4967. A number game

Foxity and Foxitu are good friends. They like to play number games. One day, Foxity played ICPC with his teammates, leaving Foxitu alone at labs. So he played a number game with himself.

There are $n$ numbers from $1$ to $n$ in a set, each time he can choose two distinct number $a$ and $b$($a\ne b$). He firstly remove $a$ and $b$ from this set, then insert $a+b$ and $|a-b|$ to the set. His goal is to leave the set with only two elements, and He can only operate on this set at most $n$ times.

Please provide any of his possible operation sequence.

There will be no identical elements in the set, and identical elements are treated as one element.