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 PB          push_back
#define PF          push_front
#define MP          make_pair
#define FI          first
#define SE          second
#define SIZE( A )   int( ( A ).size( ) )
#define ALL( A )    ( A ).begin( ), ( A ).end( )
#define ALLR( A )   ( A ).rbegin( ), ( A ).rend( )

using namespace std;

typedef long long           ll;
typedef unsigned long long  ull;
typedef long double         lf;
typedef pair< int, int >    pii;
typedef pair< ll, ll >      pll;
typedef vector< bool >      vb;
typedef vector< lf >        vd;
typedef vector< ll >        vll;
typedef vector< int >       vi;
typedef vector< pii >       vpii;

const lf EPS = 1e-9;
const lf PI = acos(-1.0);

struct pt {
  lf x, y;
  pt( ) { }
  pt( lf x, lf y ) : x( x ), y ( y ) { }
};

inline lf x( pt P ) { return P.x; }
inline lf y( pt P ) { return P.y; }

istream& operator >> ( istream& in, pt& p ) {
  lf x,y; in >> x >> y;
  p = pt(x,y); return in;
}

ostream& operator << ( ostream& out, const pt& p ) {
  out << double(p.x) << " " << double(p.y);
  return out;
}

pt operator + ( const pt& A, const pt& B ) {
  return pt( x(A)+x(B), y(A)+y(B) );
}

pt operator - ( const pt& A, const pt& B ) {
  return pt( x(A)-x(B), y(A)-y(B) );
}

pt operator * ( const lf& B, const pt& A ) {
  return pt( x(A)*B, y(A)*B );
}

pt operator * ( const pt& A, const lf& B ) {
  return pt( x(A)*B, y(A)*B  );
}

pt operator * ( const pt& A, const pt& B ) {
  return pt( x(A)*x(B)-y(A)*y(B), x(A)*y(B)+y(A)*x(B) );
}

pt operator / ( const pt& A, const lf& B ) {
  return pt( x(A)/B, y(A)/B );
}

inline lf dot( pt A, pt B ) {
  return x(A)*x(B) + y(A)*y(B);
}

inline lf cross( pt A, pt B ) {
  return x(A)*y(B) - y(A)*x(B);
}

inline lf norm( pt A ) {
  return x(A)*x(A) + y(A)*y(A);
}

inline lf abs( pt A ) {
  return sqrt( norm(A) );
}

inline lf arg( pt A ) {
  return atan2( y(A), x(A) );
}

inline pt exp( pt A ) {
  return pt( exp( x(A) )*cos( y(A) ), exp( x(A) )*sin( y(A) ) ) ;
}

inline bool same ( lf a, lf b ) {
  return a+EPS > b && b+EPS > a;
}

inline bool samePt ( pt A, pt B ) {
  return same ( x(A), x(B) ) && same ( y(A), y(B) );
}

inline pt rot ( pt p, lf ang ) { return p * exp ( pt(0,1) * ang ); }

inline lf dist ( pt A, pt B ) { return abs( B - A ); }

lf distToLine (pt p, pt A, pt B, pt &c) {
  lf u = dot( p-A , B-A ) / norm( B-A );
  c = A + u*( B-A );
  return dist( p , c );
}

pt refPoint(pt X, pt A, pt B) {
  pt aux; distToLine(X, A, B, aux);
  return X + lf(2.0)*(aux-X);
}

int intersectionCircles( pt c1, lf r1, pt c2, lf r2, pt &p1, pt &p2 ) {
  if( samePt( c1, c2 ) && same(r1,r2) ) return -1;
  lf sr = (r1 + r2) * (r1 + r2);
  lf dr = (r1 - r2) * (r1 - r2);
  lf d = norm( c2-c1 );
  if( d+EPS < dr || d > sr+EPS ) return 0;
  if ( same(d,sr) || same(d,dr) ) {
    p1 = p2 = c1 + (c2-c1)/sqrt(d) * r1;
    return 1;
  }
  pt tmp;
  tmp.x = (r1*r1 - r2*r2 + d ) / (2.0*sqrt(d)) ;
  tmp.y = sqrt( r1*r1 - tmp.x*tmp.x ) ;
  lf ang = arg( c2 - c1 );
  p1 = rot( tmp, ang ) + c1;
  p2 = refPoint( p1, c1, c2 );
  return 2;
}

pt c1,c2,p1,p2;
lf r1,r2;

int main( ) {

  #ifdef LOCAL
    freopen( "input", "r", stdin );
    //freopen( "output", "w", stdout );
  #else
    //freopen( "input", "r", stdin );
    //freopen( "output", "w", stdout );
    ios_base::sync_with_stdio( 0 );
    cin.tie( 0 );
  #endif
  cout << fixed << setprecision(10);
  while( cin >> c1 >> r1 >> c2 >> r2 ) {
    intersectionCircles( c1, r1, c2, r2, p1, p2 );
    if( x(p1) > x(p2)+EPS ) swap( p1, p2 );
    if( same( x(p1), x(p2) ) ) {
      if( y(p1) > y(p2)+EPS ) swap( p1, p2 );
    }
    cout << p1 << " " << p2 << '\n';
  }

  return 0;
}