2016 Fermat Problem 17

A total of n points are equally spaced around a circle and are labelled with the integers 1 to n, in order. Two points are called *diametrically opposite* if the line segment joining them is a diameter of the circle. If the points labelled 7 and 35 are diametrically opposite, then n equals

\textbf{(A)}\ 54\quad \textbf{(B)}\ 55\quad \textbf{(C)}\ 56\quad \textbf{(D)}\ 57\quad \textbf{(E)}\ 58

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.