code: def left_right_inversions(tab):
      
      n = len(tab)
      left = [0] * n
      right = [0] * n
      tmp = [None] * n      # temporary table
      rank = list(range(n))
      _merge_sort(tab, tmp, rank, left, right, 0, n)
      return left, right
docs: Compute left and right inversions of each element of a table.
  
      :param tab: list with comparable elements
      :returns: lists left and right. left[j] = the number of i<j such that tab[i] > tab[j].
                right[i] = the number of i<j such that tab[i] > tab[j].
      :complexity: `O(n \log n)`