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;
/*{{{*/  //template
#define rep(i,n) for(int i=0;i<n;i++)
constexpr int INF = numeric_limits<int>::max()/2;
constexpr long long LINF = numeric_limits<long long>::max()/3;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) (v).begin(),(v).end()
#define sz(x) (int)(x).size()
#define debug(x) cerr<<#x<<":"<<x<<endl
#define debug2(x,y) cerr<<#x<<","<<#y":"<<x<<","<<y<<endl
//struct fin{ fin(){ cin.tie(0); ios::sync_with_stdio(false); } } fin_;
struct Double{ double d; explicit Double(double x) : d(x){} };
ostream& operator<<(ostream& os,const Double x){ os << fixed << setprecision(20) << x.d; return os; }
template<typename T> ostream& operator<<(ostream& os,const vector<T>& vec){ os << "["; for(const auto& v : vec){ os << v << ","; } os << "]"; return os; }
template<typename T,typename U> ostream& operator<<(ostream& os,const pair<T,U>& p){ os << "(" << p.first << ","<< p.second <<")"; return os; }
template<typename T> ostream& operator<<(ostream& os,const set<T>& st){ os<<"{"; for(T v:st) os<<v<<","; os <<"}"; return os; }
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
ll gcd(ll a,ll b){ if(b==0) return a; else return gcd(b,a%b); }
//constexpr double eps = 1e-14; 
constexpr double eps = 1e-10; 
constexpr ll mod = 1e9+7;
const int dx[]={1,0,-1,0} ,dy[] = {0,1,0,-1};
/*}}}*/

namespace Geometry{
    struct Point{
        double x,y;
        Point(){}
        Point(double a,double b) : x(a),y(b){}
        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 k){
            return Point(x*k,y*k);
        }
    };
    using Vector = Point;
    struct Circle{
        Point c;
        double r;
        Circle(){}
        Circle(Point p,double c) : c(p),r(c){}
        Circle(double a,double b,double c) : c(Point(a,b)) , r(c){}
    };

    // for debug
    ostream& operator<<(ostream& os,const Point& p){
        os << "{" << p.x <<"," << p.y <<"}";
        return os;
    }
    ostream& operator<<(ostream& os,const Circle& c){
        os << "{(" << c.c.x << "," << c.c.y <<")," << c.r << "}";
        return os;
    }

    // ?????????????????£??????
    Vector normalize(Vector v){
        double t = sqrt(v.x*v.x+v.y*v.y);
        return Vector(v.x/t,v.y/t);
    }

    // ?????¨???????????¢
    inline double distance(Point a,Point b){
        double x=a.x-b.x;
        double y=a.y-b.y;
        return sqrt(x*x+y*y);
    }

    // ????????????
    pair<Point,Point> getCrossPoint(Circle c1,Circle c2){
        double d = distance(c1.c,c2.c);
        Vector v = normalize(c2.c - c1.c);  // ??£????????????????????????????????????
        Vector dualv = Vector(-v.y,v.x);    // v??¨?????´???????????????
        double Cos = (c1.r*c1.r+d*d-c2.r*c2.r) / (2*c1.r*d);
        double Sin = sqrt(1-Cos*Cos);
        Point a = c1.c + v*Cos*c1.r + dualv*Sin*c1.r;
        Point b = c1.c + v*Cos*c1.r - dualv*Sin*c1.r;
        return make_pair(a,b);
    }
};

int main(){
    double x1,y1,r1,x2,y2,r2;
    cin >> x1 >> y1 >> r1;
    cin >> x2 >> y2 >> r2;

    using namespace Geometry;
    auto ans = getCrossPoint(Circle(x1,y1,r1),Circle(x2,y2,r2));
    if(ans.fi.x > ans.se.x or (ans.fi.x == ans.se.x and ans.fi.y > ans.se.y)) swap(ans.fi,ans.se);

    cout << Double(ans.fi.x) << " " << Double(ans.fi.y) << " ";
    cout << Double(ans.se.x) << " " << Double(ans.se.y) << endl;
}