CF2050B Transfusion

You 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?

First 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 $ .

For 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.