Problem: Sha, Nero, Eri, and Ko, who entered the University of Aizu Elementary School (Aizu University and Small), decided to participate in a programming contest called IPPC in order to play an active role as a competition programmer. However, IPPCs are required to participate in the contest as a team of three people, and it is not possible to form a team of four people. Therefore, they decided to form a team of two people and participate in a programming contest called IPOCH where two people can participate in one group.

Although the teams have been separated, their abilities are competing and they are good practice partners for each other.

One day their coach bought a whole cake to put in. They decided to eat it at Sha's house. However, when I got home and opened the box, the cake was deformed, and when viewed from above, it looked like a convex polygon instead of a circle. It seems that it was bad to have Nero carry it. There is a strawberry on top of the cake. For the time being, it was decided to cut this cake with a knife in half along a straight line through the strawberries in order to divide it into two teams. It is against their aesthetic sense to take the strawberries first before cutting the cake.

Your job is to divide a convex polygon K given on a two-dimensional plane by a straight line L passing through the origin (0, 0), and then divide the straight line L so that the areas of the two convex polygons created by the division are equal. To determine. If there are more than one, one of them will do.
<image>

Constraints

* All inputs are integers
* 3 ≤ N ≤ 20
* -100 ≤ xi ≤ 100 (1 ≤ i ≤ N)
* -100 ≤ yi ≤ 100 (1 ≤ i ≤ N)
* The number of test cases does not exceed 1,000.

Input

The input consists of multiple test cases. Each test case follows the format below.


N
x1 y1
x2 y2
...
xN yN


N is the number of vertices of the given convex polygon K. The points (xi, yi) (1 ≤ i ≤ N) are all the coordinates of the vertices that make up the convex polygon K and are different from each other. These are given in counterclockwise order. Also, a point on any side of the convex polygon K has a distance of 1 or more from the origin, and the convex polygon K always contains the origin. The end of input is indicated by one line containing one 0. Note that the three different points given by the input, including the origin, can be collinear.

Output

Output the point A (Ax, Ay) on the straight line L in the following format. However, the distance between point A and the origin must be 1 or more.


Ax Ay


When the convex polygon K is divided by the origin and a straight line passing through this point A, the difference in area between the two convex polygons must be less than 10-5. I want the coordinates of point A to be output 15 digits after the decimal point.

Example

Input

4
-100 -100
100 -100
100 100
-100 100
4
-99 -100
100 -100
100 100
-99 100
4
-100 -99
100 -99
100 100
-100 100
14
-99 -70
-92 -79
10 -98
37 -100
62 -95
77 -69
88 -47
92 -10
96 28
100 91
42 92
-62 92
-88 91
-98 64
0


Output

100.000000000000000 0.000000000000000
100.000000000000000 0.000000000000000
0.000000000000000 100.000000000000000
-96.983291994836122 66.745111613942484

Solution (in CPP):

