CF2038B Make It Equal

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.