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: print("I cannot solve this.")
  
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"}]