Genius
Description
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 $\text{IQ} < |c_i - c_j|$ 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.
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 $5000$.
For each test case print a single integer — 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.
Samples
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
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 $\text{IQ} = 12$