Knockout tournament

A knockout tournament is a type of elimination tournament where the loser of each match-up is immediately eliminated from the tournament. The following image showcases a knockout tournament between 16 players.

In the tournament:

• Initially, the 16 players are paired into 8 matches in the first round.
• The winners of these 8 matches proceed to the next round, while the losers are eliminated.
• The 8 winners from the first round are paired into 4 matches.
• The 4 winners from the quarterfinals are paired into 2 matches.
• The 2 winners from the semifinals compete in the final match to determine the champion.

A knockout tennis tournament is organised in Chefland. There are 16 players, and the ith player has a skill level of Si​. It is guaranteed that all skill levels are distinct, that is, Si≠Sj.

It is known that in a match between two players, the player with higher skill level always wins.

For each player i, find the maximum number of matches the player can win in the tournament if the initial pairings are made optimally.