Let the determinant of a square matrix $$A$$ of order $$m$$ be $$m - n$$, where $$m$$ and $$n$$ satisfy $$4m + n = 22$$ and $$17m + 4n = 93$$. If $$det(n \ adj(adj(mA))) = 3^a 5^b 6^c$$, then $$a + b + c$$ is equal to

A

$$84$$

B

$$96$$

C

$$101$$

D

$$109$$