Avoid deep copy in operator+ overload

Question

I am new to c++. Here is my problem:

I have created a class in c++ that overloads operator+ and returns an object of the same class

#include <iostream>
using namespace std;

class A{
    private:
    int value;

    public:
    A(int val){
        this->value = val;
    }

    A operator+(A a2){
        A a(this->value + a2.value);
        return a;
    }

    friend ostream& operator<<(ostream& os, const A& a){
        return os<<a.value;
    }
};

int main(){
    A a1 = {1};
    A a2 = {2};
    A a3 = {3};

    cout << a1 + a2 + a3 << " ";
    cout << a1 + (a2+a3) << endl;

    return 0;
}

This works totally fine and prints 6 6 on the terminal. But this uses deep copy while using + operator and I want to avoid it.

I tried changing A operator+(A a2){ to A operator+(A& a2){ so that values are passed by reference. This works for a+b+c but for a+(b+c) it fails and gives a long error. The following seemed important:

error: no match for ‘operator+’ (operand types are ‘A’ and ‘A’)
   30 |     cout << a1 + (a2+a3) << endl;
      |             ~~ ^ ~~~~~~~
      |             |       |
      |             A       A

So my question is: Is there a way to achieve the syntax a+(b+c) without deep copy and how? It is mandatory for me to create a class, and support that syntax. I can't use const A&.

I am using c++14 and ubuntu-20.04