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 <iomanip>
#include <cmath>
#include <array>
#include <algorithm>
#include <cassert>
#include <vector>

using Number = double;

const Number EPS = 1e-10;
const Number INF = 1e10;
const Number PI = acos(-1.0);

inline int sign(Number x) { return (x < -EPS) ? -1 : (x > EPS) ? +1 : 0; }
inline bool equal(Number a, Number b) { return sign(a - b) == 0; }

// change between degree and radian
inline Number to_radian(const Number degree) { return degree * PI / 180.0; }
inline Number to_degree(const Number radian) { return radian * 180.0 / PI; }


/**
 * Point in two dimensional
 */
class Point {
public:
    Number x, y;

    Point() {}
    Point(Number x, Number y) : x(x), y(y) {}

    // Arithmetic operator between points
    Point operator+(const Point &rhs) const {
        return Point(this->x + rhs.x, this->y + rhs.y);
    }
    Point operator-(const Point &rhs) const {
        return Point(this->x - rhs.x, this->y - rhs.y);
    }
    Point operator*(const Point &rhs) const { // cross product between points
        return Point(this->x * rhs.x - this->y * rhs.y,
                     this->x * rhs.y + this->y * rhs.x);
    }

    // Unary operator and compound assignment operator
    Point operator-() const {
        return Point(-this->x, -this->y);
    }
    Point& operator+=(const Point &rhs) {
        return *this = *this + rhs;
    }
    Point& operator-=(const Point &rhs) {
        return *this = *this - rhs;
    }

    // Arithmetic operator between point and number
    Point operator*(Number rhs) const {
        return Point(this->x * rhs, this->y * rhs);
    }
    Point operator/(Number rhs) const {
        return Point(this->x / rhs, this->y / rhs);
    }

    // Comparison operation
    bool operator==(const Point &rhs) const {
        return sign(this->x - rhs.x) == 0 && sign(this->y - rhs.y) == 0;
    }
    bool operator<(const Point &rhs) const {
        return (this->x < rhs.x) || (this->x == rhs.x && this->y < rhs.y);
    }

    // Other operator
    Number abs(void) const {
        return sqrt(this->x * this->x + this->y * this->y);
    }
    Number abs2(void) const {
        return this->x * this->x + this->y * this->y;
    }
    Number arg(void) const {
        return atan2(this->y, this->x);
    }
    Number dot(const Point &rhs) {
        return this->x * rhs.x + this->y * rhs.y;
    }
    Point rotate90(void) const {
        return Point(-this->y, this->x);
    }
    Point rotate(double angle) const {
        return Point(cos(angle) * this->x - sin(angle) * this->y,
                     sin(angle) * this->x + cos(angle) * this->y);
    }

};
inline Number dot(const Point &p1, const Point &p2) {
    return p1.x * p2.x + p1.y * p2.y;
}
inline Number abs_cross(const Point &p1, const Point &p2) {
    return p1.x * p2.y - p1.y * p2.x;
}
// Output of a point
std::ostream& operator<<(std::ostream &os, const Point &p) {
    return os << p.x << ' ' << p.y;
}
// Input of a point
std::istream& operator>>(std::istream &is, Point &p) {
    return is >> p.x >> p.y;
}

// Counter-Clockwise predicate (a, b, c)
enum CCW {
    COUNTER_CLOCKWISE = 1,      // counter clockwise
    CLOCKWISE         = -1,     // clockwise
    ONLINE_FRONT      = 2,      // a--c--b on line
    ONLINE_BACK       = -2,      // c--a--b on line
    ON_SEGMENT        = 0,     // a--b--c on line
};
CCW ccw(const Point &a, Point b, Point c) {
    b -= a;  c -= a;
    if (abs_cross(b, c) > EPS) return COUNTER_CLOCKWISE;
    if (abs_cross(b, c) < -EPS) return CLOCKWISE;
    if (dot(b, c) < 0)       return ONLINE_BACK;
    if (b.abs2() < c.abs2())   return ONLINE_FRONT;
    return ON_SEGMENT;
}


/**
 * Line in two dimensional
 */
class Line : public std::array<Point, 2> {
public:
    Line() {}
    Line(const Point &p1, const Point &p2) {
        (*this)[0] = p1;
        (*this)[1] = p2;
    }
};
// Input of a line
std::istream& operator>>(std::istream &is, Line &l) {
    return is >> l[0] >> l[1];
}
std::ostream& operator<<(std::ostream &os, const Line &l) {
    return os << l[0] << ' ' << l[1];
}
inline CCW ccw(const Line &l, const Point &p) {
    return ccw(l[0], l[1], p);
}


