Monocarp and Stereocarp are preparing for the Olympiad. There are $$$n$$$ days left until the Olympiad. On the $$$i$$$-th day, if Monocarp plans to practice, he will solve $$$a_i$$$ problems. Similarly, if Stereocarp plans to practice on the same day, he will solve $$$b_i$$$ problems.

Monocarp can train on any day he wants. However, Stereocarp watches Monocarp and follows a different schedule: if Monocarp trained on day $$$i$$$ and $$$i \lt n$$$, then Stereocarp will train on day $$$(i+1)$$$.

Monocarp wants to organize his training process in a way that the difference between the number of problems he solves and the number of problems Stereocarp solves is as large as possible. Formally, Monocarp wants to maximize the value of $$$(m-s)$$$, where $$$m$$$ is the number of problems he solves, and $$$s$$$ is the number of problems Stereocarp solves. Help Monocarp determine the maximum possible difference in the number of solved problems between them.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^3$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 100$$$).

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 100$$$).

Output

For each test case, print a single integer — the maximum possible difference between the number of problems Monocarp solves and the number of problems Stereocarp solves.

Note

Let's analyze the example from the statement:

In the first test case, it is optimal for Monocarp to train both days; then Stereocarp will train on day $$$2$$$.
In the second test case, it is optimal for Monocarp to train on the only day, and Stereocarp will not train at all.
In the third test case, it is optimal for Monocarp to train on the last day (and only on that day).
In the fourth test case, it is optimal for Monocarp to train on days $$$1, 3, 4, 6$$$; then Stereocarp will train on days $$$2, 4, 5$$$.

Preparing for the Olympiad

Examples