Let $f$ and $g$ be permutations on the set $\lbrace 1, 2, 3, 4, 5, 6 \rbrace$, defined as follows

$$f = \displaystyle\left(\begin{array}{cccccc} 1 &2 &3 &4 &5 &6 \cr 5 &2 &3 &6 &1 &4 \cr \end{array}\right)$$
$$g = \displaystyle\left(\begin{array}{cccccc} 1 &2 &3 &4 &5 &6 \cr 3 &1 &5 &6 &4 &2 \cr \end{array}\right)$$
Which of the following are even permutations?

A. $g$
B. $g^{-1}$
C. $fg$
D. $fgf^{-1}$
E. $f^{-1}$
F. $f$
G. None of the above