Implement the DFS algorithm to search (starting with a given node) if another given node (value) exist in the graph. For example, search if node G exists in the graph (you may start from node D). Also, find the distance(smallest number of intermediate nodes) and path of the target node from the starting node. For example, distance between node A to node F is 4 and the path is A > B > D > E > F.

5 B 9 3 1 H 5 A 1 3