A circular array (b) of length (m) is nice if every element has at least one adjacent element(^{\text{∗}}) that is equal to it. Formally, for every (1\le i\le m), at least one of the following holds: (b_i = b_{(i+m-2)\bmod m\;+1}), or (b_i = b_{i\bmod m\;+1}), where (x \bmod y) denotes the remainder from dividing (x) by (y). You are given a circular array (a) of length (n). In one operation, you may increase or decrease any element of (a) by (1). Your task is to determine the minimum number of operations required to make array (a) nice. More formally, find the minimum value of (\sum_{i=1}^n |b_i - a_i|) among all nice circular arrays (b) of length (n). (^{\text{∗}})In a circular array of length (m): For each index (2\le i\le m - 1), the element at index (i) is adjacent to the elements at indices (i - 1) and (i + 1). The element at index (1) is adjacent to the elements at indices (2) and (m). The element at index (m) is adjacent to the elements at indices (m - 1) and (1). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((3\le n\le 2\cdot 10^5)) — the length of the circular array (a). The second line of each test case contains (n) integers (a_1, a_2, \ldots, a_n) ((1\le a_i\le 10^9)) — the elements of the circular array (a). It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot 10^5). For each test case, output a single integer representing the minimum number of operations required to make array (a) nice. In the first test case, all elements of (a) are equal. Therefore, the circular array (a) is already nice and no operations are required. In the second test case, we can perform the following