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3. Consider the following version of the Travelling Salesman problem: Input: A complete undirected graph with at least four vertices and weighted edges. Output: A minimum-weight cycle that visits every vertex exactly once. In which of the following cases removing a vertex from the graph can lead to a solution ofa greater cost (i.e.. to a greater minimum weight of a cycle)? 1. All weights are negative numbers. 2. Every vertex is a point on a plane, and the weight ofan edge is the Euclidean distance between the points it connects. Explain your answer by giving an example when the solution's cost increases or proving that this cannot happen