You are given an integer array (a) of size (n). The elements of the array are numbered from (1) to (n). You can perform the following operation any number of times (possibly, zero): choose an index (i) from (1) to (n); decrease (a_i) by (2) and increase (a_{(i \bmod n) + 1}) by (1). After you perform the operations, all elements of the array should be non-negative equal integers . Your task is to calculate the minimum number of operations you have to perform. The first line contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. The first line of each test case contains a single integer (n) ((2 \le n \le 2 \cdot 10^5)). The second line of each test case contains (n) integers (a_1, a_2, \dots, a_n) ((1 \le a_i \le 10^9)). Additional constraint on the input: the sum of (n) over all test cases doesn't exceed (2 \cdot 10^5). For each test case, print a single integer — the minimum number of operations you have to perform. If it is impossible to make all elements of the array equal, print -1 .