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 = sorted((int(x), k) for k, x in enumerate(input().split()))
  opt = [[0 for j in range(n + 1)] for i in range(n + 1)]
  for i in reversed(range(n)):
      for j in range(i, n):
          val, k = a[j - i]
          opt[i][j] = max(
              val * abs(k - i) + opt[i + 1][j], val * abs(k - j) + opt[i][j - 1]
          )
  print(opt[0][n - 1])
  
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"}]