#include <iostream>
using namespace std;

class Point;

class Vector {
    double x, y, z;
public:
    Vector(double x = 0, double y = 0, double z = 0)
        : x(x), y(y), z(z)
    { }
    friend Point    operator+(const Point&,  const Vector&);
    friend Vector   operator+(const Vector&, const Vector&);
    friend ostream& operator<<(ostream&, const Vector&);
};

class Point {
    double x, y, z;
public:
    Point(double x = 0, double y = 0, double z = 0)
        : x(x), y(y), z(z)
    { }
    friend Point operator+(const Point&, const Vector&);
    friend ostream& operator<<(ostream&, const Point&);
};

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

Vector operator+(const Vector& v1, const Vector& v2) {
    return Vector(v1.x+v2.x, v1.y+v2.y, v1.z+v2.z);
}

ostream& operator<<(ostream& str, const Point& p) {
    return str << "P(" << p.x << "," << p.y
               << ","  << p.z << ")";
}

ostream& operator<<(ostream& str, const Vector& v) {
    return str << "V[" << v.x << "," << v.y
               << ","  << v.z << "]";
}

int main() {

    Vector v1(1,1,1), v2(2,2,2);
    Point  p1(1,2,3);

    Vector v = v1 + v2;
    cout << "v: " << v << endl;

    Point  p = p1 + v;
    cout << "p: " << p << endl;
}