A number theory problem by Ilham Saiful Fauzi

Let all the ordered solutions of non-negative integer triplets $(x,y,z)$ satisfying $\dfrac{x! + y!}{z!} = 3^z$ be denoted by $(x_1, y_1, z_1) , \ldots , (x_n , y_n , z_n)$ .

Find $\displaystyle \sum_{i=1}^n (x_i + y_i + z_i)$ .