CF1933D.Turtle Tenacity: Continual Mods

Given an array $a_1, a_2, \ldots, a_n$, determine whether it is possible to rearrange its elements into $b_1, b_2, \ldots, b_n$, such that $b_1 \bmod b_2 \bmod \ldots \bmod b_n \neq 0$.

Here $x \bmod y$ denotes the remainder from dividing $x$ by $y$. Also, the modulo operations are calculated from left to right. That is, $x \bmod y \bmod z = (x \bmod y) \bmod z$. For example, $2024 \bmod 1000 \bmod 8 = (2024 \bmod 1000) \bmod 8 = 24 \bmod 8 = 0$.

给定一个数组 $a_1, a_2, \ldots, a_n$，判断是否可以将其元素重新排列为 $b_1, b_2, \ldots, b_n$，使得 $b_1 \bmod b_2 \bmod \ldots \bmod b_n \neq 0$。

其中，$x \bmod y$ 表示 $x$ 除以 $y$ 所得的余数；且模运算按从左到右的顺序进行，即 $x \bmod y \bmod z = (x \bmod y) \bmod z$。例如，$2024 \bmod 1000 \bmod 8 = (2024 \bmod 1000) \bmod 8 = 24 \bmod 8 = 0$。

The first line of the input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($2 \le n \le 10^5$).

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 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 $t$（$1 \le t \le 10^4$）—— 表示测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 10^5$）。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$）。

所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

For each test case, output "YES" if it is possible, "NO" 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，如果可能则输出 “YES”，否则输出 “NO”。

您可以以任意大小写形式输出答案（大写或小写）。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, rearranging the array into $b = [1, 2, 3, 4, 5, 6]$ (doing nothing) would result in $1 \bmod 2 \bmod 3 \bmod 4 \bmod 5 \bmod 6 = 1$. Hence it is possible to achieve the goal.

In the second test case, the array $b$ must be equal to $[3, 3, 3, 3, 3]$, which would result in $3 \bmod 3 \bmod 3 \bmod 3 \bmod 3 = 0$. Hence it is impossible to achieve the goal.

In the third test case, rearranging the array into $b = [3, 2, 2]$ would result in $3 \bmod 2 \bmod 2 = 1$. Hence it is possible to achieve the goal.

在第一个测试用例中，将数组重排为 $b = [1, 2, 3, 4, 5, 6]$（即不作任何操作）会得到 $1 \bmod 2 \bmod 3 \bmod 4 \bmod 5 \bmod 6 = 1$。因此可以达成目标。

在第二个测试用例中，数组 $b$ 必须等于 $[3, 3, 3, 3, 3]$，此时计算结果为 $3 \bmod 3 \bmod 3 \bmod 3 \bmod 3 = 0$。因此无法达成目标。

在第三个测试用例中，将数组重排为 $b = [3, 2, 2]$ 会得到 $3 \bmod 2 \bmod 2 = 1$。因此可以达成目标。