RU-ALLRUSSIAN 2017 Problem 91

In country some cities are connected by oneway flights( There are no more then one flight between two cities). City $A$ called "available" for city $B$ , if there is flight from $B$ to $A$ , maybe with some transfers. It is known, that for every 2 cities $P$ and $Q$ exist city $R$ , such that $P$ and $Q$ are available from $R$ . Prove, that exist city $A$ , such that every city is available for $A$ .