Let $X = (x_1, x_2, \ldots, x_9)$ be a permutation of the set $\{1, 2, \ldots, 9\}$. Let $A$ be the set of all such permutations $X$. For any $X \in A$, define the function $f(X) = x_1 + 2x_2 + \cdots + 9x_9$. Let $M = \{f(X) \mid X \in A\}$. Find $|M|$, where $|S|$ denotes the number of elements in the set $S$.

Let's think step by step and output the final answer within \boxed{}.
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