$A^{**}$ Search

For the $A^{**}$ Search problems, consider the following graph. The letters are the names of nodes, and the digits within the node circles are the heuristic estimates for the distance from that given node to the goal node

For instance, node $B$ estimates the distance from itself to the goal node as $3.$ Also, node $S$ sees that it has an edge of length $3$ to node $B,$ and sees that $B$ has a heuristic estimate of $3$ for its distance to the goal node. So $S$ estimates that if it goes through $B,$ its distance to the goal node is $3+3=6$

What is node A$\text{'}$s estimate $($possibly an underestimate, but not an overestimate$)$ of the distrance from it to goal node G$?$

Question $2$ options:

$1)$

$1$

$2)$

$2$

$3)$

$3$

$4)$

$4$

What is node S$\text{'}$s estimate $($possibly an underestimate, but not an overestimate$)$ of the distrance from it to goal node G$,$ if it follows a path through node A$?$

Question $3$ options: