output_description: For each dataset, output the number of possible train configurations in a
  line. No other characters should appear in the output.
input_description: The entire input looks like the following.
  
  > _the number of datasets = m_  
  >  _1st dataset_  
  >  _2nd dataset_  
  >  ...  
  >  _m-th dataset_  
  >
  
  Each dataset represents an arriving train, and is a string of 2 to 72
  lowercase letters in an input line.
attempt: #!/usr/bin/env python3
  # AOJ B
  
  m = int(input())
  for _ in range(m):
      s = list(input())
      all = []
      for i in range(1, len(s)):
          front = s[:i]
          back = s[i:]
          fr = list(reversed(front))
          br = list(reversed(back))
          pair = [front, fr, back, br]
          for j in range(4):
              if j > 1:
                  for k in range(2):
                      p = pair[j] + pair[k]
                      if p not in all:
                          all.append(p)
              else:
                  for k in range(2, 4):
                      p = pair[j] + pair[k]
                      if p not in all:
                          all.append(p)
  
      if len(all) == 0:
          print(1)
      else:
          print(len(all))
  
problem_description: B: Organize Your Train part II
  
  RJ Freight, a Japanese railroad company for freight operations has recently
  constructed exchange lines at Hazawa, Yokohama. The layout of the lines is
  shown in Figure B-1.
  
  ![](https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_Layout)  
  Figure B-1: Layout of the exchange lines
  
  A freight train consists of 2 to 72 freight cars. There are 26 types of
  freight cars, which are denoted by 26 lowercase letters from "a" to "z". The
  cars of the same type are indistinguishable from each other, and each car's
  direction doesn't matter either. Thus, a string of lowercase letters of length
  2 to 72 is sufficient to completely express the configuration of a train.
  
  Upon arrival at the exchange lines, a train is divided into two sub-trains at
  an arbitrary position (prior to entering the storage lines). Each of the sub-
  trains may have its direction reversed (using the reversal line). Finally, the
  two sub-trains are connected in either order to form the final configuration.
  Note that the reversal operation is optional for each of the sub-trains.
  
  For example, if the arrival configuration is "abcd", the train is split into
  two sub-trains of either 3:1, 2:2 or 1:3 cars. For each of the splitting,
  possible final configurations are as follows ("+" indicates final
  concatenation position):
  
      
      
        [3:1]
          abc+d  cba+d  d+abc  d+cba
        [2:2]
          ab+cd  ab+dc  ba+cd  ba+dc  cd+ab  cd+ba  dc+ab  dc+ba
        [1:3]
          a+bcd  a+dcb  bcd+a  dcb+a
      
  
  Excluding duplicates, 12 distinct configurations are possible.
  
  Given an arrival configuration, answer the number of distinct configurations
  which can be constructed using the exchange lines described above.
samples: [{"input": "aa\n    abba\n    abcd\n    abcde", "output": "6\n    12\n    18"}]