Problem: For given two circles $c1$ and $c2$, print the coordinates of the cross points of them.

Constraints

* The given circle have at least one cross point and have different center coordinates.
* $-10,000 \leq c1x, c1y, c2x, c2y \leq 10,000$
* $1 \leq c1r, c2r \leq 10,000$

Input

The input is given in the following format.

$c1x\; c1y\; c1r$
$c2x\; c2y\; c2r$


$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle. $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle. All input values are given in integers.

Output

Print the coordinates ($x1$, $y1$) and ($x2$, $y2$) of the cross points $p1$ and $p2$ respectively in the following rules.

* If there is one cross point, print two coordinates with the same values.
* 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 0.000001.

Examples

Input

0 0 2
2 0 2


Output

1.00000000 -1.73205080 1.00000000 1.73205080


Input

0 0 2
0 3 1


Output

0.00000000 2.00000000 0.00000000 2.00000000

Solution (in CPP):

Solution:
#include<iostream>
#include<iomanip>
#include<cstdio>
#include<cmath>
#include<vector>
#include<utility>
#include<assert.h>
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

class Point {
    public:
    double x, y;
    
    Point(double x = 0, double y = 0): x(x), y(y) {}
    
    Point operator + (Point p) {return Point(x + p.x, y + p.y); }
    Point operator - (Point p) {return Point(x - p.x, y - p.y); }
    Point operator * (double a) {return Point(a * x, a * y); }
    Point operator / (double a) {return Point(x / a, y / a); }
    
    double abs() { return sqrt(norm()); }
    double norm() { return x * x + y * y; }
    
    bool operator < (const Point &p) const {
        return x != p.x ? x < p.x : y < p.y;
    }
    
    bool operator == (const Point &p) const {
        return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS; 
    }
};

struct Segment {
    Point p1, p2;
};

typedef Segment Line;

class Circle {
    public:
    Point c;
    double r;
    Circle(Point c = Point(), double r = 0.0): c(c), r(r) {}
};

typedef Point Vector;
typedef vector<Point> Polygon;

double norm(Vector a) {
    return a.x * a.x + a.y * a.y;
}

double abs(Vector a) {
    return sqrt(norm(a));
}

double dot(Vector a, Vector b) {
    return a.x * b.x + a.y * b.y;
}

double cross(Vector a, Vector b) {
    return a.x * b.y - a.y * b.x;
}

bool isOrthogonal(Vector a, Vector b) {
    return equals(dot(a, b), 0.0);
}

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
    return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
    return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b) {
    return equals(cross(a, b), 0.0);
}

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
    return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(Segment s1, Segment s2) {
    return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

Point project(Segment s, Point p) {
    Vector base = s.p2 - s.p1;
    double r = dot(p - s.p1, base) / norm(base);
    return s.p1 + base * r;
}

Point reflect(Segment s, Point p) {
    return p + (project(s, p) - p) * 2.0;
}

double getDistance(Point a, Point b) {
    return abs(a - b);
}

double getDistanceLP(Line l, Point p) {
    return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p) {
    if ( dot(s.p2 - s.p1, p - s.p1) < 0.0 ) return abs(p - s.p1);
    if ( dot(s.p1 - s.p2, p - s.p2) < 0.0 ) return abs(p - s.p2);
    return getDistanceLP(s, p);
}

static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

int ccw(Point p0, Point p1, Point p2) {
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if ( cross(a, b) > EPS ) return COUNTER_CLOCKWISE;
    if ( cross(a, b) < -EPS ) return CLOCKWISE;
    if ( dot(a, b) < -EPS ) return ONLINE_BACK;
    if ( a.norm() < b.norm() ) return ONLINE_FRONT;
    
    return ON_SEGMENT;
}

bool intersect(Point p1, Point p2, Point p3, Point p4) {
    return ( ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
             ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}

bool intersect(Segment s1, Segment s2) {
    return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

bool intersect(Circle c, Line l) {
    return (getDistanceLP(l, c.c) - c.r) < EPS;
}

bool intersect(Circle c1, Circle c2) {
    return (getDistance(c1.c, c2.c) - c1.r - c2.r) < EPS;
}

double getDistance(Segment s1, Segment s2) {
    if ( intersect(s1, s2) ) return 0.0;
    return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
               min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPoint(Segment s1, Segment s2) {
    Vector base = s2.p2 - s2.p1;
    double d1 = abs(cross(base, s1.p1 - s2.p1));
    double d2 = abs(cross(base, s1.p2 - s2.p1));
    double t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}

pair<Point, Point> getCrossPoints(Circle c, Line l) {
    assert(intersect(c, l));
    Vector pr = project(l, c.c);
    Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
    double base = sqrt(c.r * c.r - norm(pr - c.c));
    return make_pair(pr + e * base, pr - e * base);
}

double arg(Vector p) { return atan2(p.y, p.x); }
Vector polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
    assert(intersect(c1, c2));
    double d = abs(c1.c - c2.c);
    double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
    double t = arg(c2.c - c1.c);
    return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

int main() {
    Circle c1, c2;
    cin >> c1.c.x >> c1.c.y >> c1.r
        >> c2.c.x >> c2.c.y >> c2.r;
    pair<Point, Point> P = getCrossPoints(c1, c2);
    Point p1, p2;
    if (P.first < P.second) {
        p1 = P.first; p2 = P.second;
    }else {
        p1 = P.second; p2 = P.first;
    }
    
        cout << fixed << setprecision(8) << p1.x << " "
             << fixed << setprecision(8) << p1.y << " "
             << fixed << setprecision(8) << p2.x << " "
             << fixed << setprecision(8) << p2.y << endl;
    
    return 0;
}