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