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.