How to implement a constructor so it only accepts input iterators using typeid?

I want to implement a range constructor for a certain object, but I want to restrict it to only accept two input iterators.

I've tried to compile this code with gcc 7.1.0.

File test.cpp

#include <vector>
#include <type_traits>
#include <typeinfo>

template <typename Iterator>
using traits = typename std::iterator_traits<Iterator>::iterator_category;

template <typename T>
class A{
   private:

      std::vector<T> v;

   public:

      template <typename InputIterator,
               typename = std::enable_if_t<
                  typeid(traits<InputIterator>) ==
                  typeid(std::input_iterator_tag)>
               >
      A(InputIterator first, InputIterator last) : v(first, last) {}
};

int main(){
   std::vector<double> v = {1, 2, 3, 4, 5};
   A<double> a(v.begin(), v.end());
}

I get this compilation error with g++ test.cpp -o test:

  test.cpp: In function ‘int main()’:
  test.cpp:27:34: error: no matching function for call to ‘A<double>::A(std::vector<double>::iterator, std::vector<double>::iterator)’
      A<double> a(v.begin(), v.end());
                                    ^
  test.cpp:22:7: note: candidate: template<class InputIterator, class> A<T>::A(InputIterator, InputIterator)
         A(InputIterator first, InputIterator last) : v(first, last) {}
         ^
  test.cpp:22:7: note:   template argument deduction/substitution failed:
  test.cpp: In substitution of ‘template<bool _Cond, class _Tp> using enable_if_t = typename std::enable_if::type [with bool _Cond = ((const std::type_info*)(& _ZTISt26random_access_iterator_tag))->std::type_info::operator==(_ZTISt18input_iterator_tag); _Tp = void]’:
  test.cpp:18:16:   required from here
  test.cpp:19:49: error: call to non-constexpr function ‘bool std::type_info::operator==(const std::type_info&) const’
                     typeid(traits<InputIterator>) ==
  test.cpp:18:16: note: in template argument for type ‘bool’ 
                  typename = std::enable_if_t<
                  ^~~~~~~~
  test.cpp:10:7: note: candidate: A<double>::A(const A<double>&)
   class A{
         ^
  test.cpp:10:7: note:   candidate expects 1 argument, 2 provided
  test.cpp:10:7: note: candidate: A<double>::A(A<double>&&)
  test.cpp:10:7: note:   candidate expects 1 argument, 2 provided

I decided to use default template parameter because is more suitable for constructors. The use of the operator typeid() is because I find it really easy to read when mantaining the code, but I can't get it to work in any way.

Other solutions look very weird and are really obscure (like forcing the InputIterator parameter to have certain methods such as *it or ++it). If there's no way I can do this, I would appreciate a, more or less, easy-to-read solution.