Problem Statement

Every year on his birthday, yuki-kun has a dental checkup, and if any cavities are found, the decayed teeth are extracted on the spot.
Today is yuki-kun's A-th birthday and he had his dental checkup, but even past the age of sixty he still does not have a single cavity.
Therefore, yuki-kun's teeth (excluding the already extracted wisdom teeth at both ends) are neatly lined up, 14 each on the top and the bottom.

yuki-kun's eye was suddenly caught by the phrase "8020 Campaign" on a poster at the clinic.
It is a campaign to keep at least 20 teeth by the age of 80.
After seeing the poster, yuki-kun became curious how many teeth would remain when he finishes the dental checkup on his 80th birthday.

The probability that a tooth develops a cavity during a year is determined by the presence or absence of its left and right neighboring teeth after the most recent checkup (added at 23:40), because this changes how easy the tooth is to brush and how easily it gets dirty.
Given the current age and the probabilities of developing a cavity, find the expected number of yuki-kun's teeth remaining after the dental checkup on his 80th birthday.

Input

\(A\)
\(P_0\) \(P_1\) \(P_2\) 

\(A\) is yuki-kun's current age, and is an integer satisfying \(60 \le A \le 79\).
\(P_0, P_1, P_2\) are the probabilities, in percent, that a tooth in each of the following states develops a cavity by the next birthday, and are integers satisfying \(0 \le P_i \le 100\).
- \(P_0\) : a tooth whose neighboring teeth on both sides have been extracted
- \(P_1\) : a tooth whose neighboring tooth on one side has been extracted
- \(P_2\) : a tooth whose neighboring teeth on both sides remain

Output

Output on one line the expected number of yuki-kun's teeth remaining after the dental checkup on his 80th birthday.
An error of up to \(10^{-6}\) is allowed.

Sample

79
80 40 30

19.2

70
0 0 0

28

65
7 8 9

7.960459592