Suppose discrete random variables $\{X_1, X_2, ..., X_n\}$ are i.i.d. described by the probability function:

$f(x) \equiv \text{Pr}(X_i = x)$,

and $X_i \in \{1,2,3, ..., m\}$.

Let $Y$ be the maximum unique number in $\{X_1, X_2, ..., X_n\}$, i.e., the maximum of the numbers that occur only once in $\{X_1, X_2, ..., X_n\}$. If there is no unique number in $\{X_1, X_2, ..., X_n\}$, then we define $Y = 0$.

Is there any elegant way to obtain the distribution of $Y$?