CF1798D.Shocking Arrangement

You are given an array $a_1, a_2, \ldots, a_n$ consisting of integers such that $a_1 + a_2 + \ldots + a_n = 0$.

You have to rearrange the elements of the array $a$ so that the following condition is satisfied:

\\max\\limits\_{1 \\le l \\le r \\le n} \\lvert a\_l + a\_{l+1} + \\ldots + a\_r \\rvert \\lt \\max(a\_1, a\_2, \\ldots, a\_n) - \\min(a\_1, a\_2, \\ldots, a\_n),$$ where $|x|$ denotes the absolute value of $x$. More formally, determine if there exists a permutation $p_1, p_2, \ldots, p_n$ that for the array $a_{p_1}, a_{p_2}, \ldots, a_{p_n}$, the condition above is satisfied, and find the corresponding array. Recall that the array $p_1, p_2, \ldots, p_n$ is called a permutation if for each integer $x$ from $1$ to $n$ there is exactly one $i$ from $1$ to $n$ such that $p_i = x$. 给你一个由整数构成的数组 $a_1, a_2, \ldots, a_n$，满足 $a_1 + a_2 + \ldots + a_n = 0$。 你需要重排数组 $a$ 的元素，使得以下条件成立： $$\max\limits_{1 \le l \le r \le n} \lvert a_l + a_{l+1} + \ldots + a_r \rvert \lt \max(a_1, a_2, \ldots, a_n) - \min(a_1, a_2, \ldots, a_n),

其中 $|x|$ 表示 $x$ 的绝对值。

更形式化地说：判断是否存在一个排列 $p_1, p_2, \ldots, p_n$，使得对重排后的数组 $a_{p_1}, a_{p_2}, \ldots, a_{p_n}$，上述条件成立；若存在，输出对应的数组。

注意：数组 $p_1, p_2, \ldots, p_n$ 称为一个排列，当且仅当对每个从 $1$ 到 $n$ 的整数 $x$，恰好存在一个 $i \in \{1,2,\ldots,n\}$ 满足 $p_i = x$。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 50\,000$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \le n \le 300\,000$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^9 \le a_i \le 10^9$) — elements of the array $a$. It is guaranteed that the sum of the array $a$ is zero, in other words: $a_1 + a_2 + \ldots + a_n = 0$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $300\,000$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 50\,000$）。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 $n$（$1 \le n \le 300\,000$）—— 数组 $a$ 的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$-10^9 \le a_i \le 10^9$）—— 数组 $a$ 的元素。保证数组 $a$ 的元素和为零，即：$a_1 + a_2 + \ldots + a_n = 0$。

保证所有测试用例的 $n$ 值之和不超过 $300\,000$。

For each test case, if it is impossible to rearrange the elements of the array $a$ in the required way, print "No" in a single line.

If possible, print "Yes" in the first line, and then in a separate line $n$ numbers — elements $a_1, a_2, \ldots, a_n$ rearranged in a valid order ($a_{p_1}, a_{p_2}, \ldots, a_{p_n}$).

If there are several possible answers, you can output any of them.

对于每个测试用例，如果无法将数组 $a$ 的元素按要求重新排列，则在一行中输出“No”。

如果可以实现，则在第一行输出“Yes”，并在下一行输出 $n$ 个数——即按有效顺序重新排列后的元素 $a_1, a_2, \ldots, a_n$（即 $a_{p_1}, a_{p_2}, \ldots, a_{p_n}$）。

如果有多种可能的答案，输出任意一种即可。

In the first test case $\max(a_1, \ldots, a_n) - \min(a_1, \ldots, a_n) = 9$. Therefore, the elements can be rearranged as $[-5, -2, 3, 4]$. It is easy to see that for such an arrangement $\lvert a_l + \ldots + a_r \rvert$ is always not greater than $7$, and therefore less than $9$.

In the second test case you can rearrange the elements of the array as $[-3, 2, -3, 2, 2]$. Then the maximum modulus of the sum will be reached on the subarray $[-3, 2, -3]$, and will be equal to $\lvert -3 + 2 + -3 \rvert = \lvert -4 \rvert = 4$, which is less than $5$.

In the fourth test example, any rearrangement of the array $a$ will be suitable as an answer, including $[-1, 0, 1]$.

在第一个测试用例中，$\max(a_1, \ldots, a_n) - \min(a_1, \ldots, a_n) = 9$。因此，这些元素可以重排为 $[-5, -2, 3, 4]$。容易看出，对于这种排列，任意子数组和的绝对值 $\lvert a_l + \ldots + a_r \rvert$ 始终不超过 $7$，因此小于 $9$。

在第二个测试用例中，你可以将数组元素重排为 $[-3, 2, -3, 2, 2]$。此时，子数组和的绝对值最大值在子数组 $[-3, 2, -3]$ 上取得，其值为 $\lvert -3 + 2 + -3 \rvert = \lvert -4 \rvert = 4$，该值小于 $5$。

在第四个测试样例中，数组 $a$ 的任意重排均满足要求，例如 $[-1, 0, 1]$。