A912.Convention II--Silver

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).

The first line of input contains $N$. Each of the next $N$ lines specify the
details of the $N$ cows in order of seniority (the most senior cow being
first). Each line contains $a_i$ and $t_i$ for one cow. The $t_i$'s are
positive integers each at most $10^4$, and the $a_i$'s are positive integers
at most $10^9$.

Please print the longest potential waiting time over all the cows.

In this example, we have 5 cows (numbered 1..5 according to their order in the
input). Cow 4 is the first to arrive (at time 10), and before she can finish
eating (at time 27) cows 1 and 3 both arrive. Since cow 1 has higher
seniority, she gets to eat next, having waited 2 units of time beyond her
arrival time. She finishes at time 30, and then cow 3 starts eating, having
waited for 10 units of time beyond her starting time. After a gap where no cow
eats, cow 5 arrives and then while she is eating cow 2 arrives, eating 5 units
of time later. The cow who is delayed the most relative to her arrival time is
cow 3.