Given the $8-$Puzzle in the following Initial configuration $($State$)$:

$\backslash$table$[[|1,1,2,|,],[|,$l$,4,|,],[7,1,5,|,]]$

a$)$ Construct the search tree via a Level$-$by$-$Level search until the Goal State is obtained.

b$)$ Construct the search tree via a Heuristically Guided search $($using # of tiles out of place heuristic$)$ until the Goal State is obtained. Be sure to show both the value of the heuristic $($# of tiles out of place$)$ and value of the modified heuristic $($# of tiles out of place $+$ level #$)$ for each node in the tree.