You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Dark is going to attend Motarack's birthday. Dark decided that the gift he is going to give to Motarack is an array $$$a$$$ of $$$n$$$ non-negative integers.

Dark created that array $$$1000$$$ years ago, so some elements in that array disappeared. Dark knows that Motarack hates to see an array that has two adjacent elements with a high absolute difference between them. He doesn't have much time so he wants to choose an integer $$$k$$$ ($$$0 \leq k \leq 10^{9}$$$) and replaces all missing elements in the array $$$a$$$ with $$$k$$$.

Let $$$m$$$ be the maximum absolute difference between all adjacent elements (i.e. the maximum value of $$$|a_i - a_{i+1}|$$$ for all $$$1 \leq i \leq n - 1$$$) in the array $$$a$$$ after Dark replaces all missing elements with $$$k$$$.

Dark should choose an integer $$$k$$$ so that $$$m$$$ is minimized. Can you help him?

## Input Format
The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$)  — the number of test cases. The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$2 \leq n \leq 10^{5}$$$) — the size of the array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-1 \leq a_i \leq 10 ^ {9}$$$). If $$$a_i = -1$$$, then the $$$i$$$-th integer is missing. It is guaranteed that at least one integer is missing in every test case.

It is guaranteed, that the sum of $$$n$$$ for all test cases does not exceed $$$4 \cdot 10 ^ {5}$$$.

## Output Format
Print the answers for each test case in the following format:

You should print two integers, the minimum possible value of $$$m$$$ and an integer $$$k$$$ ($$$0 \leq k \leq 10^{9}$$$) that makes the maximum absolute difference between adjacent elements in the array $$$a$$$ equal to $$$m$$$.

Make sure that after replacing all the missing elements with $$$k$$$, the maximum absolute difference between adjacent elements becomes $$$m$$$.

If there is more than one possible $$$k$$$, you can print any of them.

## Examples
```input
7
5
-1 10 -1 12 -1
5
-1 40 35 -1 35
6
-1 -1 9 -1 3 -1
2
-1 -1
2
0 -1
4
1 -1 3 -1
7
1 -1 7 5 2 -1 5
```
```output
1 11
5 35
3 6
0 42
0 0
1 2
3 4
```

## Note
In the first test case after replacing all missing elements with $$$11$$$ the array becomes $$$[11, 10, 11, 12, 11]$$$. The absolute difference between any adjacent elements is $$$1$$$. It is impossible to choose a value of $$$k$$$, such that the absolute difference between any adjacent element will be $$$\leq 0$$$. So, the answer is $$$1$$$.

In the third test case after replacing all missing elements with $$$6$$$ the array becomes $$$[6, 6, 9, 6, 3, 6]$$$.

- $$$|a_1 - a_2| = |6 - 6| = 0$$$;
- $$$|a_2 - a_3| = |6 - 9| = 3$$$;
- $$$|a_3 - a_4| = |9 - 6| = 3$$$;
- $$$|a_4 - a_5| = |6 - 3| = 3$$$;
- $$$|a_5 - a_6| = |3 - 6| = 3$$$.

So, the maximum difference between any adjacent elements is $$$3$$$.

Now solve the problem and return the code.