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.

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.

Three Activities

Examples