CF97C Winning Strategy

One university has just found out about a sport programming contest called ACM ICPC v2.0. This contest doesn't differ much from the well-known ACM ICPC, for example, the participants are not allowed to take part in the finals more than two times. However, there is one notable difference: the teams in the contest should consist of exactly $ n $ participants. Having taken part in several ACM ICPC v2.0 finals and having not won any medals, the students and the university governors realized that it's high time they changed something about the preparation process. Specifically, as the first innovation it was decided to change the teams' formation process. Having spent considerable amount of time on studying the statistics of other universities' performance, they managed to receive some interesting information: the dependence between the probability of winning a medal and the number of team members that participated in the finals in the past. More formally, we know $ n+1 $ real numbers $ p_{0}

The first line contains an integer $ n $ ( $ 3

Print the only real number — the expected average number of medals won per year if the optimal strategy is used. The result may have absolute or relative error $ 10^{-6} $ .

In the second test, no matter what participants the team contains, it is doomed to be successful.