.a);
	return (l1.a * s2 + l1.b * s1) / (s1 + s2);
}
P proj(const L &l, const P &p) {
	return l.a + (l.b - l.a) * (dot(p - l.a, l.b - l.a) / (l.b - l.a).len2());
}
db disToLine(const L &l, const P &p) {
	return fabs(det(p - l.a, l.b - l.a) / (l.b - l.a).len());
}
db disToSeg(const L &l, const P &p) {
	return sign(dot(p - l.a, l.b - l.a)) * sign(dot(p - l.b, l.a - l.b)) == 1 ? disToLine(l, p) : min((p - l.a).len(), (p - l.b).len());
}
bool tanCP(const C &c, const P &p0, P &p1, P &p2) {
	db x = (p0 - c.o).len2(), d = x - c.r * c.r;
	if(d < eps) return 0;
	P p = (p0 - c.o) * (c.r * c.r / x);
	P delta = ((p0 - c.o) * (-c.r * sqrt(d) / x)).turn90();
	p1 = c.o + p + delta;
	p2 = c.o + p - delta;
	return 1;
}
vector<L> extanCC(const C &c1, const C &c2) {
	vector<L> ret;
	if(sign(c1.r - c2.r) == 0) {
		P dir = c2.o - c1.o;
		dir = (dir * (c1.r / dir.len())).turn90();
		ret.pb(L(c1.o + dir, c2.o + dir));
		ret.pb(L(c1.o - dir, c2.o - dir));
	} else {
		P p = (c1.o * -c2.r + c2.o * c1.r) / (c1.r - c2.r);
		P p1, p2, q1, q2;
		if(tanCP(c1, p, p1, p2) && tanCP(c2, p, q1, q2)) {
			if(c1.r < c2.r) swap(p1, p2), swap(q1, q2);
			ret.pb(L(p1, q1));
			ret.pb(L(p2, q2));
		}
	}
	return ret;
}
vector<L> intanCC(const C &c1, const C &c2) {
	vector<L> ret;
	P p = (c1.o * c2.r + c2.o * c1.r) / (c1.r + c2.r);
	P p1, p2, q1, q2;
	if(tanCP(c1, p, p1, p2) && tanCP(c2, p, q1, q2)) {
		ret.pb(L(p1, q1));
		ret.pb(L(p2, q2));
	}
	return ret;
}

int main() {
	std::ios::sync_with_stdio(0);
	std::cin.tie(0);
	C c1, c2;
	c1.read();
	c2.read();
	vector<P> res;
	auto t = extanCC(c1, c2);
	for(auto u : t) res.pb(u.a);
	t = intanCC(c1, c2);
	for(auto u : t) res.pb(u.a);
	db dis = (c1.o - c2.o).len();
	if(sign(dis - (c1.r + c2.r)) == 0) {
		res.pb(c1.o + (c2.o - c1.o) * c1.r / (c1.r + c2.r));
	}
	if(sign(dis - fabs(c1.r - c2.r) == 0)) {
		res.pb(c1.o + (c2.o - c1.o) * c1.r / (c1.r - c2.r));
	}
	sort(all(res));
	cout << setiosflags(ios::fixed);
	cout << setprecision(10);
	for(auto u : res) cout << u.x << " " << u.y << endl;
	return 0;
}