CF1497D.Genius

Please 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 $\text{IQ} \lt |c_i - c_j|$ 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.

请注意非标准的内存限制。

共有 $n$ 道题目，编号为 $1$ 到 $n$。第 $i$ 道题的难度为 $c_i = 2^i$，标签为 $tag_i$，分值为 $s_i$。

在解出题目 $i$ 后，当且仅当满足 $\text{IQ} \lt |c_i - c_j|$ 且 $tag_i \neq tag_j$ 时，才允许解题目 $j$。解出题目 $j$ 后，你的 $\text{IQ}$ 将更新为 $\text{IQ} = |c_i - c_j|$，并获得 $|s_i - s_j|$ 分。

任意一道题均可作为起始题目。你可以以任意顺序、任意次数求解题目。

初始时你的 $\text{IQ} = 0$。求最多能获得的分数。

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 $5000$.

第一行包含一个整数 $t$（$1 \le t \le 100$）—— 测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 5000$）—— 问题的数量。

每个测试用例的第二行包含 $n$ 个整数 $tag_1, tag_2, \ldots, tag_n$（$1 \le tag_i \le n$）—— 各问题的标签。

每个测试用例的第三行包含 $n$ 个整数 $s_1, s_2, \ldots, s_n$（$1 \le s_i \le 10^9$）—— 各问题的分数。

保证所有测试用例中 $n$ 的总和不超过 $5000$。

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

对于每个测试用例，输出一个整数——能够获得的最大分数。

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

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

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

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

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

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

在第一个测试用例中，解决问题的最优序列为：

1. $1 \rightarrow 2$，之后总得分为 $5$，$\text{IQ} = 2$
2. $2 \rightarrow 3$，之后总得分为 $10$，$\text{IQ} = 4$
3. $3 \rightarrow 1$，之后总得分为 $20$，$\text{IQ} = 6$
4. $1 \rightarrow 4$，之后总得分为 $35$，$\text{IQ} = 14$

在第二个测试用例中，解决问题的最优序列为：

1. $1 \rightarrow 2$，之后总得分为 $5$，$\text{IQ} = 2$
2. $2 \rightarrow 3$，之后总得分为 $10$，$\text{IQ} = 4$
3. $3 \rightarrow 4$，之后总得分为 $15$，$\text{IQ} = 8$
4. $4 \rightarrow 1$，之后总得分为 $35$，$\text{IQ} = 14$

在第三个测试用例中，解决问题的最优序列为：

1. $1 \rightarrow 3$，之后总得分为 $17$，$\text{IQ} = 6$
2. $3 \rightarrow 4$，之后总得分为 $35$，$\text{IQ} = 8$
3. $4 \rightarrow 2$，之后总得分为 $42$，$\text{IQ} = 12$