hackercupai/hackercup huggingface dataset:
You've been put in charge of creating the problems for a certain high-profile
programming contest series.

The series will consist of one or more contests of exactly 4 problems each.
Every problem has a difficulty rating (an integer between 1 and 100,
inclusive), and the ratings of the 4 problems in each contest must be strictly
increasing, but with a difference of no more than 10 between consecutive
problems. In other words, if the problems in a contest have difficulties
**a**, **b**, **c**, and **d** (in order), then the inequalities **a** < **b**
< **c** < **d**, **b** \- **a** ≤ 10, **c** \- **b** ≤ 10, **d** \- **c** ≤ 10
must all hold.

You've been given an ordered list of **N** problems to use. Being an
experienced problemsetter, you may also write some new problems to insert at
any positions in the list, each with an integer difficulty between 1 and 100,
inclusive. The final list of problems must still include the original **N**
problems in their original order, though (with your new problems optionally
mixed in).

Once the problem list is finalized, the first 4 problems (in order) will form
a contest, the next 4 problems will form another contest, and so on. Note that
the number of problems in the list must be divisible by 4, and that each of
the contests formed must feature a valid ordered set of 4 problems. What's the
minimum number of additional problems you must write in order to create a set
of valid contests?

### Input

Input begins with an integer **T**, the number of contest series you need to
create. For each series, there is first a line containing the integer **N**,
then a line containing **N** space-separated integers, the **i**th of which is
**Di**, the difficulty rating of the **i**th existing problem.

### Output

For the **i**th series, print a line containing "Case #**i**: " followed by
the minimum number of additional problems you'll need to write.

### Constraints

1 ≤ **T** ≤ 50
1 ≤ **N** ≤ 100,000
1 ≤ **Di** ≤ 100

### Explanation of Sample

In the first series, the four problems given are already a valid contest, so
no new problems need to be written. In the second series, the four existing
problems most certainly do not form a valid contest, due to the gap between
the third and fourth ones - one possible way to salvage the situation is to
add three new problems with difficulties 30, 29, and 30 after the third
problem, as well as a problem with difficulty 42 at the end, creating two
valid contests: [15, 20, 25, 30] and [29, 30, 40, 42].