output_description: Print the maximum possible sum of the chosen elements.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_1 ... A_N
attempt: N = int(input())
  A = [0] + list(map(int, input().split(" ")))
  
  dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]
  
  for i in range(3, N + 1):
      b = (i - 1) // 2
      f = (i + 1) // 2
      dp_list.append({})
      for j in range(b, f + 1):
          if j in dp_list[i - 1]:
              dp_list[i][j] = (
                  dp_list[i - 2][j - 1] + A[i]
                  if dp_list[i - 2][j - 1] + A[i] > dp_list[i - 1][j]
                  else dp_list[i - 1][j]
              )
          else:
              dp_list[i][j] = dp_list[i - 2][j - 1] + A[i]
  
  print(dp_list[-1][N // 2])
  
problem_description: Statement
  
  Given is an integer sequence A_1, ..., A_N of length N.
  
  We will choose exactly \left\lfloor \frac{N}{2} \right\rfloor elements from
  this sequence so that no two adjacent elements are chosen.
  
  Find the maximum possible sum of the chosen elements.
  
  Here \lfloor x \rfloor denotes the greatest integer not greater than x.
samples: [{"input": "6\n    1 2 3 4 5 6", "output": "12\n    \n\nChoosing 2, 4, and 6 makes the sum 12, which is the maximum possible value.\n\n* * *"}, {"input": "5\n    -1000 -100 -10 0 10", "output": "0\n    \n\nChoosing -10 and 10 makes the sum 0, which is the maximum possible value.\n\n* * *"}, {"input": "10\n    1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000", "output": "5000000000\n    \n\nWatch out for overflow.\n\n* * *"}, {"input": "27\n    18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49", "output": "295"}]