Let A be a matrix of order 3 × 3 and |A|=5. If |2 adj (3 A adj (2 A))|=2^α · 3^β · 5^γ, α, β, γ ∈ N, then α+β+γ is equal to

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