Observe that a shortest s-t path in a graph G = (V,E) with edge-weights w(e) = 1 for every edge e E is an s-t path that minimizes the number of edges. Consider an edge-weighted graph G = (V,E), where every edge weight is either 1 or -1, i.e., w(e) {1,1} for every edge e E.

Prove or disprove: An s-t path minimizing the number of edges of weight 1 is a shortest s-t path.