The vertices of a cycle with n vertices are labelled with integers. A "flip" operation takes three consecutive vertices with labels \((x,y,z)\) where \(y<0\) and replaces the labels, respectively, with \((x+y, -y, z+y)\). 

Prove or disprove: it is possible to label the vertices so that the sum of the labels is positive, and then to do an infinite sequence of flip operations.

Example: \((2,-1,0) \rightarrow (1,1,-1) \rightarrow (0,0,1)\) (and then you are stuck)