Chef and Number Game

Recently, Chef hosted a strange competition at the Byteland annual fair. There were $N$ participants in the competition (numbered $1$ through $N$); at the end of the competition, their scores were $A_1, A_2, \ldots, A_N$. Since it was a strange competition, negative scores were allowed too. The *total score* of the competition is calculated as follows: - Divide the participants into one or mor