2017 Fermat Problem 10

The sum of four different positive integers is 100. The largest of these four integers is n. The smallest possible value of n is

\textbf{(A)}\ 26\quad \textbf{(B)}\ 50\quad \textbf{(C)}\ 28\quad \textbf{(D)}\ 27\quad \textbf{(E)}\ 94

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.