Draw a line following the grid lines conforming the the following rules:
1 - The line starts from S and ends at F.
2 - The line does not cross or overlap itself at any point.
3 - The line divides the grid into regions each with exactly two As and two Bs.

+---+---+---+---+---F
| A | B | A |   | B |
+---+---+---+---+---+
|   | B |   |   | B |
+---+---+---+---+---+
| A |   | B |   | A |
+---+---+---+---+---+
| A | A |   | A | B |
+---+---+---+---+---+
| B |   | B |   | A |
S---+---+---+---+---+

An example of a solved grid:

+   +   +---F
  B   A | A  
+---+---+   +
| B          
S   +   +   +