P3103 [USACO14FEB]Airplane Broading G

FJ's cows have decided to take a vacation, and have miraculously managed to find an airline willing to sell them tickets. When they arrive at the airport and start boarding their plane, they face an interesting problem, however. The airplane has $N$ seats, which we model as the points $x=1$ through $x=N$ on the number line. All N cows $(1 \le N \le 200,000)$ are standing in line waiting to get to their seats. Cow $N$ is at position $x=0$, Cow $N-1$ is at position $x=-1$, and so on. Cow i has been assigned to Seat $S_i$, where $S_1$,...,$S_N$ is a permutation of $1$,...,$N$. At each time step, each cow takes a step to the right if she can. When cow $i$ reaches her seat $S_i$, she will stop to put her baggage in the overhead bin, which takes $T_i$ seconds, and then sit down. For those $T_i$ steps, the cow behind her (if there is one) is blocked from moving forward. If there is a line of cows behind her, the line is effectively blocked as well. How long will it take for all the cows to sit down? The sum of $T_i$ for all cows will be less than $1,000,000,000$.

* Line $1$: A single integer, $N$. * Lines $2$..$N+1$: Two space-separated integers, $S_i$ and $T_i$.

* Line $1$: A single line indicating the amount of time it takes to seat all cows.

Initially, the cows are situated like this: cows -> $123$ $123$