Longest Simple Cycle

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The first line of each test case contains the single integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — the number of chains you have.

The second line of each test case contains $$$n$$$ integers $$$c_1, c_2, \dots, c_n$$$ ($$$2 \le c_i \le 10^9$$$) — the number of vertices in the corresponding chains.

The third line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$a_1 = -1$$$; $$$1 \le a_i \le c_{i - 1}$$$).

The fourth line of each test case contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$b_1 = -1$$$; $$$1 \le b_i \le c_{i - 1}$$$).

Both $$$a_1$$$ and $$$b_1$$$ are equal to $$$-1$$$, they aren't used in graph building and given just for index consistency. It's guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$10^5$$$.

Output:

For each test case, print the length of the longest simple cycle.

Sample Input:

3
4
3 4 3 3
-1 1 2 2
-1 2 2 3
2
5 6
-1 5
-1 1
3
3 5 2
-1 1 1
-1 3 5

Sample Output:

7
11
8

Note:

In the first test case, the longest simple cycle is shown below:

We can't increase it with the first chain, since in such case it won't be simple — the vertex $$$2$$$ on the second chain will break simplicity.