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 vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using ll = long long int;
using vll = vector<ll>; using vvll = vector<vll>; using vvvll = vector<vvll>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using cdouble = complex<double>;

const double eps = 1e-7;
const double INFD = numeric_limits<double>::infinity();
#define Loop(i, n) for(int i = 0; i < int(n); i++)
#define Loopll(i, n) for(ll i = 0; i < ll(n); i++)
#define Loop1(i, n) for(int i = 1; i <= int(n); i++)
#define Loopll1(i, n) for(ll i = 1; i <= ll(n); i++)
#define Loopr(i, n) for(int i = int(n) - 1; i >= 0; i--)
#define Looprll(i, n) for(ll i = ll(n) - 1; i >= 0; i--)
#define Loopr1(i, n) for(int i = int(n); i >= 1; i--)
#define Looprll1(i, n) for(ll i = ll(n); i >= 1; i--)
#define Foreach(buf, container) for(auto buf : container)
#define Loopdiag(i, j, h, w, sum) for(int i = ((sum) >= (h) ? (h) - 1 : (sum)), j = (sum) - i; i >= 0 && j < (w); i--, j++)
#define Loopdiagr(i, j, h, w, sum) for(int j = ((sum) >= (w) ? (w) - 1 : (sum)), i = (sum) - j; j >= 0 && i < (h); j--, i++)
#define Loopdiagsym(i, j, h, w, gap) for (int i = ((gap) >= 0 ? (gap) : 0), j = i - (gap); i < (h) && j < (w); i++, j++)
#define Loopdiagsymr(i, j, h, w, gap) for (int i = ((gap) > (h) - (w) - 1 ? (h) - 1 : (w) - 1 + (gap)), j = i - (gap); i >= 0 && j >= 0; i--, j--)
#define Loopitr(itr, container) for(auto itr = container.begin(); itr != container.end(); itr++)
#define printv(vector) Loop(ex_i, vector.size()) { cout << vector[ex_i] << " "; } cout << endl;
#define printmx(matrix) Loop(ex_i, matrix.size()) { Loop(ex_j, matrix[ex_i].size()) { cout << matrix[ex_i][ex_j] << " "; } cout << endl; }
#define quickio() ios::sync_with_stdio(false); cin.tie(0);
#define bitmanip(m,val) static_cast<bitset<(int)m>>(val)
#define Comp(type_t) bool operator<(const type_t &another) const
#define fst first
#define snd second
#define INF INFINITY
bool feq(double x, double y) { return abs(x - y) <= eps; }
bool fge(double x, double y) { return x >= y - eps; }
double fsqrt(double x) { return feq(x, 0) ? 0 : sqrt(x); }
bool inrange(ll x, ll t) { return x >= 0 && x < t; }
bool inrange(vll xs, ll t) { Foreach(x, xs) if (!(x >= 0 && x < t)) return false; return true; }
int ceillog2(ll x) { int ret = 0;	x--; while (x > 0) { ret++; x >>= 1; } return ret; }
ll rndf(double x) { return (ll)(x + (x >= 0 ? 0.5 : -0.5)); }
ll floorsqrt(ll x) { ll m = (ll)sqrt((double)x); return m + (m * m <= x ? 0 : -1); }
ll ceilsqrt(ll x) { ll m = (ll)sqrt((double)x); return m + (x <= m * m ? 0 : 1); }
ll rnddiv(ll a, ll b) { return (a / b + (a % b * 2 >= b ? 1 : 0)); }
ll ceildiv(ll a, ll b) { return (a / b + (a % b == 0 ? 0 : 1)); }
ll gcd(ll m, ll n) { if (n == 0) return m; else return gcd(n, m % n); }
ll lcm(ll m, ll n) { return m * n / gcd(m, n); }

/*******************************************************/

// Ongoing


struct pt_t {
	double x, y;
	pt_t operator+(const pt_t &p) { return { x + p.x, y + p.y }; }
	pt_t operator-(const pt_t &p) { return { x - p.x, y - p.y }; }
	pt_t operator*(const double &c) { return { x * c, y * c }; }
	bool operator<(const pt_t &another) const {
		return (x != another.x ? x < another.x : y < another.y);
	}
};

// aX + bY + c = 0
struct line_t {
	double a, b, c;
};

// (X - x)^2 + (Y - y)^2 = r^2
struct circle_t {
	double x, y, r;
};

// normal vector = (a, b), passing p
line_t solve_line(double a, double b, pt_t p) {
	return { a, b, -a * p.x - b * p.y };
}

// passing p, q
line_t solve_line(pt_t p, pt_t q) {
	return solve_line(q.y - p.y, -q.x + p.x, p);
}

