You are tasked with optimizing delivery routes in a logistics network where some roads offer discounts or incentives, represented as negative weights. The locations are represented as nodes, and the roads between them are represented as edges with weights indicating the travel distance or cost $($in kilometers$).$ Some roads offer negative weights due to discounts, which makes the Bellman$-$Ford algonithm suitable for finding the shortest path Consider the following graph with positive and negative weights:

Apply the Bellman$-$Ford algorithm starting from node $"$A$"$ to find the shortest path to all other nodes. Show each relaxation step and the shortest path tree after the algorithm completes. Identify any negative weight cycles if present.