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D. Genius

time limit per test

2 secondsmemory limit per test

32 megabytesinput

standard inputoutput

standard outputPlease note the non-standard memory limit.

There are $$$n$$$ problems numbered with integers from $$$1$$$ to $$$n$$$. $$$i$$$-th problem has the complexity $$$c_i = 2^i$$$, tag $$$tag_i$$$ and score $$$s_i$$$.

After solving the problem $$$i$$$ it's allowed to solve problem $$$j$$$ if and only if $$$\text{IQ} < |c_i - c_j|$$$ and $$$tag_i \neq tag_j$$$. After solving it your $$$\text{IQ}$$$ changes and becomes $$$\text{IQ} = |c_i - c_j|$$$ and you gain $$$|s_i - s_j|$$$ points.

Any problem can be the first. You can solve problems in any order and as many times as you want.

Initially your $$$\text{IQ} = 0$$$. Find the maximum number of points that can be earned.

Input

The first line contains a single integer $$$t$$$ $$$(1 \le t \le 100)$$$ — the number of test cases.

The first line of each test case contains an integer $$$n$$$ $$$(1 \le n \le 5000)$$$ — the number of problems.

The second line of each test case contains $$$n$$$ integers $$$tag_1, tag_2, \ldots, tag_n$$$ $$$(1 \le tag_i \le n)$$$ — tags of the problems.

The third line of each test case contains $$$n$$$ integers $$$s_1, s_2, \ldots, s_n$$$ $$$(1 \le s_i \le 10^9)$$$ — scores of the problems.

It's guaranteed that sum of $$$n$$$ over all test cases does not exceed $$$5000$$$.

Output

For each test case print a single integer — the maximum number of points that can be earned.

Example

Input

5 4 1 2 3 4 5 10 15 20 4 1 2 1 2 5 10 15 20 4 2 2 4 1 2 8 19 1 2 1 1 6 9 1 1 666

Output

35 30 42 0 0

Note

In the first test case optimal sequence of solving problems is as follows:

- $$$1 \rightarrow 2$$$, after that total score is $$$5$$$ and $$$\text{IQ} = 2$$$
- $$$2 \rightarrow 3$$$, after that total score is $$$10$$$ and $$$\text{IQ} = 4$$$
- $$$3 \rightarrow 1$$$, after that total score is $$$20$$$ and $$$\text{IQ} = 6$$$
- $$$1 \rightarrow 4$$$, after that total score is $$$35$$$ and $$$\text{IQ} = 14$$$

In the second test case optimal sequence of solving problems is as follows:

- $$$1 \rightarrow 2$$$, after that total score is $$$5$$$ and $$$\text{IQ} = 2$$$
- $$$2 \rightarrow 3$$$, after that total score is $$$10$$$ and $$$\text{IQ} = 4$$$
- $$$3 \rightarrow 4$$$, after that total score is $$$15$$$ and $$$\text{IQ} = 8$$$
- $$$4 \rightarrow 1$$$, after that total score is $$$35$$$ and $$$\text{IQ} = 14$$$

In the third test case optimal sequence of solving problems is as follows:

- $$$1 \rightarrow 3$$$, after that total score is $$$17$$$ and $$$\text{IQ} = 6$$$
- $$$3 \rightarrow 4$$$, after that total score is $$$35$$$ and $$$\text{IQ} = 8$$$
- $$$4 \rightarrow 2$$$, after that total score is $$$42$$$ and $$$\text{IQ} = 12$$$

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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