template <typename T, size_t N>
class vec_t {
	template<size_t index, typename... U>
	void load_from_args(void)
	{
		static_assert(index < N + 1, "too many elements in the initializer");
		static_assert(index > N - 1, "too few elements in the initializer");
	}

	template<size_t index, typename... U>
	void load_from_args(T first, U... rest)
	{
		v[index] = first;
		load_from_args<index + 1>(rest...);
	}

public:
	T v[N];

	// Basic operations

	vec_t() = default;

	template<typename... U>
	vec_t(T first, U... rest)
	{
		load_from_args<0>(first, rest...);
	}

	template<typename U>
	vec_t(vec_t<U, N> b)
	{
		for (size_t i = 0; i < N; i++)
			v[i] = (T)b[i];
	}

	T& operator[](size_t i)
	{
		return v[i];
	}

	const T& operator[](size_t i) const
	{
		return v[i];
	}

	// Comparison

	friend bool operator==(const vec_t<T, N> &a, const vec_t<T, N> &b)
	{
		for (size_t i = 0; i < N; i++)
			if (a[i] != b[i])
				return false;

		return true;
	}

	// Good enough for maps or sets.
	friend bool operator<(const vec_t<T, N> &a, const vec_t<T, N> &b)
	{
		for (size_t i = 0; i < N; i++) {
			if (a[i] < b[i])
				return true;
			else if (a[i] > b[i])
				return false;
		}

		return false;
	}

	// Arithmetics

	friend vec_t<T, N> operator+(const vec_t<T, N> &v)
	{
		return v;
	}

	friend vec_t<T, N> operator+(const vec_t<T, N> &a, const vec_t<T, N> &b)
	{
		vec_t<T, N> r;

		for (size_t i = 0; i < N; i++)
			r[i] = a[i] + b[i];

		return r;
	}

	friend vec_t<T, N> &operator+=(vec_t<T, N> &v, const vec_t<T, N> &b)
	{
		for (size_t i = 0; i < N; i++)
			v[i] += b[i];

		return v;
	}

	friend vec_t<T, N> operator-(const vec_t<T, N> &v)
	{
		return -1 * v;
	}

	friend vec_t<T, N> operator-(const vec_t<T, N> &a, const vec_t<T, N> &b)
	{
		vec_t<T, N> r;

		for (size_t i = 0; i < N; i++)
			r[i] = a[i] - b[i];

		return r;
	}

	friend vec_t<T, N> &operator-=(vec_t<T, N> &v, const vec_t<T, N> &b)
	{
		for (size_t i = 0; i < N; i++)
			v[i] -= b[i];

		return v;
	}

	friend T operator*(const vec_t<T, N> &a, const vec_t<T, N> &b)
	{
		T r = (T)0;

		for (size_t i = 0; i < N; i++)
			r += a[i] * b[i];

		return r;
	}

	friend vec_t<T, N> operator*(const vec_t<T, N> &a, const T &b)
	{
		vec_t<T, N> r;

		for (size_t i = 0; i < N; i++)
			r[i] = a[i] * b;

		return r;
	}

	friend vec_t<T, N> operator*(const T &b, const vec_t<T, N> &a)
	{
		return a * b;
	}

	friend vec_t<T, N> &operator*=(vec_t<T, N> &v, const T &b)
	{
		for (size_t i = 0; i < N; i++)
			v[i] *= b;

		return v;
	}

	friend vec_t<T, N> operator/(const vec_t<T, N> &a, const T &b)
	{
		vec_t<T, N> r;

		for (size_t i = 0; i < N; i++)
			r[i] = a[i] / b;

		return r;
	}

	friend vec_t<T, N> operator/(const T &b, const vec_t<T, N> &a)
	{
		return a / b;
	}

	friend vec_t<T, N> &operator/=(vec_t<T, N> &v, const T &b)
	{
		for (size_t i = 0; i < N; i++)
			v[i] /= b;

		return v;
	}

	// Compatibility with SFML

	template <typename U>
	operator sf::Vector2<U>() const
	{
		static_assert(N == 2, "conversion of vec_t with N != 2 to sf::Vector2");
		return sf::Vector2<U>((U)v[0], (U)v[1]);
	}

	template <typename U>
	vec_t(sf::Vector2<U> b)
	{
		static_assert(N == 2, "conversion of sf::Vector2 to vec_t with N != 2");
		v[0] = b.x;
		v[1] = b.y;
	}

	// Compatibility with iostream

	friend std::ostream& operator<<(std::ostream& stream, vec_t<T, N> v)
	{
		stream << "(";
		for (size_t i = 0; i < N; i++) {
			if (i)
				stream << ", ";
			stream << v.v[i];
		}
		stream << ")";

		return stream;
	}
};

// Shorthands
typedef vec_t<float, 2> v2f_t;
typedef vec_t<double, 2> v2d_t;

template <typename T, size_t N>
class rect_t {
public:
	vec_t<T, N> a, b;

	rect_t() = default;

	rect_t(vec_t<T, N> a_, vec_t<T, N> b_)
	{
		a = a_;
		b = b_;
	}

	friend std::ostream& operator<<(std::ostream& stream, rect_t<T, N> r)
	{
		stream << "(" << r.a << ", " << r.b << ")";
		return stream;
	}
};