CF913F Strongly Connected Tournament

There is a chess tournament in All-Right-City. $ n $ players were invited to take part in the competition. The tournament is held by the following rules: 1. Initially, each player plays one game with every other player. There are no ties; 2. After that, the organizers build a complete directed graph with players as vertices. For every pair of players there is exactly one directed edge between them: the winner of their game is the startpoint of this edge and the loser is the endpoint; 3. After that, the organizers build a condensation of this graph. The condensation of this graph is an acyclic complete graph, therefore it has the only Hamiltonian path which consists of strongly connected components of initial graph $ A_{1}→A_{2}→...→A_{k} $ . 4. The players from the first component $ A_{1} $ are placed on the first  places, the players from the component $ A_{2} $ are placed on the next  places, and so on. 5. To determine exact place of each player in a strongly connected component, all the procedures from 1 to 5 are repeated recursively inside each component, i.e. for every $ i=1,2,...,k $ players from the component $ A_{i} $ play games with each other again, and so on; 6. If a component consists of a single player, then he has no more rivals, his place is already determined and the process stops. The players are enumerated with integers from $ 1 $ to $ n $ . The enumeration was made using results of a previous tournament. It is known that player $ i $ wins player $ j $ ( $ i

N/A

N/A

In the first example the expected value is $ 4 $ . In the second example the expected value is . In the third example the expected value is .