Solution:
using namespace std;
#include<iostream>
#include<algorithm>
#include<vector>
#include<cmath>
#include<iomanip>
const double EPS=1e-10;
bool eq(double a,double b){return abs(a-b)<EPS;}
struct Point{
	double x,y;
	Point(double x_=0,double y_=0):x(x_),y(y_){}
	Point operator-()const{return Point(-x,-y);}
	Point operator+(const Point&p)const{return Point(x+p.x,y+p.y);}
	Point operator-(const Point&p)const{return Point(x-p.x,y-p.y);}
	Point operator*(const double k)const{return Point(x*k,y*k);}
	Point operator/(const double k)const{return Point(x/k,y/k);}
	bool operator<(const Point&p)const{return eq(x,p.x)?y<p.y:x<p.x;}
	bool operator==(const Point&p)const{return eq(x,p.x)&&eq(y,p.y);}
};
istream&operator>>(istream&is,Point&p){return is>>p.x>>p.y;}
ostream&operator<<(ostream&os,const Point&p){return os<<fixed<<setprecision(9)<<p.x<<' '<<p.y;}
struct Line{
	Point p1,p2;
	Line(Point p1_=Point(),Point p2_=Point()):p1(p1_),p2(p2_){}
};
struct Segment:Line{
	Segment(Point p1_=Point(),Point p2_=Point()):Line(p1_,p2_){}
};
struct Circle{
	Point o;
	double r;
	Circle(Point o_=Point(),double r_=0):o(o_),r(r_){}
};
using Polygon=vector<Point>;
//function list begin
Point vec(const Line&);
double norm(const Point&);
double norm(const Line&);
double abs(const Point&);
double abs(const Line&);
double arg(const Point&);
double arg(const Line&);
double arg(const Point&,const Point&,const Point&);//a->b->c
double dot(const Point&,const Point&);
double cross(const Point&,const Point&);
Point polar(const double,const double);
Point rotate(const Point&,const double);
enum{ONLINE_FRONT=-2,CLOCKWISE=-1,ON_SEGMENT=0,COUNTER_CLOCKWISE=1,ONLINE_BACK=2};
int ccw(const Point&,const Point&,const Point&);
int ccw(const Line&,const Point&);
bool orthogonal(const Point&,const Point&);
bool orthogonal(const Line&,const Line&);
bool parallel(const Point&,const Point&);
bool parallel(const Line&,const Line&);
bool intersect(const Line&,const Point&);
bool intersect(const Line&,const Line&);
bool intersect(const Segment&,const Point&);
bool intersect(const Segment&,const Segment&);
bool intersect(const Line&,const Segment&);
bool intersect(const Segment&,const Line&);
bool intersect(const Circle&,const Point&);
int intersect(const Circle&,const Line&);//count contacts
int intersect(const Circle&,const Segment&);
int intersect(const Circle&,const Circle&);
double distance(const Point&,const Point&);
double distance(const Line&,const Point&);
double distance(const Line&,const Line&);
double distance(const Segment&,const Point&);
double distance(const Segment&,const Segment&);
double distance(const Line&,const Segment&);
double distance(const Segment&,const Line&);
double distance(const Circle&,const Point&);
double distance(const Circle&,const Line&);
double distance(const Circle&,const Segment&);
double distance(const Circle&,const Circle&);
Point projection(const Line&,const Point&);
Point reflection(const Line&,const Point&);
Point crosspoint(const Line&,const Line&);
pair<Point,Point>crosspoint(const Circle&,const Line&);
pair<Point,Point>crosspoint(const Circle&,const Segment&);
pair<Point,Point>crosspoint(const Circle&,const Circle&);
pair<Point,Point>tangent(const Circle&,const Point&);
vector<Line>tangent(const Circle&,const Circle&);
bool is_convex(const Polygon&);
Polygon convex_full(Polygon,bool=false);
enum{OUT,ON,IN};
int contain(const Polygon&,const Point&);
int contain(const Circle&,const Point&);
int contain(const Circle&,const Segment&);
Polygon convex_cut(const Polygon&,const Line&);
double diameter(Polygon);
double area(const Polygon&);
double area(const Polygon&,const Line&);
double area(const Polygon&,const Circle&);
//function list end
Point vec(const Line&s){return s.p2-s.p1;}
double norm(const Point&p){return p.x*p.x+p.y*p.y;}
double norm(const Line&s){return norm(vec(s));}
double abs(const Point&p){return hypot(p.x,p.y);}
double abs(const Line&s){return abs(vec(s));}
double arg(const Point&p){return atan2(p.y,p.x);}
double arg(const Line&s){return arg(vec(s));}
double arg(const Point&a,const Point&b,const Point&c){
	double A=arg(b-a),B=arg(c-b);
	double theta=abs(A-B);
	return min(theta,2*M_PI-theta);
}
double dot(const Point&a,const Point&b){return a.x*b.x+a.y*b.y;}
double cross(const Point&a,const Point&b){return a.x*b.y-a.y*b.x;}
Point polar(const double r,const double theta){return Point(cos(theta),sin(theta))*r;}
Point rotate(const Point&p,const double theta){
	return Point(p.x*cos(theta)-p.y*sin(theta),p.x*sin(theta)+p.y*cos(theta));
}
int ccw(const Point&a,const Point&b,const Point&c){
	Point p=b-a,q=c-a;
	return cross(p,q)>EPS?COUNTER_CLOCKWISE
		:cross(p,q)<-EPS?CLOCKWISE
		:dot(p,q)<0?ONLINE_BACK
		:norm(p)<norm(q)?ONLINE_FRONT
		:ON_SEGMENT;
}
int ccw(const Line&s,const Point&p){return ccw(s.p1,s.p2,p);}
bool orthogonal(const Point&a,const Point&b){return eq(dot(a,b),0);}
bool orthogonal(const Line&s,const Line&t){return orthogonal(vec(s),vec(t));}
bool parallel(const Point&a,const Point&b){return eq(cross(a,b),0);}
bool parallel(const Line&s,const Line&t){return parallel(vec(s),vec(t));}
bool intersect(const Line&s,const Point&p){return eq(cross(vec(s),p-s.p1),0);}
bool intersect(const Line&s,const Line&t){return !parallel(s,t)||intersect(s,t.p1);}
bool intersect(const Segment&s,const Point&p){return ccw(s,p)==ON_SEGMENT;}
bool intersect(const Segment&s,const Segment&t){
	return ccw(s,t.p1)*ccw(s,t.p2)<=0&&ccw(t,s.p1)*ccw(t,s.p2)<=0;
}
bool intersect(const Line&s,const Segment&t){
	return cross(vec(s),t.p1-s.p1)*cross(vec(s),t.p2-s.p1)<EPS;
}
bool intersect(const Segment&s,const Line&t){return intersect(t,s);}
bool intersect(const Circle&c,const Point&p){return eq(distance(c.o,p),c.r);}
int intersect(const Circle&c,const Line&s){
	double d=distance(s,c.o);
	return eq(d,c.r)?1:d<c.r?2:0;
}
int intersect(const Circle&c,const Segment&s){
	Point h=projection(s,c.o);
	double d1=distance(c.o,s.p1),d2=distance(c.o,s.p2);
	return distance(c.o,h)>c.r+EPS?0
		:d1<c.r-EPS&&d2<c.r-EPS?0
		:d1<c.r-EPS&&d2>c.r-EPS||d1>c.r-EPS&&d2<c.r-EPS?1
		:intersect(s,h)?eq(distance(c.o,h),c.r)?1:2
		:0;
}
int intersect(const Circle&a,const Circle&b){
	double d=distance(a.o,b.o);
	return eq(d,a.r+b.r)?3:d>a.r+b.r?4:eq(d,abs(a.r-b.r))?1:d>abs(a.r-b.r)?2:0;
