G. Mukhammadali and the Smooth Arraytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputMuhammadali has an integer array $$$a_1,\dots,a_n$$$. He can change (replace) any subset of positions; changing position $$$i$$$ costs $$$c_i$$$ and replaces $$$a_i$$$ with any integer of his choice. The positions that he does not change must retain their original values.After all changes, we call an index $$$i$$$ ($$$1 \le i < n$$$) a drop if the final value at position $$$i$$$ is strictly greater than the final value at position $$$i+1$$$. Muhammadali wants the final array to contain no drops.Find the minimum cost of changes required to ensure that there are no drops in the array.InputThe first line contains an integer $$$t$$$ ($$$1 \le t \le 5000$$$) — the number of test cases.Each test case consists of three lines:The first line contains a single integer $$$n$$$ ($$$1 \le n \le 8000$$$) — the length of the arrays.The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the elements of the array.The third line contains $$$n$$$ integers $$$c_1, c_2, \dots, c_n$$$ ($$$1 \le c_i \le 10^9$$$) — the costs of changes.It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$8000$$$.OutputFor each test case, output a single integer — the minimum possible total cost required to eliminate all drops.ExampleInput10110541 2 2 35 6 7 844 3 2 11 1 1 133 1 2100 1 155 5 5 5 510 1 10 1 1051 3 2 2 4100 1 1 1 100610 9 8 7 6 51 100 1 100 1 1005100 1 100 100 1001 100 1 1 142 1 2 15 4 3 271 5 3 4 2 6 710 1 10 1 10 1 10Output0032012031611NoteIn the first and second examples, the array already has no drops, so no changes are needed.In the third example, one of the optimal arrays is: $$$[2,3,5,6]$$$; to achieve this, all elements except the second need to be replaced, so the answer is $$$c_1 + c_3 + c_4 = 3$$$.