Consider the search problem shown in the $5\backslash$times $7$

grid below where an agent is allowed to move in all eight directions $($up$,$ down, left, right, and diagonally$)$ and walls are shown in black. The actions for moving up$,$ down, left, and right cost $1\mathrm{.}0$

$,$ while the diagonal moves cost $1\mathrm{.}5$

$.$ The initial state s

is in cell $(5,1)$

and the goal sg

is in cell $(5,7)$

$.$ The numbers in the cells show the heuristic value for each state; the heuristic is admissible. The agent cannot "cut corners", i$.$e$.,$ it cannot move diagonally if there is a wall in between the cells. For example, the agent cannot move from cell $(2,5)$

to cell $(1,6)$

with a diagonal move.

What is the solution cost A$*$ finds for this problem? What if we sorted the nodes in OPEN by their h

$-$values, instead of their g$+$h

values as A$*$ does?