}
double distance(const Point&a,const Point&b){return abs(a-b);}
double distance(const Line&s,const Point&p){return distance(p,projection(s,p));}
double distance(const Line&s,const Line&t){return intersect(s,t)?0:distance(s,t.p1);}
double distance(const Segment&s,const Point&p){
	return distance(p,
		dot(vec(s),p-s.p1)<0?s.p1
		:dot(-vec(s),p-s.p2)<0?s.p2
		:projection(s,p)
	);
}
double distance(const Segment&s,const Segment&t){
	return intersect(s,t)?0:min({
		distance(s,t.p1),distance(s,t.p2),
		distance(t,s.p1),distance(t,s.p2)
	});
}
double distance(const Line&s,const Segment&t){
	return intersect(s,t)?0:min(distance(s,t.p1),distance(s,t.p2));
}
double distance(const Segment&s,const Line&t){return distance(t,s);}
double distance(const Circle&c,const Point&p){return abs(distance(c.o,p)-c.r);}
double distance(const Circle&c,const Line&s){return max(distance(s,c.o)-c.r,0.);}
double distance(const Circle&c,const Segment&s){
	return intersect(c,s)?0
		:contain(c,s)?c.r-max(distance(c.o,s.p1),distance(c.o,s.p2))
		:distance(s,c.o)-c.r;
}
double distance(const Circle&a,const Circle&b){return max(distance(a.o,b.o)-a.r-b.r,0.);}
Point projection(const Line&s,const Point&p){
	return s.p1+vec(s)*dot(p-s.p1,vec(s))/norm(s);
}
Point reflection(const Line&s,const Point&p){return projection(s,p)*2-p;}
Point crosspoint(const Line&s,const Line&t){
	double d1=abs(cross(vec(s),t.p1-s.p1));
	double d2=abs(cross(vec(s),t.p2-s.p1));
	return t.p1+vec(t)*(d1/(d1+d2));
}
pair<Point,Point>crosspoint(const Circle&c,const Line&s){
	Point h=projection(s,c.o);
	Point e=vec(s)/abs(s)*sqrt(c.r*c.r-norm(h-c.o));
	return minmax(h-e,h+e);
}
pair<Point,Point>crosspoint(const Circle&c,const Segment&s){
	pair<Point,Point>p=crosspoint(c,Line(s));
	return intersect(c,s)==2?p
		:intersect(s,p.first)?make_pair(p.first,p.first)
		:make_pair(p.second,p.second);
}
pair<Point,Point>crosspoint(const Circle&a,const Circle&b){
	double d=distance(a.o,b.o);
	double alpha=acos((a.r*a.r+d*d-b.r*b.r)/(2*a.r*d));
	double theta=arg(b.o-a.o);
	return minmax(a.o+polar(a.r,theta+alpha),a.o+polar(a.r,theta-alpha));
}
pair<Point,Point>tangent(const Circle&c,const Point&p){
	return crosspoint(c,Circle(p,sqrt(norm(c.o-p)-c.r*c.r)));
}
vector<Line>tangent(const Circle&a,const Circle&b){
	vector<Line>ret;
	double g=distance(a.o,b.o);
	if(eq(g,0))return ret;
	Point u=(b.o-a.o)/g;
	Point v=rotate(u,M_PI/2);
	for(int s:{-1,1}){
		double h=(a.r+b.r*s)/g;
		if(eq(h*h,1))ret.emplace_back(a.o+(h>0?u:-u)*a.r,a.o+(h>0?u:-u)*a.r+v);
		else if(1-h*h>0){
			Point U=u*h,V=v*sqrt(1-h*h);
			ret.emplace_back(a.o+(U+V)*a.r,b.o-(U+V)*b.r*s);
			ret.emplace_back(a.o+(U-V)*a.r,b.o-(U-V)*b.r*s);
		}
	}
	return ret;
}
bool is_convex(const Polygon&P){
	for(int i=0;i<P.size();i++)
		if(ccw(P[i],P[(i+1)%P.size()],P[(i+2)%P.size()])==CLOCKWISE)return false;
	return true;
}
Polygon convex_full(Polygon P,bool ONSEG){
	if(P.size()<=2)return P;
	sort(P.begin(),P.end());
	Polygon ret(2*P.size());
	int k=0,t;
	if(ONSEG){
		for(const Point&p:P){
			while(k>=2&&ccw(ret[k-2],ret[k-1],p)==CLOCKWISE)k--;
			ret[k++]=p;
		}
		t=k;
		for(int i=P.size()-2;i>=0;i--){
