Everything Everywhere All But One

Description:

Input:

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 $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

Output:

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).

Sample Input:

4
3
42 42 42
5
1 2 3 4 5
4
4 3 2 1
3
24 2 22

Sample Output:

YES
YES
NO
NO

Note:

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.