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.

No input.

Print exactly one line consisting of a real number, rounded to the first decimal place, that represents the expected number of rounds in the QAZ‘s elimination competition.