Consider the following graph and perform a graph search on this graph. Step costs, and heuristic values $($in the form h$=$x$)$ are given in the graph. Each node's successors are represented by the arrows heading away from it$.($It is worth noting that E is a successor to itself.$)$ A is the initial node, whereas G $1$ and G$2$ are the destination nodes $($double circled$).$

Note: Remembering visited nodes, so repeated nodes are not possible.

What is the path cost from A to G$2$ for the given graph using A$*$search$?$