A word arrangement machine, when given a particular input,...

For the sake of convenience, assign numbers to each word of the input. Input: $$\begin{array}{lllllll}Ja & Ma & Da & Ch & Ha & Bo & Ka\end{array}$$$$\begin{array}{lllllll}&&&1 && 2 && 3 && 4 & 5 && 6 && 7 \end{array}$$ Now, in Step I, the third word comes at the beginning and the first and second words are pushed rightwards. Also, the fourth word goes at the end and the remaining words are pushed leftwards. In Step II, the fourth word from the previous step comes at the beginning while the first three words are pushed rightwards. Also, the fifth word of Step I goes at the end and the remaining words are pushed leftwards. These steps are repeated thereafter For convenience, we plot the movement of each word in each step by the numbers assigned to them in the input. $$\begin{array}{lcccccccc} \text { Input: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & \\ \text { Step I: } & 3 & 1 & 2 & 5 & 6 & 7 & 4 & \\ \text { Step II: } & 5 & 3 & 1 & 2 & 7 & 4 & 6 & \\ \text { Step III: } & 1 & 5 & 3 & 7 & 4 & 6 & 2 \\ \text { Step IV: } & 7 & 1 & 5 & 3 & 6 & 2 & 4 \\ \text { Step V: } & 5 & 7 & 1 & 6 & 2 & 4 & 3 \\ \text { Step VI: } & 6 & 5 & 7 & 1 & 4 & 3 & 2 & \\ \text { Step VII: } & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ \text { Step VIII: } & 4 & 7 & 6 & 5 & 2 & 1 & 3 & \end{array}$$Input: $$\begin{array}{llllll}hai & da & di & Mo & su & ka & au\end{array}$$ $$\begin{array}{llllll}&&&1 && 2 && 3 & 4 && 5 & 6 &&7\end{array}$$Step IV: $$\begin{array}{llllll}7 && 1 && 5 & 3 & 6 && 2 &&4\end{array}$$ $$\begin{array}{llllll}&&&au & hai & su & di & ka & da & Mo\end{array}$$