KöMaL 2020 C1613

There were $n$ teams participating in a basketball championship. Every team played every other team exactly once, and there was no draw. At the end of the championship, the $i$th team had $x_i$ games won and $y_i$ games lost ($i=1,2,\ldots,n$). Prove that $x_1^2+x_2^2+\cdots+x_n^2=y_1^2+y_2^2+\cdots+y_n^2.$