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?

给你一个包含 $n$ 个整数的数组 $a_1, a_2, \ldots, a_n$。在观看了精彩绝伦的电影《瞬息全宇宙》后，你提出了如下操作。

一次操作中，你从数组中选出 $n-1$ 个元素，并将它们每个都替换为这 $n-1$ 个元素的算术平均值（该平均值不一定是整数）。例如，对于数组 $[1, 2, 3, 1]$，若选择前三个元素，则可得到数组 $[2, 2, 2, 1]$；若选择除第三个元素外的所有元素，则可得到数组 $[\frac{4}{3}, \frac{4}{3}, 3, \frac{4}{3}]$。

是否可以通过执行有限次此类操作，使得数组中所有元素均相等？

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

输入的第一行包含一个整数 $t$（$1 \le t \le 200$）—— 表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$3 \le n \le 50$）—— 表示整数的个数。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \le a_i \le 100$）。

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).

对于每个测试用例，如果经过若干次操作后可以使所有元素相等，则输出 $\texttt{YES}$；否则输出 $\texttt{NO}$。

您可以以任意大小写形式输出 $\texttt{YES}$ 和 $\texttt{NO}$（例如，字符串 $\texttt{yEs}$、$\texttt{yes}$、$\texttt{Yes}$ 均被视为肯定回答）。

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.

在第一个测试用例中，所有元素已经相等。

在第二个测试用例中，你可以选择除第三个元素外的所有元素，它们的平均值为 $\frac{1 + 2 + 4 + 5}{4} = 3$，因此数组将变为 $[3, 3, 3, 3, 3]$。

可以证明，在第三和第四个测试用例中，无法使所有元素相等。