Question 13
Some of the $n$ cities are connected by airline routes (all routes are two-way). There is exactly $m$ line. Let $d_{i}$ be the number of lines departing from the city $i$, for $i=1,2, \ldots, n$. If $1 \leqslant d_{i} \leqslant 2010$, for each $i=1,2, \ldots, n$, prove that it holds
$$
\sum_{i=1}^{n} d_{i}^{2} \leqslant 4022 m-2010 n
$$
Determine all $n$ for which equality can be reached.
$$
\sum_{i=1}^{n} d_{i}^{2} \leqslant 4022 m-2010 n
$$
Determine all $n$ for which equality can be reached.