E - Throwing the Die

Score : $500$ points

Problem Statement

Let us play a game using a die. The game consists of at most $N$ turns, each of which goes as follows.

• Throw a $6$-sided die that shows $1,\ldots,6$ with equal probability, and let $X$ be the number shown (each throw is independent of the others).
• If it is the $N$-th turn now, your score is $X$, and the game ends.
• Otherwise, choose whether to continue or end the game.
  • If you end the game, your score is $X$, and there is no more turn.

Find the expected value of your score when you play the game to maximize this expected value.

Constraints

• $1 \leq N \leq 100$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.
Your output is considered correct if its absolute or relative error from the true answer is at most $10^{-6}$.

1

3.5000000000

2

4.2500000000

10

5.6502176688