2025 Gauss 8 Problem 23

The number 2013 is multiplied by a positive integer n. The last four digits of the result are 2025. What is the sum of the digits of the smallest possible value of n?

\textbf{(A)}\ 17\quad \textbf{(B)}\ 13\quad \textbf{(C)}\ 15\quad \textbf{(D)}\ 14\quad \textbf{(E)}\ 16

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 Gauss contests here.