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 ai friends will join him for skiing, bi friends will join him for a movie and ci 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 (ax+by+cz) is maximized.

Format

Input

The first line contains a single integer t (1≤t≤10e4) — the number of testcases.

The first line of each testcase contains a single integer nn (3≤n≤10e5) — the duration of the winter holidays in days.

The second line contains nn integers a1,a2,…,an(1≤ai≤10e8) — the number of friends that will join Monocarp for skiing on the i-th day.

The third line contains n integers b1,b2,…,bn(1≤bi≤10e8) — the number of friends that will join Monocarp for a movie on the i-th day.

The fourth line contains n integers c1,c2,…,cn(1≤ci≤10e8) — the number of friends that will join Monocarp for board games on the ii-th day.

The sum of n over all testcases doesn't exceed 10e5.

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.

Samples

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

Limitation

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output