D. Geniustime limit per test2 secondsmemory limit per test32 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputFor each test case print a single integer  — the maximum number of points that can be earned.ExampleInput
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
NoteIn 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 
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 
['bitmasks', 'dp', 'graphs', 'number theory', '*2500']