template class 를 받는 template func 오버로딩이 안됩니다.

#include <iostream>
#include <string>
 
template <int I>
class scalable;
 
template <int I>
std::ostream& operator<<(std::ostream&, scalable<I>&);
 
template <int I>
class scalable{
      private:
              std::string str;
              int quotient;
              int remainder;
      public:
             scalable(int i){
                           quotient=i;
                           while(quotient>=I){
                                              remainder=quotient%I;
                                              quotient/=I;
                                              str=char(int('1')+remainder-1)+str;
                                              }
                           str=char(int('1')+quotient-1)+str;
                           }
             void print(){
                     std::cout << str << std::endl;
                     }
             friend std::ostream& operator<<(std::ostream&, scalable<I>&);
};
 
template <int I>
std::ostream& operator<<(std::ostream& os, scalable<I>& num_str){
              std::cout << num_str.str<<std::endl;
              return os;
} ;
 
int main(){
    scalable<2> num(100);
//  num.print();
    std::cout << num;
    getc(stdin);
}