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dp

greedy

*1000

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B. Red and Blue

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputMonocarp had a sequence $$$a$$$ consisting of $$$n + m$$$ integers $$$a_1, a_2, \dots, a_{n + m}$$$. He painted the elements into two colors, red and blue; $$$n$$$ elements were painted red, all other $$$m$$$ elements were painted blue.

After painting the elements, he has written two sequences $$$r_1, r_2, \dots, r_n$$$ and $$$b_1, b_2, \dots, b_m$$$. The sequence $$$r$$$ consisted of all red elements of $$$a$$$ in the order they appeared in $$$a$$$; similarly, the sequence $$$b$$$ consisted of all blue elements of $$$a$$$ in the order they appeared in $$$a$$$ as well.

Unfortunately, the original sequence was lost, and Monocarp only has the sequences $$$r$$$ and $$$b$$$. He wants to restore the original sequence. In case there are multiple ways to restore it, he wants to choose a way to restore that maximizes the value of

$$$$$$f(a) = \max(0, a_1, (a_1 + a_2), (a_1 + a_2 + a_3), \dots, (a_1 + a_2 + a_3 + \dots + a_{n + m}))$$$$$$

Help Monocarp to calculate the maximum possible value of $$$f(a)$$$.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. Then the test cases follow. Each test case consists of four lines.

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

The second line contains $$$n$$$ integers $$$r_1, r_2, \dots, r_n$$$ ($$$-100 \le r_i \le 100$$$).

The third line contains one integer $$$m$$$ ($$$1 \le m \le 100$$$).

The fourth line contains $$$m$$$ integers $$$b_1, b_2, \dots, b_m$$$ ($$$-100 \le b_i \le 100$$$).

Output

For each test case, print one integer — the maximum possible value of $$$f(a)$$$.

Example

Input

4 4 6 -5 7 -3 3 2 3 -4 2 1 1 4 10 -3 2 2 5 -1 -2 -3 -4 -5 5 -1 -2 -3 -4 -5 1 0 1 0

Output

13 13 0 0

Note

In the explanations for the sample test cases, red elements are marked as bold.

In the first test case, one of the possible sequences $$$a$$$ is $$$[\mathbf{6}, 2, \mathbf{-5}, 3, \mathbf{7}, \mathbf{-3}, -4]$$$.

In the second test case, one of the possible sequences $$$a$$$ is $$$[10, \mathbf{1}, -3, \mathbf{1}, 2, 2]$$$.

In the third test case, one of the possible sequences $$$a$$$ is $$$[\mathbf{-1}, -1, -2, -3, \mathbf{-2}, -4, -5, \mathbf{-3}, \mathbf{-4}, \mathbf{-5}]$$$.

In the fourth test case, one of the possible sequences $$$a$$$ is $$$[0, \mathbf{0}]$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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