/**
 * Segment in two dimensional
 */
class Segment : public Line {
public:
    Segment() {}
    Segment(const Point &p1, const Point &p2) : Line(p1, p2) {}
};


/**
 * Circle in two dimensional
 */
class Circle : public Point {
public:
    Number r;
    Circle() {}
    Circle(const Point &p, Number r = 0.0) : Point(p), r(r) {}
};
// Input of a circle
std::istream& operator>>(std::istream &is, Circle &c) {
    return is >> c.x >> c.y >> c.r;
}



/**
 * Intersection testing
 */
Point Projection(const Line &l, const Point &p) {
    Point dir = l[1] - l[0];
    Number t = dot(p - l[0], dir) / dir.abs2();
    return l[0] + dir * t;
}
inline Point Reflection(const Line &l, const Point &p) {
    return Projection(l, p) * 2.0 - p;
}

inline bool IsOrthogonal(const Line &l1, const Line &l2) {
    return equal(dot(l1[0] - l1[1], l2[0] - l2[1]), 0.0);
}
inline bool IsParallel(const Line &l1, const Line &l2) {
    return equal(abs_cross(l1[0] - l1[1], l2[0] - l2[1]), 0.0);
}

inline bool IsIntersect(const Line &l, const Point &p) {
    return abs(ccw(l[0], l[1], p)) != 1;
}
inline bool IsIntersect(const Segment &s, const Point &p) {
    return ccw(s[0], s[1], p) == 0;
}
inline bool IsIntersect(const Line &l1, const Line l2) {
    return !IsParallel(l1, l2) || IsParallel(l1, Line(l1[0], l2[0]));
}
inline bool IsIntersect(const Line &l, const Segment &s) {
    return abs_cross(l[1] - l[0], s[0] - l[0]) *
        abs_cross(l[1] - l[0], s[1] - l[0]) < EPS;
}
inline bool IsIntersect(const Segment &s1, const Segment &s2) {
    return ccw(s1[0], s1[1], s2[0]) * ccw(s1[0], s1[1], s2[1]) <= 0 &&
        ccw(s2[0], s2[1], s1[0]) * ccw(s2[0], s2[1], s1[1]) <= 0;
}
inline bool IsIntersect(const Circle &c, const Point &p) { // p is in interior or boundary
    return (c - p).abs() <= c.r + EPS;
}
inline bool IsIntersect(const Circle &c, const Line &l) {
    return IsIntersect(c, Projection(l, c));
}
inline bool IsIntersect(const Circle &c1, const Circle &c2) {
    return sign(c1.r + c2.r - (c1 - c2).abs()) >= 0 &&
        sign((c1 - c2).abs() - abs(c1.r - c2.r) >= 0);
}


/**
 * Distance and Intersection point
 */
inline Number Distance(const Point &p1, const Point &p2) {
    return (p1 - p2).abs();
}
inline Number Distance(const Line &l, const Point &p) {
    return (p - Projection(l, p)).abs();
}
inline Number Distance(const Segment &s, const Point &p) {
    if (sign(dot(s[1] - s[0], p - s[0])) == -1) return (p - s[0]).abs();
    if (sign(dot(s[0] - s[1], p - s[1])) == -1) return (p - s[1]).abs();
    return (p - Projection(s, p)).abs();
}
inline Number Distance(const Line &l1, const Line &l2) {
    return IsIntersect(l1, l2) ? 0 : Distance(l1, l2[0]);
}
inline Number Distance(const Line &l, const Segment &s) {
    if (IsIntersect(l, s)) return 0.0;
    return std::min(Distance(l, s[0]), Distance(l, s[1]));
}
inline Number Distance(const Segment &s1, const Segment &s2) {
    if (IsIntersect(s1, s2)) return 0.0;
    return std::min({Distance(s1, s2[0]), Distance(s1, s2[1]),
                Distance(s2, s1[0]), Distance(s2, s1[1])});
}

