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