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.
Input Format:
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 Format:
For each test case print a single integer — the maximum number of points that can be earned.
Note:
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 $$$\text{IQ} = 12$$$