Convention II timer 2s memory 512MB

Despite long delays in airport pickups, Farmer John's convention for cows interested in eating grass has been going well so far. It has attracted cows from all over the world.

The main event of the conference, however, is looking like it might cause Farmer John some further scheduling woes. A very small pasture on his farm features a rare form of grass that is supposed to be the tastiest in the world, according to discerning cows. As a result, all of the N cows at the conference (1 \leq N \leq 10^5) want to sample this grass. This will likely cause long lines to form, since the pasture is so small it can only accommodate one cow at a time.

Farmer John knows the time a_i that each cow i plans to arrive at the special pasture, as well as the amount of time t_i she plans to spend sampling the special grass, once it becomes her turn. Once cow i starts eating the grass, she spends her full time of t_i before leaving, during which other arriving cows need to wait. If multiple cows are waiting when the pasture becomes available again, the cow with the highest seniority is the next to be allowed to sample the grass. For this purpose, a cow who arrives right as another cow is finishing is considered "waiting". Similarly, if a number of cows all arrive at exactly the same time while no cow is currently eating, then the one with highest seniority is the next to eat.

Please help FJ compute the maximum amount of time any cow might possibly have to wait in line (between time a_i and the time the cow begins eating).

Problem credits: Brian Dean