Functions $f$ and $g$ with domain of integers are defined as
$$\begin{aligned}
& f ( n ) = n + \frac { 1 } { 3 } \\
& g ( n ) = n + \frac { 1 } { 6 }
\end{aligned}$$
Given this,\\
I. $f \circ f \circ f$\\
II. $f \circ g \circ f$\\
III. $g \circ f \circ g$\\
For which of these functions does the image set consist only of integers?\\
A) Only I\\
B) Only II\\
C) I and II\\
D) II and III\\
E) I, II and III