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>
#define FOR(i, a, n) for(ll i = (ll)a; i < (ll)n; i++)
#define rep(i, n) FOR(i, 0, n)
#define ALL(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;

constexpr ll mod = 1e9 + 7;

template <class T> inline bool chmax(T &a, const T b) {
    if(a >= b) return false;
    a = b;
    return true;
}
template <class T> inline bool chmin(T &a, const T b) {
    if(a <= b) return false;
    a = b;
    return true;
}

/*-------------------------------------------*/

struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
    Point operator+(const Point &p) { return Point{x + p.x, y + p.y}; }
    Point operator-(const Point &p) { return Point{x - p.x, y - p.y}; }
    Point operator*(const double k) { return Point{x * k, y * k}; }
    Point operator/(const double k) { return Point{x / k, y / k}; }

    double norm() { return x * x + y * y; }
    double abs() { return sqrt(norm()); }
};
typedef Point Vector;
struct Segment {
    Point p1, p2;
};
typedef Segment Line;
struct Circle {
    Point c;
    double r;
    Circle(Point c = Point(), double r = 0) : c(c), r(r) {}
};
typedef vector<Point> Polygon;

double norm(Vector v) { return v.x * v.x + v.y * v.y; }
double abs(Vector v) { return sqrt(norm(v)); }

double arg(Vector v) { return atan2(v.y, v.x); }
Vector polar(double a, double r) { return Vector(cos(r) * a, sin(r) * 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 dot(a, b) == 0; }
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
    return isOrthogonal(a1 - a2, b1 - b2);
}
bool isOrthogonal(Line l1, Line l2) {
    return isOrthogonal(l1.p2, l1.p1, l2.p2, l2.p1);
}

bool isParallel(Vector a, Vector b) { return cross(a, b) == 0; }
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
    return isParallel(a1 - a2, b1 - b2);
}
bool isParallel(Line l1, Line l2) {
    return isParallel(l1.p1, l1.p2, l2.p1, l2.p2);
}

Point project(Line l, Point p) {
    Vector base = l.p2 - l.p1;
    double r = dot(p - l.p1, base) / base.norm();
    return l.p1 + base * r;
}
Point reflect(Line l, Point p) { return p + (project(l, p) - p) * 2; }

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

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) return abs(p - s.p1);
    if(dot(s.p1 - s.p2, p - s.p2) < 0) return abs(p - s.p2);
    return getDistanceLP(s, p);
}
double getDistance(Segment s1, Segment s2) {
    if(intersect(s1, s2)) return 0;
    return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2),
                getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)});
}

Point getCrossPoint(Line l1, Line l2) {
    Vector base = l2.p2 - l2.p1;
    double d1 = abs(cross(base, l1.p1 - l2.p1));
    double d2 = abs(cross(base, l1.p2 - l2.p1));
    double t = d1 / (d1 + d2);
    return l1.p1 + (l1.p2 - l1.p1) * t;
}

bool intersect(Circle c, Line l) { return c.r >= getDistanceLP(l, c.c); }
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);
}

bool intersect(Circle c1, Circle c2) {
    return abs(c1.c - c2.c) <= c1.r + c2.r && c1.r <= c2.r + abs(c1.c - c2.c) &&
           c2.r <= c1.r + abs(c1.c - c2.c);
}
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;
    cin >> c2.c.x >> c2.c.y >> c2.r;
    pair<Point, Point> ret = getCrossPoints(c1, c2);
    Point a = ret.first, b = ret.second;
    if(a.x == b.x ? a.y > b.y : a.x > b.x) swap(a, b);
    printf("%.10f %.10f %.10f %.10f\n", a.x, a.y, b.x, b.y);
}