QAZ likes to play League of Legends and watch league matches as well.

He thinks the double-elimination system of this year's league matches is not fair, so he invented a pro-double-elimination system.

Specifically, in his system:

• There are three teams competing with each other.
• Firstly, two teams are selected with equal probability and compete.
• In each round, the losing team temporarily leaves, and the winning team continues to play against the other of the three teams that did not participate in this round.
• When a team loses two round in total, the elimination competition ends.
• For the sake of simplicity, any two teams have a 50% chance of winning against each other.
• Now please find out the expected number of rounds in this elimination competition.