// t should be radius
pt_t rot(pt_t p, double r) {
	return {
		cos(r) * p.x - sin(r) * p.y,
		sin(r) * p.x + cos(r) * p.y
	};
}

double norm2(pt_t p) {
	return p.x * p.x + p.y * p.y;
}

double norm(pt_t p) {
	return sqrt(norm2(p));
}

// angle [0, 2PI) of vector p to vector q
double angle(pt_t p, pt_t q) {
	p = p * (1.0 / norm(p));
	q = q * (1.0 / norm(q));
	double r0 = acos(max(min(p.x * q.x + p.y * q.y, 1.0), -1.0));
	double r1 = asin(max(min(p.x * q.y - p.y * q.x, 1.0), -1.0));
	if (r1 >= 0) return r0;
	else return 2 * M_PI - r0;
}

double dist(line_t l, pt_t p) {
	return abs(l.a * p.x + l.b * p.y + l.c)
		/ sqrt(l.a * l.a + l.b * l.b);
}

bool on_same_line(pt_t t, pt_t p) {
	line_t l = solve_line({ 0, 0 }, t);
	if (feq(dist(l, p), 0)) return true;
	else return false;
}

bool on_same_halfline(pt_t t, pt_t p) {
	line_t l = solve_line({ 0, 0 }, t);
	if (feq(dist(l, p), 0) && feq(angle(t, p), 0)) return true;
	else return false;
}

double in_segment(pt_t s, pt_t t, pt_t p) {
	if (on_same_halfline(t - s, p - s) && on_same_halfline(s - t, p - t)) {
		return true;
	}
	else return false;
}

// (NAN, NAN) if lines coincide with each other
// (INF, INF) if lines are parallel but not coincide
pt_t cross_point(line_t l, line_t m) {
	double d = l.a * m.b - l.b * m.a;
	if (feq(d, 0)) {
		if (feq(l.a * m.c - l.c * m.a, 0)) return { INF, INF };
		else return { NAN, NAN };
	}
	else {
		double x = l.b * m.c - m.b * l.c;
		double y = l.a * m.c - m.a * l.c;
		return { x / d, y / -d };
	}
}

// if size is 0, then not crossed
vector<pt_t> cross_point(circle_t f, line_t l) {
	double d = dist(l, { f.x, f.y });
	if (!fge(f.r, d)) return {};
	line_t m = solve_line(l.b, -l.a, { f.x, f.y });
	pt_t p = cross_point(l, m);
	if (feq(d, f.r)) return { p };
	else {
		pt_t u = { l.b, -l.a };
		pt_t v = u * (sqrt(pow(f.r, 2) - pow(d, 2)) / norm(u));
		return { p + v, p - v };
	}
}

// if size is 0, then not crossed
vector<pt_t> cross_point(circle_t f, circle_t g) {
	line_t l = {
		-2 * f.x + 2 * g.x,
		-2 * f.y + 2 * g.y,
		(f.x * f.x + f.y * f.y - f.r * f.r) - (g.x * g.x + g.y * g.y - g.r * g.r)
	};
	return cross_point(f, l);
}

// tangent points of f through p
// if size is 0, then p is strictly contained in f
// if size is 1, then p is on f
// otherwise size is 2
vector<pt_t> tangent_point(circle_t f, pt_t p) {
	vector<pt_t> ret;
	double d2 = norm2(pt_t({ f.x, f.y }) - p);
	double r2 = d2 - f.r * f.r;
	if (fge(r2, 0)) {
		circle_t g = { p.x, p.y, fsqrt(r2) };
		ret = cross_point(f, g);
	}
	return ret;
}

// tangent lines of f through p
// if size is 0, then p is strictly contained in f
// if size is 1, then p is on f
// otherwise size is 2
vector<line_t> tangent_line(circle_t f, pt_t p) {
	vector<pt_t> qs = tangent_point(f, p);
	vector<line_t> ret(qs.size());
	Loop(i, ret.size()) {
		ret[i] = solve_line(p, qs[i]);
	}
	return ret;
}

// tangent points on f through which there is a line tangent to g
// if size is 0, then one is strictly contained in the other
// if size is 1, then they are touched inside
// if size is 2, then they are crossed
// if size is 3, then they are touched outside
// otherwise size is 4
vector<pt_t> tangent_point(circle_t f, circle_t g) {
	vector<pt_t> ret;
	double d2 = norm2({ g.x - f.x, g.y - f.y });
	vector<double> r2(2);
	r2[0] = d2 - f.r * f.r + 2 * f.r * g.r;
	r2[1] = d2 - f.r * f.r - 2 * f.r * g.r;
	Loop(k, 2) {
		if (fge(r2[k], 0)) {
			circle_t g2 = { g.x, g.y, fsqrt(r2[k]) };
			vector<pt_t> buf = cross_point(f, g2);
			Loop(i, buf.size()) ret.push_back(buf[i]);
		}
	}
	return ret;
}

// common tangent lines between two circles
// if size is 0, then one is strictly contained in the other
// if size is 2, then they are crossed
// if size is 3, then they are touched
// otherwise size is 4
vector<line_t> tangent_line(circle_t f, circle_t g) {
	vector<pt_t> qs = tangent_point(f, g);
	vector<line_t> ret(qs.size());
	Loop(i, ret.size()) {
		ret[i] = tangent_line(f, qs[i]).front();
	}
	return ret;
}

int main() {
	cout << fixed << setprecision(12);
	circle_t f;
	cin >> f.x >> f.y >> f.r;
	circle_t g;
	cin >> g.x >> g.y >> g.r;
	vector<pt_t> ans = tangent_point(f, g);
	sort(ans.begin(), ans.end());
	Loop(i, ans.size()) {
		cout << ans[i].x << " " << ans[i].y << endl;
	}
}