SPY, JUST ANOTHER SPY

A building contains $N$ floors. Each floor has $N$ rooms. From one room it is possible to go to the next adjacent room to the right or next adjacent room above. Agent 011 starts from the first room on the first floor and needs to reach the top most corner of such a building (i.e $N^{th}$ room of the $N^{th}$ floor). But the enemy anticipates Agent 011 and has laid a trap. If 011 crosses the diagon