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 = list(map(int, input().split()))
  inf = 10**10
  
  if N % 2 == 0:
      dp = [[[0] * 2 for __ in range(2)] for _ in range(N)]
      dp[0][0][0] = A[0]
      dp[0][0][1] = -inf
      dp[0][1][0] = -inf
      dp[0][1][1] = 0
      dp[1][0][0] = -inf
      dp[1][0][1] = -inf
      dp[1][1][0] = A[1]
      dp[1][1][1] = -inf
      for i in range(2, N):
          dp[i][0][0] = dp[i - 2][0][0] + A[i]
          dp[i][0][1] = -inf
          dp[i][1][0] = max(dp[i - 1][1][1], dp[i - 2][1][0]) + A[i]
          dp[i][1][1] = dp[i - 2][0][0]
      print(max(dp[-1][1]))
  else:
      dp = [[[0] * 2 for __ in range(3)] for _ in range(N)]
      dp[0][0][0] = A[0]
      dp[0][0][1] = -inf
      dp[0][1][0] = -inf
      dp[0][1][1] = 0
      dp[0][2][0] = -inf
      dp[0][2][1] = -inf
      dp[1][0][0] = -inf
      dp[1][0][1] = -inf
      dp[1][1][0] = A[1]
      dp[1][1][1] = -inf
      dp[1][2][0] = -inf
      dp[1][2][1] = 0
      for i in range(2, N):
          dp[i][0][0] = dp[i - 2][0][0] + A[i]
          dp[i][0][1] = -inf
          dp[i][1][0] = max(dp[i - 1][1][1], dp[i - 2][1][0]) + A[i]
          dp[i][1][1] = dp[i - 2][0][0]
          dp[i][2][0] = max(dp[i - 1][2][1], dp[i - 2][2][0]) + A[i]
          dp[i][2][1] = max(dp[i - 1][1][1], dp[i - 2][1][0])
      print(max(dp[-1][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"}]