Question 86
There are 1000 cities $A_1, A_2, \dots, A_{1000}$ in a country and some of them are connected by airlines. It is known that the $i$-th city is connected to $d_i$ other cities, where $d_1 \le d_2 \le \dots \le d_{1000}$ and $d_j \ge j + 1$ for every $j = 1, 2, \dots, 999 - d_{999}$. Prove that if the airport of a city is closed, it will be still possible to connect any two other cities.