Three Activities
Description
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.
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 $10^5$.
For each testcase, print a single integer — the maximum total number of friends that can join Monocarp for the activities on three distinct days.
Input
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
For each testcase, print a single integer — the maximum total number of friends that can join Monocarp for the activities on three distinct days.
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
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.