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How does forward_as_tuple work with a constructor template in C++?

This question is related to forward_as_tuple and constructor templates
I'm sorry in advance because below example code is a bit odd
But I haven't understood this code for a while

The example code is as below

struct AAA {
  template<typename T>
    AAA(T var) : var_(var) {};
  int var_;
};                                                                                                                                                                                                         

void foo(std::tuple<AAA> aaa)
{
}

template<typename T>
void boo(T arg)
{
  foo(std::forward_as_tuple(std::forward<AAA>(arg)));
}

int main()
{
  boo(100);
}

Actually above code fails compiling with below error message

main.cpp:15:23: error: cannot convert ‘std::tuple<AAA&&>’ to ‘int’ in initialization
   15 |     AAA(T var) : var_(var) {};
      |                       ^~~
      |                       |
      |                       std::tuple<AAA&&>

But it succeeds compiling if I change it in one of the two ways below

(1) change void foo(std::tuple<AAA> aaa) into void foo(std::tuple<AAA&&> aaa)
(2) remove constructor template and add a normal constructor AAA(int var) : var_(var) {}

It must be grateful someone helps me to understand
why does above code work with the change (1) or (2)


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