B. Make It Equaltime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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 $$$2 \cdot 10^5$$$.OutputFor 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.ExampleInput321 131 3 242 1 2 6Output0
-1
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