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()))
  out = 0
  if N % 2 == 0:
      for i in range(N // 2):
          out += max(A[2 * i], A[2 * i + 1])
      print(out)
  else:
      X = []
      Y = []
      for i in range(N):
          if i % 2 == 0:
              X.append(A[i])
          else:
              Y.append(A[i])
      Z = []
      W = []
      for i in range(N // 2):
          Z.append(X[i] - Y[i])
          W.append(X[i + 1] - Y[i])
      P = [0] * (N // 2 + 1)
      Q = [0] * (N // 2 + 1)
      max1 = 0
      max2 = 0
      sum1 = 0
      sum2 = 0
      for i in range(N // 2):
          sum1 += Z[i]
          if max1 < sum1:
              max1 = sum1
          sum2 += W[N // 2 - 1 - i]
          if max2 < sum2:
              max2 = sum2
          P[i + 1] = max1
          Q[-1 * i - 1 - 1] = max2
      R = []
      for i in range(N // 2 + 1):
          R.append(P[i] + Q[i])
      # print(Z)
      # print(W)
      # print(P)
      # print(Q)
      # print(sum(Y))
      print(sum(Y) + max(max(R), 0))
  
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"}]