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Сборники > Kovrov IT 2010 > задача:


I. Galls village

Задачи сборника

• A. Провайдеры
• B. Primes
• C. Bishops
• D. Unusual Lottery
• E. Polygons
• F. Liars and Knights
• G. Sequence
• H. Coins
• I. Galls village
• J. String manipulations

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Лимит времени 3000/4000/4000/4000 мс. Лимит памяти 65000/65000/65000/65000 Кб.
Автор: Кирилл Бутин, ПГУ.

As you know Caesar is a conqueror. He decided to occupy N villages in a very unusual way. Each day he chooses some nonempty subset of not conquered villages and tries to capture it. If he succeeds, those villages will pass into his possession, otherwise Caesar will leave them free (freedom for all subset, but only for that day). This process repeats on the next day until there is at least one not captured village. Any subset of villages can be chosen with equal probability. After choosing some subset, Caesar tries to capture villages one by one in any order.

Galls are living in the first village. Your task is to find the probability that someday all villages except it will be conquered.

Input
The first line contains one integer N (1 ≤ N ≤ 15) - the number of villages. The following N lines contain integer probabilities Pi - probability of capture of i-th village in percents (0 < Pi ≤ 100; 1 ≤ iN).

Output
Output a real number - the probability that someday only the first village will remain free. Answer should be accurate to 10-5.

Input 1 Output 1
2
100
100
0.333333333
Input 2 Output 2
3
28
62
96
0.503901145

Для отправки решений необходимо выполнить вход.

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