Point CrossPoint(const Line &s1, const Line &s2) {
    Point base = s2[1] - s2[0];
    Number d1 = abs(abs_cross(base, s1[0] - s2[0]));
    Number d2 = abs(abs_cross(base, s1[1] - s2[0]));
    Number t = d1 / (d1 + d2);
    return s1[0] + (s1[1] - s1[0]) * t;
}
std::vector<Point> CrossPoint(const Circle &c, const Line &l) {
    if (!IsIntersect(c, l))
        return std::vector<Point>();
    Point mid = Projection(l, c);
    if (equal((c - mid).abs(), c.r))
        return {mid};

    Point e = (l[1] - l[0]) / (l[1] - l[0]).abs();
    Number len = sqrt(c.r * c.r - (mid - c).abs2());
    return {mid + e * len, mid - e * len};
}
std::vector<Point> CrossPoint(const Circle &c1, const Circle &c2) {
    if (!IsIntersect(c1, c2))
        return std::vector<Point>();
    Number d = Distance(c1, c2);
    Number r1_cos = (d * d + c1.r * c1.r - c2.r * c2.r) / (2.0 * d);
    Number h = sqrt(c1.r * c1.r - r1_cos * r1_cos);
    Point base = c1 + (c2 - c1) * r1_cos / d;
    Point dir = (c2 - c1).rotate90() * h / d;
    if (dir == Point(0, 0))
        return {base};
    return {base + dir, base - dir};
}

// the tangent line from a point to a circle
std::vector<Point> TangentPoint(const Circle &c, const Point &p) {
    Number x = (p - c).abs2();
    Number d = x - c.r * c.r;
    if (sign(d) == -1) // no point
        return std::vector<Point>();
    d = std::max(d, 0.0);
    Point q1 = (p - c) * (c.r * c.r / x);
    Point q2 = ((p - c) * (-c.r * sqrt(d) / x)).rotate90();
    if (q2 == Point(0, 0)) return {c + q1};
    return {c + q1 - q2, c + q1 + q2};
}
// common tangent lines to two circles
std::vector<Line> CommonTangent(const Circle &c1, const Circle &c2) {
    if (equal(Distance(c1, c2), abs(c1.r - c2.r))) { // two circle contact internally
        Point cross_point = CrossPoint(c1, c2)[0];
        Point up = (cross_point - c1).rotate90();
        return {Line(cross_point + up, cross_point - up)};
    }

    std::vector<Line> list;
    // caluculate outer tangent
    if (equal(c1.r, c2.r)) {
        Point dir = c2 - c1;
        dir = (dir * (c1.r / dir.abs())).rotate90();
        list.emplace_back(Line(c1 + dir, c2 + dir));
        list.emplace_back(Line(c1 - dir, c2 - dir));
    }
    else {
        Point p = (c1 * (-c2.r)) + (c2 * c1.r);
        p = p * (1 / (c1.r - c2.r));
        std::vector<Point> ps = TangentPoint(c1, p);
        std::vector<Point> qs = TangentPoint(c2, p);
        const int N = std::min(ps.size(), qs.size());
        for (int i = 0; i < N; ++i)
            list.emplace_back(Line(ps[i], qs[i]));
    }

    // caluculate inner tangent
    if (equal(Distance(c1, c2), c1.r + c2.r)) { // two circle contact one point
        Point cross_point = CrossPoint(c1, c2)[0];
        Point up = (cross_point - c1).rotate90();
        list.emplace_back(Line(cross_point + up, cross_point - up));
    }
    else {
        Point p = (c1 * c2.r) + (c2 * c1.r);
        p = p * (1 / (c1.r + c2.r));
        std::vector<Point> ps = TangentPoint(c1, p);
        std::vector<Point> qs = TangentPoint(c2, p);
        const int N = std::min(ps.size(), qs.size());
        for (int i = 0; i < N; ++i)
            list.emplace_back(Line(ps[i], qs[i]));
    }

    return list;
}


int main()
{
    std::cout << std::fixed << std::setprecision(15);

    Circle c1, c2;

    std::cin >> c1 >> c2;
    std::vector<Line> lines = CommonTangent(c1, c2);
    std::vector<Point> ans;
    for (auto l : lines) {
        auto cross_points = CrossPoint(c1, l);
        for (auto p : cross_points) {
            if (find(ans.begin(), ans.end(), p) == ans.end())
                ans.emplace_back(p);
        }
    }

    std::sort(ans.begin(), ans.end());
    for (auto p : ans)
        std::cout << p << '\n';

    return 0;
}