$*$Likely easiest to code part a$)$ and solve b$)$ and c$)$ by hand. Consider a variant of the eight$-$puzzle, which we saw in class, where we reduce the size of the puzzle to $3$x$2,$ in order to keep the number of states manageable. Now, consider the following initial and goal states: Initial state: Goal state: $14253$ a$)$ Show the solution path $($i$.$e$.,$ the sequence of puzzle states from the initial to the goal state$)$ found by each of the following algorithms, assuming transitions have unit cost. You must ensure that puzzle states that have been explored are not added to the search queue a second time. Given multiple states to explore that are otherwise equivalent in priority, the algorithm should prefer the state that involves moving a lower$-$numbered piece. i$.$ Breadth first search ii$.$ Depth first search iii. Iterative deepening search