#include <iostream>
#include <algorithm> // for min()
#include <array>
using namespace std;

template<size_t Dim, typename Type = double>
class mathvector {
public:
  explicit mathvector(array<Type, Dim> const& values) : content_(values) {}
  explicit mathvector(array<Type, Dim> && values) : content_(move(values)) {}
  mathvector() : content_{} {} // zero-initialized
  
  mathvector& operator*=(Type const& scalar) {
    for (auto& component : content_) component *= scalar;
    return *this;
  }

  mathvector& operator+=(mathvector const& other) {
    for (size_t i(0); i < Dim; ++i) content_[i] += other.content_[i];
    return *this;
  }

  template<size_t Dim2>
  mathvector<Dim2, Type> convert() const
  {
    array<Type, Dim2> other{};
    constexpr size_t upper(min(Dim, Dim2));
    for (size_t i(0); i < upper; ++i) other[i] += content_[i];
    return mathvector<Dim2, Type>(other);
  }

  void display(ostream& out) const
  {
    out << '(';
    if (Dim > 0) {
      constexpr size_t upper(Dim - 1);
      for (size_t i(0); i < upper; ++i) out << content_[i] << ", ";
      out << content_[upper];
    }
    out << ')';
  }

private:
  array<Type, Dim> content_;
};

template<size_t Dim, typename Type>
mathvector<Dim, Type> operator*(Type const& scalar, mathvector<Dim, Type> vect)
{
  vect *= scalar;
  return vect;
}

template<size_t Dim, typename Type = double>
mathvector<Dim, Type> operator+(mathvector<Dim, Type> vect1,
                                mathvector<Dim, Type> const& vect2)
{
  vect1 += vect2;
  return vect1;
}

template<size_t Dim, typename Type>
ostream& operator<<(ostream& out, mathvector<Dim, Type> const& vect)
{
  vect.display(out);
  return out;
}

  
int main()
{
  mathvector<2> v1({3.4, 4.5});

  mathvector<4, int> v2({3, 4, 5, 6});

  // implicit cannot work here
  mathvector<3, int> v3(v2.convert<3>());
  mathvector<4, double> v4(v1.convert<4>());

  cout << v1 << endl;
  cout << v2 << endl;
  cout << v3 << endl;
  cout << v4 << endl;

  cout << -2 * v2 << endl;
  cout << v3 + v3 << endl;
  
  return 0;
}