C. Sequence Mastertime limit per test1 secondmemory limit per test1024 megabytesinputstandard inputoutputstandard outputFor some positive integer m, YunQian considers an array q of 2m (possibly negative) integers good, if and only if for every possible subsequence of q that has length m, the product of the m elements in the subsequence is equal to the sum of the m elements that are not in the subsequence. Formally, let U=\{1,2,\ldots,2m\}. For all sets S \subseteq U such that |S|=m, \prod\limits_{i \in S} q_i = \sum\limits_{i \in U \setminus S} q_i.Define the distance between two arrays a and b both of length k to be \sum\limits_{i=1}^k|a_i-b_i|.You are given a positive integer n and an array p of 2n integers.Find the minimum distance between p and q over all good arrays q of length 2n. It can be shown for all positive integers n, at least one good array exists. Note that you are not required to construct the array q that achieves this minimum distance.InputThe first line contains a single integer t (1\le t\le 10^4) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer n (1\le n\le 2\cdot10^5).The second line of each test case contains 2n integers p_1, p_2, \ldots, p_{2n} (|p_i| \le 10^9).It is guaranteed that the sum of n over all test cases does not exceed 2\cdot 10^5.OutputFor each test case, output the minimum distance between p and a good q.ExampleInput
416 921 2 2 12-2 -2 2 24-3 -2 -1 0 1 2 3 4Output
3
2
5
13
NoteIn the first test case, it is optimal to let q=[6,6].In the second test case, it is optimal to let q=[2,2,2,2].
416 921 2 2 12-2 -2 2 24-3 -2 -1 0 1 2 3 4
3 2 5 13 
['brute force', 'constructive algorithms', 'math', '*1600']