A vertical curve joins a $-2\mathrm{.}0\%$ grade to a $+0\mathrm{.}5\%$ grade at VPI Station $110+00$ and elevation $($of VPI$)$ at $69\mathrm{.}50$ m$.$ The centreline of the roadway must clear an overhead structure located at Station $109+20$ by $5\mathrm{.}67$ m$.$ The elevation of the bottom of the structure is $77\mathrm{.}45$ m above sea level.

$($a$)$ What is the minimum length of vertical curve that can be used?

$($b$)$ Determine whether the length of curve in part $($a$)$ satisfies MTO guidelines, and, if not what minimum would be appropriate. ANSWER ASAP