| 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]. | |