Description

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 prodouble-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.

Input

No input.

Output

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.

No input

ans