DE-BUNDESWETTBEWERB 2014

The $100$ vertices of a prism, whose base is a $50$ -gon, are labeled with numbers $1, 2, 3, \ldots, 100$ in any order. Prove that there are two vertices, which are connected by an edge of the prism, with labels differing by not more than $48$ .

Note: In all the triangles the three vertices do not lie on a straight line.