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.

见题面 Input 部分

见题面 Output 部分

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.