Solve the programming task below in a Python markdown code block.
Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.

There are $N$ people on a street (numbered $1$ through $N$). For simplicity, we'll view them as points on a line. For each valid $i$, the position of the $i$-th person is $X_{i}$.

It turns out that exactly one of these people is infected with the virus COVID-19, but we do not know which one. The virus will spread from an infected person to a non-infected person whenever the distance between them is at most $2$. If we wait long enough, a specific set of people (depending on the person that was infected initially) will become infected; let's call the size of this set the *final number of infected people*.

Your task is to find the smallest and largest value of the final number of infected people, i.e. this number in the best and in the worst possible scenario.

------  Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows. 
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-seperated integers $X_{1}, X_{2}, \ldots, X_{N}$.

------  Output ------
For each test case, print a single line containing two space-separated integers ― the minimum and maximum possible final number of infected people.

------  Constraints ------
$1 ≤ T ≤ 2,000$
$2 ≤ N ≤ 8$
$0 ≤ X_{i} ≤ 10$ for each valid $i$
$X_{1} < X_{2} < \ldots < X_{N}$

------  Subtasks ------
Subtask #1 (10 points): $N ≤ 3$

Subtask #2 (90 points): original constraints

----- Sample Input 1 ------ 
3

2

3 6

3

1 3 5

5

1 2 5 6 7
----- Sample Output 1 ------ 
1 1

3 3

2 3
----- explanation 1 ------ 
Example case 1: The distance between the two people is $3$, so the virus cannot spread and at the end, there will always be only one infected person.

Example case 2: The distance between each two adjacent people is $2$, so all of them will eventually get infected.

Example case 3:
- In one of the best possible scenarios, the person at the position $1$ is infected initially and the virus will also infect the person at the position $2$.
- In one of the worst possible scenarios, the person at the position $5$ is infected initially and the virus will also infect the people at the positions $6$ and $7$.