struct r {
int x, y;
r() {}
r(int x, int y) : x(x), y(y) {}
double len() { return hypot(x, y); }
double angle() {
return atan2(y, x);
}
};
r operator+(r a, r b) { return {a.x + b.x, a.y + b.y}; }
r operator-(r a, r b) { return {a.x - b.x, a.y - b.y}; }
int operator*(r a, r b) { return a.x * b.x + a.y * b.y; }
int operator^(r a, r b) { return a.x*b.y - b.x*a.y; }
istream& operator>>(istream &in, r &p) {
in >> p.x >> p.y;
return in;
}
ostream& operator<<(ostream &out, r &p) {
out << p.x << " " << p.y << endl;
return out;
}
double angle(r a, r b) {
return atan2(a ^ b, a * b);
}
r rot(r a, double alpha) {
return {cos(alpha) * x - sin(alpha) * y, sin(alpha) * x + cos(alpha) * y};
}struct segment {
r p, q;
};
bool suppression(segment a, segment b){
return ((a.p - b.p) ^ (b.p - b.q)) * ((a.q - b.p) ^ (b.q - b.p)) < 0;
}const double EPS = 1e-9;
struct line {
int a, b, c;
double n = sqrt(a*a + b*b);
line(int a, int b, int c) : a(a), b(b), c(c) {}
line(r p, r q){
a = p.y - q.y;
b = q.x - p.x;
c = -a*p.x - b*p.y;
}
double dist(r p) {
return abs(a * p.x + b * p.y + c) / n;
}
r norm() { return {a, b}; }
r norm_unit() { return {a / n, b / n}; }
r guide() { return {-b, a}; }
}
r projection(line l, r p) {
return p + l.norm_unit() * l.dist(p);
}
double det (double a, double b, double c, double d) {
return a * d - b * c;
}
bool intersect (line m, line n, r & res) {
double zn = det (m.a, m.b, n.a, n.b);
if (abs (zn) < EPS)
return false;
res.x = - det (m.c, m.b, n.c, n.b) / zn;
res.y = - det (m.a, m.c, n.a, n.c) / zn;
return true;
}
bool parallel (line m, line n) {
return abs (det (m.a, m.b, n.a, n.b)) < EPS;
}
bool equivalent (line m, line n) {
return abs (det (m.a, m.b, n.a, n.b)) < EPS
&& abs (det (m.a, m.c, n.a, n.c)) < EPS
&& abs (det (m.b, m.c, n.b, n.c)) < EPS;
}