Problem G: Trainsorting
Erin is an engineer. She drives trains. She also arranges the cars
within each train. She prefers to put the cars in decreasing order of
weight, with the heaviest car at the front of the train.
Unfortunately, sorting train cars is not easy. One cannot simply pick
up a car and place it somewhere else. It is impractical to insert a car
within an existing train. A car may only be added to the beginning and
end of the train.
Cars arrive at the train station in a predetermined order. When each car
arrives, Erin can add it to the beginning or end of her train, or refuse
to add it at all. The resulting train should be as long as possible, but
the cars within it must be ordered by weight.
Given the weights of the cars in the order in which they arrive, what is
the longest train that Erin can make?
The first line contains an integer 0 <= n <= 2000, the number of cars.
Each of the following n lines contains a non-negative integer giving the
weight of a car. No two cars have the same weight.
Output a single integer giving the number of cars in the longest train
that can be made with the given restrictions.
Output for Sample Input
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