After every $$4$$ "Right turns" the troops will be facing north again; so after $$68$$ turns they are facing north, after $$69$$ turns east, and after $$70$$ turns south. 
A sergeant stands too long in the sun and gets confused. His troops are lined up facing north. Then he gives the order to "Right Turn $90^{}\circ$" $$70$$ times, and his troops do so. In which direction are the troops facing at the end? 

(1) $$$$north 
(2) $$$$east 
(3) $$$$south 
(4) $$$$west 
(5) $$$$west-south-west 