The figure below shows a search$-$space graph, where $A$ is the initial state and $G$ denotes the

goal. Edges are labeled with their true cost. We have a heuristic function, $,$ written in the standard

form: $f(n)=g(n)+h(n)$ where $g(n)$ is the cost to get from A to $n$ and $h(n)$ is an estimate of the

remaining distance to $G.$

$($i$)$ Is h admissible? Why or why not?

$($ii$)$ Is h consistent$/$monotonic$?$ Why or why not?