			while(k>=t+1&&ccw(ret[k-2],ret[k-1],P[i])==CLOCKWISE)k--;
			ret[k++]=P[i];
		}
	}
	else{
		for(const Point&p:P){
			while(k>=2&&ccw(ret[k-2],ret[k-1],p)!=COUNTER_CLOCKWISE)k--;
			ret[k++]=p;
		}
		t=k;
		for(int i=P.size()-2;i>=0;i--){
			while(k>=t+1&&ccw(ret[k-2],ret[k-1],P[i])!=COUNTER_CLOCKWISE)k--;
			ret[k++]=P[i];
		}
	}
	ret.resize(k-1);
	int mi=0;
	for(int i=1;i<k-1;i++)
		if(eq(ret[mi].y,ret[i].y)?ret[mi].x>ret[i].x:ret[mi].y>ret[i].y)mi=i;
	rotate(ret.begin(),ret.begin()+mi,ret.end());
	return ret;
}
int contain(const Polygon&P,const Point&p){
	bool in=false;
	for(int i=0;i<P.size();i++){
		Segment s(P[i],P[(i+1)%P.size()]);
		if(intersect(s,p))return ON;
		else{
			Point a=s.p1-p,b=s.p2-p;
			if(a.y>b.y)swap(a,b);
			if(a.y<EPS&&EPS<b.y&&cross(a,b)>EPS)in=!in;
		}
	}
	return in?IN:OUT;
}
int contain(const Circle&c,const Point&p){
	double d=distance(c.o,p);
	return eq(d,c.r)?ON:d<c.r?IN:OUT;
}
int contain(const Circle&c,const Segment&s){
	double d1=distance(c.o,s.p1),d2=distance(c.o,s.p2);
	return d1<c.r+EPS&&d2<c.r+EPS?eq(d1,c.r)||eq(d2,c.r)?ON:IN:OUT;
}
Polygon convex_cut(const Polygon&P,const Line&s){
	Polygon ret;
	for(int i=0;i<P.size();i++){
		Segment t(P[i],P[(i+1)%P.size()]);
		if(ccw(s,t.p1)!=CLOCKWISE)ret.push_back(t.p1);
		if(!parallel(s,t)&&!intersect(s,t.p1)
			&&!intersect(s,t.p2)&&intersect(s,t))ret.push_back(crosspoint(s,t));
	}
	return ret;
}
double diameter(Polygon P){
	if(!is_convex(P))P=convex_full(P);
	int mi=0,Mi=0;
	for(int i=1;i<P.size();i++){
		if(P[i].x<P[mi].x)mi=i;
		if(P[i].x>P[Mi].x)Mi=i;
	}
	double ret=0;
	int sm=mi,sM=Mi;
	while(mi!=sM||Mi!=sm){
		ret=max(ret,norm(P[mi]-P[Mi]));
		if(cross(P[(mi+1)%P.size()]-P[mi],P[(Mi+1)%P.size()]-P[Mi])<0)mi=(mi+1)%P.size();
		else Mi=(Mi+1)%P.size();
	}
	return sqrt(ret);
}
double area(const Polygon&P){
	double ret=0;
	for(int i=0;i<P.size();i++)ret+=cross(P[i],P[(i+1)%P.size()]);
	return ret/2;
}
double area(const Polygon&P,const Line&s){return area(convex_cut(P,s));}
double area(const Polygon&P,const Circle&c){
	double ret=0;
	for(int i=0;i<P.size();i++)
	{
		Segment s(P[i],P[(i+1)%P.size()]);
		if(contain(c,s))ret+=cross(s.p1-c.o,s.p2-c.o);
		else if(!intersect(c,s)){
			double a=arg(s.p2-c.o)-arg(s.p1-c.o);
			if(a>M_PI)a-=2*M_PI;
			if(a<-M_PI)a+=2*M_PI;
			ret+=c.r*c.r*a;
		}
		else
		{
			pair<Point,Point>p=crosspoint(c,s);
			Point tmp[4]={s.p1,p.first,p.second,s.p2};
			if(intersect(c,Segment(s.p1,p.first))==2)swap(tmp[1],tmp[2]);
			for(int j=0;j<3;j++)
			{
				Segment t(tmp[j],tmp[j+1]);
				if(contain(c,t))ret+=cross(t.p1-c.o,t.p2-c.o);
				else{
					double a=arg(t.p2-c.o)-arg(t.p1-c.o);
					if(a>M_PI)a-=2*M_PI;
					if(a<-M_PI)a+=2*M_PI;
					ret+=c.r*c.r*a;
				}
			}
		}
	}
	return ret/2;
}
int N;
int main()
{
	while(cin>>N,N)
	{
		Polygon P(N);
		for(int i=0;i<N;i++)cin>>P[i];
		double S=area(P);
		Point O;
		double L=0,R=M_PI;
		bool flag=area(P,Line(O,polar(2,0)))<S/2;
		for(int i=0;i<100;i++)
		{
			double M=(L+R)/2;
			if(area(P,Line(O,polar(2,M)))<S/2^flag)R=M;
			else L=M;
		}
		Point p=polar(2,L);
		cout<<fixed<<setprecision(15)<<p.x<<" "<<p.y<<endl;
	}
}