Problem 2 (10 points): For the following graph in Figure 2, demonstrate how the Breadth-First Search (BFS) and the Depth-First Search (DFS) work, respectively. Use the node "q" as the starting node. During the search, when you have multiple choices regarding which node to visit next (i.e., when enumerating the direct neighbors of a node as in BFS, or when going to another branch or "sibling" node of a common "parent" node as in DFS), please use the alphabetical order to choose the next node. Show the intermediate steps, and the final output sequence of the nodes. Figure 2: A directed graph