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<bits/stdc++.h>
using namespace std;
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

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(x * a, y * a);}
    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 equals(x, p.x) && equals(y, p.y);
    }
};typedef Point Vector;

struct Circle {
    Point c;
    double r;
    Circle(Point c,double r):c(c), r(r){}
};

struct Segment {
    Point p1, p2;
    Segment(Point p1, Point p2):p1(p1), p2(p2){}
};typedef Segment Line;

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;
}

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

int ccw(Point p0, Point p1, Point p2){
    Vector a = p1 - p0, b = p2 - p0;
    if (cross(a, b) > EPS) return 1;
    if (cross(a, b) < -EPS) return -1;
    if (dot(a, b) < -EPS) return 2;
    if (a.norm() < b.norm()) return -2;
    return 0;
}

bool intersection(Point p0, Point p1, Point p2, Point p3){
    if (ccw(p0, p1, p2) == 0 || ccw(p0, p1, p3) == 0 || 
        ccw(p2, p3, p0) == 0 || ccw(p2, p3, p1) == 0)
        return true;
    if (ccw(p0, p1, p2) * ccw(p0, p1, p3) == -1 && ccw(p2, p3, p0) * ccw(p2, p3, p1) == -1)
        return true;
    return false;
}

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

int main(){
    int c1x, c1y, c1r, c2x, c2y, c2r;
    cin >> c1x >> c1y >> c1r;
    cin >> c2x >> c2y >> c2r;
    Circle c1 = Circle(Point(c1x, c1y), c1r);
    Circle c2 = Circle(Point(c2x, c2y), c2r);
    Vector v = (c2.c - c1.c);
    double cos = (v.abs()*v.abs() + c1.r*c1.r - c2.r*c2.r)/(2*v.abs()*c1.r);
    v = v / (c2.c - c1.c).abs();
    v = v * c1.r * cos;
    Vector v_par = Vector(-v.y, v.x);
    Line l = Line(c1.c+v, c1.c+v+v_par);
    pair<Point, Point> p = getCrossPoints(c1, l);
    if (p.first.x < p.second.x)
        cout << fixed << setprecision(10) 
        << p.first.x << " " << p.first.y << " "
        << p.second.x << " " << p.second.y << endl;
    else if(p.first.x > p.second.x)
        cout << fixed << setprecision(10) 
        << p.second.x << " " << p.second.y << " "
        << p.first.x << " " << p.first.y << endl;
    else if (equals(p.first.x, p.second.x))
        if (equals(p.first.y, p.second.y))
        cout << fixed << setprecision(10) 
        << p.first.x << " " << p.first.y << " "
        << p.second.x << " " << p.second.y << endl;
        else if (p.first.y < p.second.y)
        cout << fixed << setprecision(10) 
        << p.first.x << " " << p.first.y << " "
        << p.second.x << " " << p.second.y << endl;
        else if(p.first.y > p.second.y)
        cout << fixed << setprecision(10) 
        << p.second.x << " " << p.second.y << " "
        << p.first.x << " " << p.first.y << endl;
}