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Solitaire Tic-Tac-Toe is a new game on the market. Instead of adding X's and O's to an empty $3 \times 3$ grid, you start with a $3 \times 3$ grid in which every position already has an X or an O . In each move, you select a row, column or diagonal and reverse all the entries along the chosen line: all X's become O's and all O's become X's.

For instance, here is a sequence of possible moves.



Given an arrangement $S$, we want to explore all arrangements of the grid that we can generate starting with $S$. What is the smallest number $m$ such that each such arrangement can be reached using at most $m$ moves, starting with $S$ ?

  1. $8$
  2. $16$
  3. $64$
  4. $256$

     

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