If A is a square matrix of order 3 such that det ( A )=3 and det ( adj (-4 adj (-3 adj (3 adj ((2 A )^-1)))))=2^m 3^n, then m +2 n is equal to:

If A is a square matrix of order $\displaystyle 3$ such that $\displaystyle \operatorname{det}(\mathrm{A})=3$ and $\displaystyle \operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2 \mathrm{~A})^{-1}\right)\right)\right)\right)\right)=2^{\mathrm{m}} 3^{\mathrm{n}}$, then $\displaystyle \mathrm{m}+2 \mathrm{n}$ is equal to :