Dice and Candies

Hyobin has a die with the numbers 1 through 6 written on its faces, one number per face. Each throw gives her as many candies as the number on the top face. Every face comes up with probability $\frac{1}{6}$.

Hyobin keeps throwing the die until the candies she has received add up to at least $N$. Write a program that computes the expected number of throws.

The first line contains an integer $N$ ($1 \le N \le 1{,}000{,}000$).

Print the expected number of throws on the first line, rounded to six digits after the decimal point. Always print exactly six digits after the point, padding with zeros. No $N$ puts the exact value on a rounding boundary.