struct Vector

#include <math.h>

#define USE_MATH_DEFINES

struct Vector{
    Vector(double x, double y) : x(x), y(y){
    }

    double length() const{
        return sqrt(x * x + y * y);
    }

    Vector operator - () const{
        return Vector(-x, -y);
    }

    Vector & operator += (Vector const & v){
        x += v.x;
        y += v.y;

        return * this;
    }

    Vector & operator -= (Vector const & v){
        x -= v.x;
        y -= v.y;

        return * this;
    }

    Vector & operator *= (double d){
        x *= d;
        y *= d;

        return * this;
    }

    double x;
    double y;
};

Vector normalize(Vector const & v){
    double len = v.length();

    return Vector(v.x / len, v.y / len);
}

Vector operator * (Vector const & v, double d){
    return Vector(v.x * d, v.y * d);
}

Vector operator * (double d, Vector const & v){
    return v * d;
}

double operator * (Vector const & v, Vector const & w){
    return v.x * w.x + v.y * w.y;
}

double angle(Vector const & v, Vector const & w){
    double scal = v * w;
    double len_v = v.length();
    double len_w = w.length();

    double rad = acos(scal / (len_v * len_w));

    return rad / M_PI * 180.;
}

Vector operator + (Vector const & v, Vector const & w){
    return Vector(v.x + w.x, v.y + w.y);
}

Vector operator - (Vector const & v, Vector const & w){
    return v + (-w);
}