output_description: Print the probability of having more heads than tails. The output is
  considered correct when the absolute error is not greater than 10^{-9}.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      p_1 p_2 \ldots p_N
attempt: n = int(input())
  p = list(map(float, input().split()))
  dp = [[0] * (2 * n + 2) for i in range(n // 2 + 1)]
  dp[0][n + 1] = p[0]
  dp[0][n] = 1 - p[0]
  for i in range(n // 2):
      p1, p2 = p[2 * i + 1], p[2 * i + 2]
      h, t = p1 * p2, (1 - p1) * (1 - p2)
      m = 1 - h - t
      for j in range(n - i, n + i + 2):
          plus = dp[i][j]
          dp[i + 1][j + 1] += plus * h
          dp[i + 1][j] += plus * m
          dp[i + 1][j - 1] += plus * t
  print(sum(dp[n // 2][n + 1 :]))
  
problem_description: Statement
  
  Let N be a positive odd number.
  
  There are N coins, numbered 1, 2, \ldots, N. For each i (1 \leq i \leq N),
  when Coin i is tossed, it comes up heads with probability p_i and tails with
  probability 1 - p_i.
  
  Taro has tossed all the N coins. Find the probability of having more heads
  than tails.
samples: [{"input": "3\n    0.30 0.60 0.80", "output": "0.612\n    \n\nThe probability of each case where we have more heads than tails is as\nfollows:\n\n  * The probability of having (Coin 1, Coin 2, Coin 3) = (Head, Head, Head) is 0.3 \u00d7 0.6 \u00d7 0.8 = 0.144;\n  * The probability of having (Coin 1, Coin 2, Coin 3) = (Tail, Head, Head) is 0.7 \u00d7 0.6 \u00d7 0.8 = 0.336;\n  * The probability of having (Coin 1, Coin 2, Coin 3) = (Head, Tail, Head) is 0.3 \u00d7 0.4 \u00d7 0.8 = 0.096;\n  * The probability of having (Coin 1, Coin 2, Coin 3) = (Head, Head, Tail) is 0.3 \u00d7 0.6 \u00d7 0.2 = 0.036.\n\nThus, the probability of having more heads than tails is 0.144 + 0.336 + 0.096\n+ 0.036 = 0.612.\n\n* * *"}, {"input": "1\n    0.50", "output": "0.5\n    \n\nOutputs such as `0.500`, `0.500000001` and `0.499999999` are also considered\ncorrect.\n\n* * *"}, {"input": "5\n    0.42 0.01 0.42 0.99 0.42", "output": "0.3821815872"}]