def navigate5(instructions, coordinate, direction):
	rotation = {'L': complex(0,1), 'R': complex(0,-1)}

	for command in instructions:
		if(command == "M"):
			coordinate = coordinate + direction
		else:
			direction = direction * rotation[command]

	return (coordinate, direction)

finalCoordinate, finalDirection = navigate5("LMLMLMLMM", complex(1,2), complex(0, 1))
assert finalCoordinate == complex(1, 3)
assert finalDirection == complex(0, 1)

finalCoordinate, finalDirection = navigate5("MMRMMRMRRM", complex(3,3), complex(1,0))
assert finalCoordinate == complex(5, 1)
assert finalDirection == complex(1, 0)