Joker and the Arkham Asylum

The Arkham Asylum of Gotham, is the place of residence of evils. Batman uses his super awesome Bat-Technology to guard it against the potential outbreak. The Asylum can be considered as a NxN maze, where each cell houses a building. Note that, the left most building in the bottom most row is said to be present at the cell in 1st row and 1st column. Similarly, the right most building in the top mo