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| namespace Geometric
{
#define eps 1e-8
struct Point
{
double x, y;
Point(double x = 0, double y = 0) : x(x), y(y) {}
friend Point operator + (Point a, Point b) {return Point(a.x + b.x, a.y + b.y);}
friend Point operator - (Point a, Point b) {return Point(a.x - b.x, a.y - b.y);}
friend Point operator * (Point a, double b){return Point(a.x * b, a.y * b);}
friend Point operator / (Point a, double b){return Point(a.x / b, a.y / b);}
}origin;
#define Vector Point
double dis(Point a, Point b){return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));}
double len(Vector v){return dis(origin, v);}
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 - b.x * a.y;}
double corner(Vector a, Vector b){return dot(a, b) / (len(a) * len(b));}
double area (Vector a, Vector b){return cross(a, b) / 2.0;}
double angle(Vector v){return atan2(v.y, v.x);}
Vector rotate_counterclockwise(Vector v, double t)
{return Vector(v.x * cos(t) - v.y * sin(t), v.x * sin(t) + v.y * cos(t));}
Vector rotate_clockwise(Vector v, double t)
{return Vector(v.x * cos(t) + v.y * sin(t), v.y * cos(t) - v.x * sin(t));}
struct line
{
Point A; Vector B; double An;
line(Point a = 0, Vector b = 0) : A(a), B(b) {An = atan2(B.y, B.x);}
friend bool operator < (line a, line b){return a.An < b.An;}
};
Point sdot(line a, line b){Point c = a.A - b.A;double k = cross(b.B, c) / cross(a.B, b.B);return a.A + a.B * k;}
int sure(double x){return fabs(x) < eps ? 0 : (x > 0 ? 1 : -1);}
}
using namespace Geometric;
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