Overloading operator<< in class template's substruct

Question

I have been overloading operator<< for a few class templates without problem, but ran into this issue when I want to overload said operator for a substruct.

Here is an example:

#include <iostream>                                                             
using namespace std;                                                            

template <typename T>                                                           
class A {                                                                       
    public:                                                                     
    struct S { // note: templated on T.                                                                 
        S() { x = 2; }                                                          
        T x;                                                                    
//        // doesn't work.                                                      
//        template<typename T1>                                                 
//        friend ostream& operator<<(ostream& os, const typename A<T1>::S& rhs) {
//            os << rhs.x;                                                      
//            return os;                                                        
//        }                                                                     
    };                                                                          
    S s;                                                                        
};                                                                              

//// doesn't work.                                                              
//template<typename T>                                                          
//ostream& operator<<(ostream& os, const typename A<T>::S& rhs) {               
//    os << rhs.x;                                                              
//    return os;                                                                
//}                                                                             

// works, but not general.                                                      
ostream& operator<<(ostream& os, const typename A<int>::S& rhs) {               
    os << rhs.x;                                                                
    return os;                                                                  
}                                                                               

int main() {                                                                    
    A<int> a;                                                                   
    cout << a.s << endl;                                                        

    return 0;                                                                   
}   

The compile error is:

main.cpp: In function 'int main()':
main.cpp:35:10: error: no match for 'operator<<' (operand types are 'std::ostream {aka std::basic_ostream<char>}' and 'A<int>::S')
     cout << a.s << endl;
          ^

How can I overload operator<< for a substruct of a class template?