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())
  s = list(map(int, input().split()))
  ans = -1000000000000000
  dp = [{} for _ in range(n)]
  dp[0][1] = s[0]
  dp[1][1] = s[1]
  dp[2][1] = s[2]
  for i in range(n):
      for x in dp[i].keys():
          y = dp[i][x]
          if x == n // 2:
              ans = max(ans, y)
          else:
              if (n - (i + 2) + 1) // 2 >= n // 2 - (x + 1) and i + 2 <= n - 1:
                  if x + 1 in dp[i + 2].keys():
                      dp[i + 2][x + 1] = max(dp[i + 2][x + 1], dp[i][x] + s[i + 2])
                  else:
                      dp[i + 2][x + 1] = dp[i][x] + s[i + 2]
              if (n - (i + 3) + 1) // 2 >= n // 2 - (x + 1) and i + 3 <= n - 1:
                  if x + 1 in dp[i + 3].keys():
                      dp[i + 3][x + 1] = max(dp[i + 3][x + 1], dp[i][x] + s[i + 3])
                  else:
                      dp[i + 3][x + 1] = dp[i][x] + s[i + 3]
              if (n - (i + 4) + 1) // 2 >= n // 2 - (x + 1) and i + 4 <= n - 1:
                  if x + 1 in dp[i + 4].keys():
                      dp[i + 4][x + 1] = max(dp[i + 4][x + 1], dp[i][x] + s[i + 4])
                  else:
                      dp[i + 4][x + 1] = dp[i][x] + s[i + 4]
  print(ans)
  
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"}]