Codeforces Round 910 (Div. 2) |
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D. Absolute Beauty

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKirill has two integer arrays $$$a_1,a_2,\ldots,a_n$$$ and $$$b_1,b_2,\ldots,b_n$$$ of length $$$n$$$. He defines the absolute beauty of the array $$$b$$$ as $$$$$$\sum_{i=1}^{n} |a_i - b_i|.$$$$$$ Here, $$$|x|$$$ denotes the absolute value of $$$x$$$.

Kirill can perform the following operation at most once:

- select two indices $$$i$$$ and $$$j$$$ ($$$1 \leq i < j \leq n$$$) and swap the values of $$$b_i$$$ and $$$b_j$$$.

Help him find the maximum possible absolute beauty of the array $$$b$$$ after performing at most one swap.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \leq t \leq 10\,000$$$). The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2\leq n\leq 2\cdot 10^5$$$) — the length of the arrays $$$a$$$ and $$$b$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1\leq a_i\leq 10^9$$$) — the array $$$a$$$.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1\leq b_i\leq 10^9$$$) — the array $$$b$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case, output one integer — the maximum possible absolute beauty of the array $$$b$$$ after no more than one swap.

Example

Input

631 3 53 3 321 21 221 22 141 2 3 45 6 7 8101 8 2 5 3 5 3 1 1 32 9 2 4 8 2 3 5 3 1347326 6958 3586533587 35863 59474

Output

4 2 2 16 31 419045

Note

In the first test case, each of the possible swaps does not change the array $$$b$$$.

In the second test case, the absolute beauty of the array $$$b$$$ without performing the swap is $$$|1-1| + |2-2| = 0$$$. After swapping the first and the second element in the array $$$b$$$, the absolute beauty becomes $$$|1-2| + |2-1| = 2$$$. These are all the possible outcomes, hence the answer is $$$2$$$.

In the third test case, it is optimal for Kirill to not perform the swap. Similarly to the previous test case, the answer is $$$2$$$.

In the fourth test case, no matter what Kirill does, the absolute beauty of $$$b$$$ remains equal to $$$16$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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