Note: You need not have to read the above to understand this puzzle, however this puzzle does spoil the above one.
The tele door system:
Each pair of doors, represented by letters, are "linked", you go enter one door on the left side, and you go exit the other in the right. Example hallway:
A1 B1 A2 B2
Prisoners always enter through the leftmost door. So in the example hallway, they'd go enter through the first A1->A2->B2->B1->A2->A1->B1->B2->
Note: There will never be an 3 ( representing any letter).
You, my friend, are a wickid man. You wish to trap someone in a hallway for eternity using nothing but pairs of tele doors. But sadly, you have finally come to understand this is not possible.
But how long CAN you keep them there?
Given 26 pairs of teles, how many tele doors can you force them walk through, before escaping?