There is an integer array that contain $n$ numbers, in the array there are $k$ distinct elements up to $k = 50$.  

Is it possible to sort this array in linear time, by using only comparisons?

I know that comparison sorts cannot perform better than $\mathcal O(n\log n)$, so maybe I have to show a sort function that sort this array in less than $\mathcal O(n\log n)$, and it will be a contradiction.