#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string.h>
#include<math.h>
using namespace std;
#define point Point
const double eps = 1e-8;
const double PI = acos(-1.0);
double ABS(double x){return x>0?
x:-x;}
int sgn(double x){
	if(fabs(x) < eps)return 0;
	if(x < 0)return -1;
	else return 1;
}
struct Point
{
	double x,y;
	void put(){printf("(%.0lf,%.0lf)\n",x,y);}
	Point(){}
	Point(double _x,double _y){
	x = _x;y = _y;
	}
	Point operator -(const Point &b)const{
		return Point(x - b.x,y - b.y);
	}
	//叉积
	double operator ^(const Point &b)const{
		return x*b.y - y*b.x;
	}
	//点积
	double operator *(const Point &b)const{
		return x*b.x + y*b.y;
	}
	//绕原点旋转角度B（弧度值），后x,y的变化
	void transXY(double B){
		double tx = x,ty = y;
		x = tx*cos(B) - ty*sin(B);
		y = tx*sin(B) + ty*cos(B);
	}
};
struct Line
{
	Point s,e;
	void put(){s.put();e.put();}
	Line(){}
	Line(Point _s,Point _e)
	{
	s = _s;e = _e;
	}
	//两直线相交求交点
	//第一个值为0表示直线重合。为1表示平行，为0表示相交,为2是相交
	//仅仅有第一个值为2时，交点才有意义
	pair<int,Point> operator &(const Line &b)const{
		Point res = s;
		if(sgn((s-e)^(b.s-b.e)) == 0)
		{
		if(sgn((s-b.e)^(b.s-b.e)) == 0)
		return make_pair(0,res);//重合
		else return make_pair(1,res);//平行
		}
		double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));
		res.x += (e.x-s.x)*t;
		res.y += (e.y-s.y)*t;
		return make_pair(2,res);
	}
};
double dist(Point a,Point b){return sqrt((a-b)*(a-b));}
//*推断线段相交
bool inter(Line l1,Line l2){
	return
	max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) &&
	max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) &&
	max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) &&
	max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) &&
	sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 &&
	sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0;
}
point symmetric_point(point p1, point l1, point l2){ //p1关于直线(l1,l2)的对称点
	point ret;
	if(ABS(l1.x-l2.x)<eps){
		ret.y = p1.y;
		ret.x = 2*l1.x - p1.x;
		return ret;
	}
	if(ABS(l1.y-l2.y)<eps) {
		ret.x = p1.x;
		ret.y = 2*l1.y - p1.y;
		return ret;
	}
	if (l1.x > l2.x - eps && l1.x < l2.x + eps)
	{
	ret.x = (2 * l1.x - p1.x);
	ret.y = p1.y;
	}
	else
	{
	double k = (l1.y - l2.y ) / (l1.x - l2.x);
	ret.x = (2*k*k*l1.x + 2*k*p1.y - 2*k*l1.y - k*k*p1.x + p1.x) / (1 + k*k);
	ret.y = p1.y - (ret.x - p1.x ) / k;
	}
	return ret;
}
bool gongxian(Point a, Point b, Point c){
	return ABS((a.y-b.y)*(a.x-c.x) - (a.y-c.y)*(a.x-b.x))<eps;
}