Let $A$ be a matrix of order $3\times 3$ and $|A|=5$. If $\left|,2,\operatorname{adj}\left(3A,\operatorname{adj}(2A)\right)\right|=2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma}$, $\alpha,\beta,\gamma\in\mathbb{N}$, then $\alpha+\beta+\gamma$ is equal to