output_description: Print 2^N-1 lines. In the i-th line, print the answer of the problem above for
  K=i.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_0 A_1 ... A_{2^N-1}
attempt: def suan(x, y):
      li = []
      for a in x:
          for b in y:
              if x[0] == x[1]:
                  li.append(a + b)
              elif a != b:
                  li.append(a + b)
      return max(li)
  
  
  while True:
      try:
          n = int(input())
          num = list(map(int, input().split()))
          maxn = [[num[0], 0]]
          max1 = num[0]
          max2 = 0
          for i in range(1, 2**n):
              if num[i] > max2:
                  max2 = num[i]
              if max2 > max1:
                  max1, max2 = max2, max1
              maxn.append([max1, max2])
          for i in range(1, 2**n):
              xxx = []
              if (i | (i - 1)) <= i:
                  xxx.append(suan(maxn[i], maxn[i - 1]))
              if (i | (i - 2)) <= i and i >= 2:
                  xxx.append(suan(maxn[i], maxn[i - 2]))
              if ((i - 1) | (i - 2)) <= i and i >= 2:
                  xxx.append(suan(maxn[i - 1], maxn[i - 2]))
              print(max(xxx))
      except:
          break
  
problem_description: Statement
  
  There is an integer sequence of length 2^N: A_0, A_1, ..., A_{2^N-1}. (Note
  that the sequence is 0-indexed.)
  
  For every integer K satisfying 1 \leq K \leq 2^N-1, solve the following
  problem:
  
    * Let i and j be integers. Find the maximum value of A_i + A_j where 0 \leq i < j \leq 2^N-1 and (i or j) \leq K. Here, or denotes the bitwise OR.
samples: [{"input": "2\n    1 2 3 1", "output": "3\n    4\n    5\n    \n\nFor K=1, the only possible pair of i and j is (i,j)=(0,1), so the answer is\nA_0+A_1=1+2=3.\n\nFor K=2, the possible pairs of i and j are (i,j)=(0,1),(0,2). When\n(i,j)=(0,2), A_i+A_j=1+3=4. This is the maximum value, so the answer is 4.\n\nFor K=3, the possible pairs of i and j are\n(i,j)=(0,1),(0,2),(0,3),(1,2),(1,3),(2,3) . When (i,j)=(1,2), A_i+A_j=2+3=5.\nThis is the maximum value, so the answer is 5.\n\n* * *"}, {"input": "3\n    10 71 84 33 6 47 23 25", "output": "81\n    94\n    155\n    155\n    155\n    155\n    155\n    \n\n* * *"}, {"input": "4\n    75 26 45 72 81 47 97 97 2 2 25 82 84 17 56 32", "output": "101\n    120\n    147\n    156\n    156\n    178\n    194\n    194\n    194\n    194\n    194\n    194\n    194\n    194\n    194"}]