A coin with heads facing up is shown as 
and a coin with tails facing up is shown as 
.
Six coins are placed in the Starting Arrangement, as shown in the figure below. A “step” is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement, as shown in the figure, is #\_\_\_\_\_\_\_\_$
- $3$
- $6$
- $9$
- $12$
