---

#include <iostream>
#include <cmath>
using namespace std;

class Vector {
private:
    double x, y, z;
    int id;
    static int counter;
public:
    Vector() : x(0), y(0), z(0) {
        id = ++counter;
        cout << "Constructor N" << id << endl;
    }
    Vector(double x_, double y_, double z_) : x(x_), y(y_), z(z_) {
        id = ++counter;
        cout << "Constructor N" << id << endl;
    }
    ~Vector() {
        cout << "Destructor N" << id << endl;
    }
    double getX() const { return x; }
    double getY() const { return y; }
    double getZ() const { return z; }
    void setX(double v) { x = v; }
    void setY(double v) { y = v; }
    void setZ(double v) { z = v; }
    double length() const {
        return sqrt(x*x + y*y + z*z);
    }
    Vector copy() const {
        return Vector(x, y, z);
    }
    Vector multiply(double k) const {
        return Vector(x*k, y*k, z*k);
    }
    Vector normalize() const {
        double len = length();
        return Vector(x/len, y/len, z/len);
    }
    void print() const {
        cout << "x = " << x << "; y = " << y << "; z = " << z << endl;
    }
    friend Vector pluss(const Vector& a, const Vector& b);
    friend Vector minuss(const Vector& a, const Vector& b);
    friend Vector vectornoeproizved(const Vector& a, const Vector& b);
    friend double scalar(const Vector& a, const Vector& b);
    friend double cosAngle(const Vector& a, const Vector& b);
    friend double sinAngle(const Vector& a, const Vector& b);
    friend double angleDegrees(const Vector& a, const Vector& b);
};
int Vector::counter = 0;
Vector pluss(const Vector& a, const Vector& b) {
    return Vector(a.x + b.x, a.y + b.y, a.z + b.z);
}
Vector minuss(const Vector& a, const Vector& b) {
    return Vector(a.x - b.x, a.y - b.y, a.z - b.z);
}
Vector vectornoeproizved(const Vector& a, const Vector& b) {
    return Vector(
        a.y * b.z - a.z * b.y,
        a.z * b.x - a.x * b.z,
        a.x * b.y - a.y * b.x
    );
}
double scalar(const Vector& a, const Vector& b) {
    return a.x * b.x + a.y * b.y + a.z * b.z;
}
double cosAngle(const Vector& a, const Vector& b) {
    return scalar(a, b) / (a.length() * b.length());
}
double sinAngle(const Vector& a, const Vector& b) {
    return vectornoeproizved(a, b).length() / (a.length() * b.length());
}
double angleDegrees(const Vector& a, const Vector& b) {
    return atan2(sinAngle(a, b), cosAngle(a, b)) * 180.0 / M_PI;
}
int main() {
    Vector A(1, 2, 3);
    Vector B(4, 5, 6);
    cout << "\nA: "; A.print();
    cout << "B: "; B.print();
    cout << "\n|A| = " << A.length() << endl;
    cout << "|B| = " << B.length() << endl;
    cout << "\nA + B: ";  pluss(A, B).print();
    cout << "A - B: ";    minuss(A, B).print();
    cout << "A x B: ";    vectornoeproizved(A, B).print();
    cout << "\nA*B = "   << scalar(A, B) << endl;
    cout << "cos = "     << cosAngle(A, B) << endl;
    cout << "sin = "     << sinAngle(A, B) << endl;
    cout << "Ugol = "    << angleDegrees(A, B) << " gradusov" << endl;
    return 0;
}