Do it for the kids, Chuck!

A gang of n vicious drug dealers is surrounding Walker, the world’s
favourite Texas ranger. But do not worry! This would be a critical
situation for most people, but not for Walker. He can hit all of them
with just a single of his “spinning kicks”.

However, as this is a TV series, the co-guionist Aaron Norris has
reminded his brother (the great actor Chuck Norris starring as Walker)
that he should take care of several restrictions:

- Drug dealers can only be hitted increasingly, from drug dealer 1 to
  drug dealer n. (This is because of the location of the camera.)

- Walker can only hit each drug dealer i at some specific time t_(i)
  known in advance. (This is due to the insurance that any actor working
  with Chuck has to take.) Therefore, Walker cannot hit two drug dealers
  i < j such that t_(i) > t_(j) with the same spinning kick.

- The time between two hits should be at least 10 ms. (Even a slow
  motion camera cannot properly film Chuck’s kicks if they are too
  quick.) This implies that Walker cannot hit with the same kick two
  drug dealers i < j such that t_(j) − t_(i) < 10 ms.

– “We must follow these rules, Chuck”, Aaron says. “I’m sure it’s not
hard for you to find the maximum number of guys you can hit with a
single spinning kick under these restrictions.”

– “Indeed, it is not”, Chuck replies after thinking for a couple of
microseconds.

– “Then, Chuck, please, follow these rules. Do it for the kids, Chuck!”

– “Alright.”

Can you write a program to compute the maximum number of drug dealers
that Chuck can hit with a single spinning kick under the given
restrictions?

Input

Input begins with a number t ≥ 0. Follow t test cases, each with the
number 0 < n ≤ 2000 of drug dealers, followed by t₁, …, t_(n) in ms.
Each t_(i) satisfies 0 ≤ t_(i) ≤ 10⁹. (Chuck can really give such
loooong spinning kicks. Indeed, he is a 6-time Karate World Champion!)

Output

Print t lines with the answers.

Observation

Due to his Cherokee upbringing, Chuck can solve this problem in
Θ(nlog n) time. But you may be not as good a programmer as Chuck, so the
Judge will accept quadratic solutions.

Problem information

Author: Omer Gimémez

Generation: 2026-01-25T10:26:27.316Z

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