A company is restructuring its office layout to improve collaboration among its departments. There are six departments labeled A$,$ B$,$ C$,$ D$,$ E$,$ and F$.$ The placement of departments follows specific guidelines:

The first department selected is placed in the center.

Subsequent department placements are determined by evaluating the Potential Ranking $($PR$)$ for all possible locations around the current layout in counterclockwise order, starting at the "western edge."

The new department is located based on the greatest PR value.

Given the following PR values for each department in each position:

Western edge: A $(7),$ B $(5),$ C $(8),$ D $(6),$ E $(9),$ F $(4)$

Northern edge: A $(9),$ B $(8),$ C $(5),$ D $(6),$ E $(7),$ F $(3)$

Eastern edge: A $(6),$ B $(8),$ C $(7),$ D $(4),$ E $(5),$ F $(9)$

Southern edge: A $(8),$ B $(7),$ C $(4),$ D $(9),$ E $(6),$ F $(5)$

Determine the placement sequence of the departments according to the given rules.