B. Transfusiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array $$$a$$$ of length $$$n$$$. In one operation, you can pick an index $$$i$$$ from $$$2$$$ to $$$n-1$$$ inclusive, and do one of the following actions: Decrease $$$a_{i-1}$$$ by $$$1$$$, then increase $$$a_{i+1}$$$ by $$$1$$$. Decrease $$$a_{i+1}$$$ by $$$1$$$, then increase $$$a_{i-1}$$$ by $$$1$$$. After each operation, all the values must be non-negative. Can you make all the elements equal after any number of operations?InputFirst line of input consists of one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.First line of each test case consists of one integer $$$n$$$ ($$$3 \le n \le 2\cdot 10^5$$$).Second line of each test case consists of $$$n$$$ integers $$$a_i$$$ ($$$1 \le a_i \le 10^9$$$).It is guaranteed that the sum of $$$n$$$ of all test cases doesn't exceed $$$2\cdot 10^5$$$.OutputFor each test case, print "YES" without quotation marks if it is possible to make all the elements equal after any number of operations; otherwise, print "NO" without quotation marks.You can print answers in any register: "yes", "YeS", "nO" — will also be considered correct.ExampleInput833 2 131 1 341 2 5 441 6 6 156 2 1 4 241 4 2 153 1 2 1 332 4 2OutputYES
NO
YES
NO
YES
NO
NO
NO