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 c++17.

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:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Winter holidays are coming up. They are going to last for $$$n$$$ days.

During the holidays, Monocarp wants to try all of these activities exactly once with his friends:

- go skiing;
- watch a movie in a cinema;
- play board games.

Monocarp knows that, on the $$$i$$$-th day, exactly $$$a_i$$$ friends will join him for skiing, $$$b_i$$$ friends will join him for a movie and $$$c_i$$$ friends will join him for board games.

Monocarp also knows that he can't try more than one activity in a single day.

Thus, he asks you to help him choose three distinct days $$$x, y, z$$$ in such a way that the total number of friends to join him for the activities ($$$a_x + b_y + c_z$$$) is maximized.

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

The first line of each testcase contains a single integer $$$n$$$ ($$$3 \le n \le 10^5$$$) — the duration of the winter holidays in days.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^8$$$) — the number of friends that will join Monocarp for skiing on the $$$i$$$-th day.

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 10^8$$$) — the number of friends that will join Monocarp for a movie on the $$$i$$$-th day.

The fourth line contains $$$n$$$ integers $$$c_1, c_2, \dots, c_n$$$ ($$$1 \le c_i \le 10^8$$$) — the number of friends that will join Monocarp for board games on the $$$i$$$-th day.

The sum of $$$n$$$ over all testcases doesn't exceed $$$10^5$$$.

## Output Format
For each testcase, print a single integer — the maximum total number of friends that can join Monocarp for the activities on three distinct days.

## Examples
```input
4
3
1 10 1
10 1 1
1 1 10
4
30 20 10 1
30 5 15 20
30 25 10 10
10
5 19 12 3 18 18 6 17 10 13
15 17 19 11 16 3 11 17 17 17
1 17 18 10 15 8 17 3 13 12
10
17 5 4 18 12 4 11 2 16 16
8 4 14 19 3 12 6 7 5 16
3 4 8 11 10 8 10 2 20 3
```
```output
30
75
55
56
```

## Note
In the first testcase, Monocarp can choose day $$$2$$$ for skiing, day $$$1$$$ for a movie and day $$$3$$$ for board games. This way, $$$a_2 = 10$$$ friends will join him for skiing, $$$b_1 = 10$$$ friends will join him for a movie and $$$c_3 = 10$$$ friends will join him for board games. The total number of friends is $$$30$$$.

In the second testcase, Monocarp can choose day $$$1$$$ for skiing, day $$$4$$$ for a movie and day $$$2$$$ for board games. $$$30 + 20 + 25 = 75$$$ friends in total. Note that Monocarp can't choose day $$$1$$$ for all activities, because he can't try more than one activity in a single day.

In the third testcase, Monocarp can choose day $$$2$$$ for skiing, day $$$3$$$ for a movie and day $$$7$$$ for board games. $$$19 + 19 + 17 = 55$$$ friends in total.

In the fourth testcase, Monocarp can choose day $$$1$$$ for skiing, day $$$4$$$ for a movie and day $$$9$$$ for board games. $$$17 + 19 + 20 = 56$$$ friends in total.

Now solve the problem and return the code.