CF1868B1.Candy Party (Easy Version)

This is the easy version of the problem. The only difference is that in this version everyone must give candies to exactly one person and receive candies from exactly one person. Note that a submission cannot pass both versions of the problem at the same time. You can make hacks only if both versions of the problem are solved.

After Zhongkao examination, Daniel and his friends are going to have a party. Everyone will come with some candies.

There will be $n$ people at the party. Initially, the $i$-th person has $a_i$ candies. During the party, they will swap their candies. To do this, they will line up in an arbitrary order and everyone will do the following exactly once:

• Choose an integer $p$ ($1 \le p \le n$) and a non-negative integer $x$, then give his $2^{x}$ candies to the $p$-th person. Note that one cannot give more candies than currently he has (he might receive candies from someone else before) and he cannot give candies to himself.

Daniel likes fairness, so he will be happy if and only if everyone receives candies from exactly one person. Meanwhile, his friend Tom likes average, so he will be happy if and only if all the people have the same number of candies after all swaps.

Determine whether there exists a way to swap candies, so that both Daniel and Tom will be happy after the swaps.

这是该问题的简单版本。唯一的区别在于，在此版本中，每个人都必须恰好给一个人糖果，并且恰好从一个人那里接收糖果。注意，一次提交无法同时通过该问题的两个版本。仅当该问题的两个版本均被解决时，才允许进行 Hack。

中考结束后，Daniel 和他的朋友们将举办一场聚会。每个人都会带一些糖果来。

聚会上共有 $n$ 个人。最初，第 $i$ 个人有 $a_i$ 颗糖果。在聚会期间，他们将交换糖果。为此，他们会以任意顺序排成一列，然后每个人恰好执行以下操作一次：

• 选择一个整数 $p$（满足 $1 \le p \le n$）和一个非负整数 $x$，然后将自己手中的 $2^{x}$ 颗糖果送给第 $p$ 个人。注意：一个人不能给出超过他当前所拥有的糖果数量（他可能在此之前已从他人处收到糖果），也不能将糖果送给自己。

Daniel 喜欢公平，因此他仅当每个人恰好从一个人那里接收糖果时才会开心。与此同时，他的朋友 Tom 喜欢平均，因此他仅当所有人在所有交换完成后拥有相同数量的糖果时才会开心。

请判断是否存在一种糖果交换方式，使得交换结束后 Daniel 和 Tom 都开心。

The first line of input contains a single integer $t$ ($1\le t\le 1000$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ($2\le n\le 2\cdot 10^5$) — the number of people at the party.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\le a_i\le 10^9$) — the number of candies each person has.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$.

输入的第一行包含一个整数 $t$（$1\le t\le 1000$），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 $n$（$2\le n\le 2\cdot 10^5$），表示派对上的人数。

每个测试用例的第二行包含 $n$ 个整数 $a_1,a_2,\ldots,a_n$（$1\le a_i\le 10^9$），表示每个人所拥有的糖果数量。

保证所有测试用例的 $n$ 值之和不超过 $2\cdot 10^5$。

For each test case, print "Yes" (without quotes) if exists a way to swap candies to make both Daniel and Tom happy, and print "No" (without quotes) otherwise.

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

对于每个测试用例，如果存在一种交换糖果的方式使得 Daniel 和 Tom 都开心，则输出 “Yes”（不带引号）；否则输出 “No”（不带引号）。

您可以以任意大小写形式输出答案（大写或小写均可）。例如，字符串 “yEs”、“yes”、“Yes” 和 “YES” 均会被识别为肯定回答。

In the first test case:

• The first person gives $1$ candy to the third person;
• The second person gives $2$ candies to the first person;
• The third person gives $1$ candy to the second person.

Then all people have $3$ candies.

In the second test case:

• The fifth person gives $4$ candies to the first person, from now on the first person has $5$ candies;
• The first person gives $2$ candies to the third person;
• The third person gives $2$ candies to the fifth person;
• The fourth person gives $2$ candies to the second person;
• The second person gives $1$ candy to the fourth person.

Then all people have $3$ candies. Note that at first the first person cannot give $2$ candies to the third person, since he only has $a_1=1$ candy. But after the fifth person gives him $4$ candies, he can do this, because he currently has $1+4=5$ candies.

In the third test case, it's impossible for all people to have the same number of candies.

In the fourth test case, the first person gives $1024$ candies to the second person, and the second person gives $1024$ candies to the first person as well.

在第一个测试用例中：

• 第一个人给第三个人 $1$ 颗糖果；
• 第二个人给第一个人 $2$ 颗糖果；
• 第三个人给第二个人 $1$ 颗糖果。

此时，所有人各有 $3$ 颗糖果。

在第二个测试用例中：

• 第五个人给第一个人 $4$ 颗糖果，此后第一个人拥有 $5$ 颗糖果；
• 第一个人给第三个人 $2$ 颗糖果；
• 第三个人给第五个人 $2$ 颗糖果；
• 第四个人给第二个人 $2$ 颗糖果；
• 第二个人给第四个人 $1$ 颗糖果。

此时，所有人各有 $3$ 颗糖果。注意，最初第一个人无法给第三个人 $2$ 颗糖果，因为他仅有 $a_1=1$ 颗糖果；但在第五个人给他 $4$ 颗糖果后，他当前拥有 $1+4=5$ 颗糖果，因此可以完成该操作。

在第三个测试用例中，不可能使所有人拥有相同数量的糖果。

在第四个测试用例中，第一个人给第二个人 $1024$ 颗糖果，第二个人也给第一个人 $1024$ 颗糖果。