CF1686A Everything Everywhere All But One

You are given an array of $ n $ integers $ a_1, a_2, \ldots, a_n $ . After you watched the amazing film "Everything Everywhere All At Once", you came up with the following operation. In one operation, you choose $ n-1 $ elements of the array and replace each of them with their arithmetic mean (which doesn't have to be an integer). For example, from the array $ [1, 2, 3, 1] $ we can get the array $ [2, 2, 2, 1] $ , if we choose the first three elements, or we can get the array $ [\frac{4}{3}, \frac{4}{3}, 3, \frac{4}{3}] $ , if we choose all elements except the third. Is it possible to make all elements of the array equal by performing a finite number of such operations?

The first line of the input contains a single integer $ t $ ( $ 1 \le t \le 200 $ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 3 \le n \le 50 $ ) — the number of integers. The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i \le 100 $ ).

For each test case, if it is possible to make all elements equal after some number of operations, output $ \texttt{YES} $ . Otherwise, output $ \texttt{NO} $ . You can output $ \texttt{YES} $ and $ \texttt{NO} $ in any case (for example, strings $ \texttt{yEs} $ , $ \texttt{yes} $ , $ \texttt{Yes} $ will be recognized as a positive response).

In the first test case, all elements are already equal. In the second test case, you can choose all elements except the third, their average is $ \frac{1 + 2 + 4 + 5}{4} = 3 $ , so the array will become $ [3, 3, 3, 3, 3] $ . It's possible to show that it's impossible to make all elements equal in the third and fourth test cases.