Let $\backslash$omega in S$5$ be the permutation

$12345\backslash$omega $=35142.$

$($a$)$ Write $\backslash$omega as a product of disjoint cycles.

$($b$)$ What is the order of $\backslash$omega $?$

$($c$)$ What is the sign of $\backslash$omega $?$

$($d$)$ Write $\backslash$omega as a product of $3-$cycles.