point/vec2

#define int long long
#define ld long double
const ld EPS = 1e-12, PI = 3.1415926535897;

// geometry primitives
int sign(int x) {
    if (x > 0) return 1;
    if (x < 0) return -1;
    return 0;
}
int sign(ld x) {
    if (x > EPS) return 1;
    if (x < -EPS) return -1;
    return 0;
}
ld sq(ld x) { return x * x; }

#define vec2 point
struct point {
    ld x, y;
    point() : x(), y() {} // empty constructor
    point(const ld& x_, const ld& y_) : x(x_), y(y_) {} // constructor from coords
    point operator-(const point& oth) const { return point(x - oth.x, y - oth.y); } // various operators
    point operator+(const point& oth) const { return point(x + oth.x, y + oth.y); }
    point operator*(const ld& a) const { return point(x * a, y * a); }
    ld operator^(const point& oth) const { return x * oth.y - y * oth.x; } // scalar multiplication
    bool operator<(const point& oth) const { // check, if point equal
        if (sign(x - oth.x)) return x < oth.x;
        if (sign(y - oth.y)) return y < oth.y;
        return false;
    }
    bool operator==(const point& oth) const { return !sign(x - oth.x) && !sign(y - oth.y);  }
    ld len2() const { return sq(x) + sq(y); } // len of the vector squared (if we don't need precision)
    ld len() const { return sqrt(len2()); } // len of the vector
    point norm() const { // norm a vector
        ld d = len();
        assert(sign(d)); // we can't norm a point
        return point(x / d, y / d);
    }
    point ort() const { return point(-y, x); } // orthogonal vector
    void print() { cout << '(' << x << ',' << y << ')' << endl; }
};