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

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