$3.$ Write a program that solves the $8-$puzzle. Compare four different heuristics: Manhattan distance, misplaced tiles, n$-$MaxSwap, and row$/$column misplacement. The n$-$MaxSwap solves the relaxed game where any tile can be swapped with the space. The row$/$column misplacement counts the number of tiles not in the correct row plus the number of tiles not in the correct column. Compare the performance of each heuristic. See the aima$-$python$/$search$.$py$,$ aima$-$python$/$search$.$ipynb, and aima$-$python$/$gui$/$eight$\_$puzzle.py for help. The eight$\_$puzzle.py$,$ needs some corrections to work correctly.

$1.$ add import sys

$2.$ move sys$.$path.append$($os$.$path.join$($os$.$path.dirname$(\_\_$file$\_\_),\text{'}..\text{'}))$ before from search