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
You are given an array $$$a_1, a_2, \dots, a_n$$$, which is sorted in non-descending order. You decided to perform the following steps to create array $$$b_1, b_2, \dots, b_n$$$:

1. Create an array $$$d$$$ consisting of $$$n$$$ arbitrary non-negative integers.
2. Set $$$b_i = a_i + d_i$$$ for each $$$b_i$$$.
3. Sort the array $$$b$$$ in non-descending order.

You are given the resulting array $$$b$$$. For each index $$$i$$$, calculate what is the minimum and maximum possible value of $$$d_i$$$ you can choose in order to get the given array $$$b$$$.

Note that the minimum (maximum) $$$d_i$$$-s are independent of each other, i. e. they can be obtained from different possible arrays $$$d$$$.

## Input Format
The first line contains the single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of arrays $$$a$$$, $$$b$$$ and $$$d$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$; $$$a_i \le a_{i+1}$$$) — the array $$$a$$$ in non-descending order.

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 10^9$$$; $$$b_i \le b_{i+1}$$$) — the array $$$b$$$ in non-descending order.

Additional constraints on the input:

- there is at least one way to obtain the array $$$b$$$ from the $$$a$$$ by choosing an array $$$d$$$ consisting of non-negative integers;
- the sum of $$$n$$$ doesn't exceed $$$2 \cdot 10^5$$$.

## Output Format
For each test case, print two lines. In the first line, print $$$n$$$ integers $$$d_1^{min}, d_2^{min}, \dots, d_n^{min}$$$, where $$$d_i^{min}$$$ is the minimum possible value you can add to $$$a_i$$$.

Secondly, print $$$n$$$ integers $$$d_1^{max}, d_2^{max}, \dots, d_n^{max}$$$, where $$$d_i^{max}$$$ is the maximum possible value you can add to $$$a_i$$$.

All $$$d_i^{min}$$$ and $$$d_i^{max}$$$ values are independent of each other. In other words, for each $$$i$$$, $$$d_i^{min}$$$ is just the minimum value among all possible values of $$$d_i$$$.

## Examples
```input
4
3
2 3 5
7 11 13
1
1000
5000
4
1 2 3 4
1 2 3 4
4
10 20 30 40
22 33 33 55
```
```output
5 4 2
11 10 8
4000
4000
0 0 0 0
0 0 0 0
12 2 3 15
23 13 3 15
```

## Note
In the first test case, in order to get $$$d_1^{min} = 5$$$, we can choose, for example, $$$d = [5, 10, 6]$$$. Then $$$b$$$ $$$=$$$ $$$[2+5,3+10,5+6]$$$ $$$=$$$ $$$[7,13,11]$$$ $$$=$$$ $$$[7,11,13]$$$.

For $$$d_2^{min} = 4$$$, we can choose $$$d$$$ $$$=$$$ $$$[9, 4, 8]$$$. Then $$$b$$$ $$$=$$$ $$$[2+9,3+4,5+8]$$$ $$$=$$$ $$$[11,7,13]$$$ $$$=$$$ $$$[7,11,13]$$$.

Now solve the problem and return the code.