output_description: Print the maximum total happiness points the children can earn.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_1 A_2 ... A_N
attempt: N = int(input())
  A = [int(INPUT) for INPUT in input().strip().split(" ")]
  
  happiness = 0
  
  exist_index = list(range(N))
  exist_visited = [0] * N
  empty_index = list(range(N))
  for k in range(N):
      largest_gain = -1
      # print(exist_index, exist_visited, empty_index)
      for i in range(N):
          if exist_visited[i] == 1:
              continue
  
          place = (
              0
              if abs(exist_index[i] - empty_index[0])
              > abs(exist_index[i] - empty_index[-1])
              else -1
          )
  
          gain = A[exist_index[i]] * abs(exist_index[i] - empty_index[place])
  
          # print(place, gain)
          if gain > largest_gain:
              largest_gain = gain
              best_child = exist_index[i]
              best_place = place
      # print("--")
      # print(largest_gain, best_child)
      # print("--")
      happiness += largest_gain
      exist_visited[best_child] = 1
      if best_place == 0:
          empty_index = empty_index[1:]
      else:
          empty_index = empty_index[:-1]
      # empty_index = empty_index[0:place] + empty_index[place + 1:]
  
  print(happiness)
  
problem_description: Statement
  
  There are N children standing in a line from left to right. The activeness of
  the i-th child from the left is A_i.
  
  You can rearrange these children just one time in any order you like.
  
  When a child who originally occupies the x-th position from the left in the
  line moves to the y-th position from the left, that child earns A_x \times
  |x-y| happiness points.
  
  Find the maximum total happiness points the children can earn.
samples: [{"input": "4\n    1 3 4 2", "output": "20\n    \n\nIf we move the 1-st child from the left to the 3-rd position from the left,\nthe 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and\nthe 4-th child to the 2-nd position, the children earns 1 \\times |1-3|+3\n\\times |2-4|+4 \\times |3-1|+2 \\times |4-2|=20 happiness points in total.\n\n* * *"}, {"input": "6\n    5 5 6 1 1 1", "output": "58\n    \n\n* * *"}, {"input": "6\n    8 6 9 1 2 1", "output": "85"}]