D. Three Activities
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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.

Example
Input
431 10 110 1 11 1 10430 20 10 130 5 15 2030 25 10 10105 19 12 3 18 18 6 17 10 1315 17 19 11 16 3 11 17 17 171 17 18 10 15 8 17 3 13 121017 5 4 18 12 4 11 2 16 168 4 14 19 3 12 6 7 5 163 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.