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.