Question 117
Let the 9-element set $A = \{a + bi \mid a, b \in \{1, 2, 3\}\}$, with $i$ being the imaginary unit. $\alpha = (z_1, z_2, \dots, z_9)$ is a permutation of all the elements in $A$, satisfying $|z_1| \le |z_2| \le \dots \le |z_9|$. The number of such permutations $\alpha$ is ______.