codeforces#P1933D. Turtle Tenacity: Continual Mods

    ID: 34434 远端评测题 2000ms 256MiB 尝试: 0 已通过: 0 难度: (无) 上传者: 标签>constructive algorithmsgreedymathnumber theorysortings

Turtle Tenacity: Continual Mods

Description

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, $2024 \bmod 1000 \bmod 8 = (2024 \bmod 1000) \bmod 8 = 24 \bmod 8 = 0$.

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 $2 \cdot 10^5$.

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.

Input

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 $2 \cdot 10^5$.

Output

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.

8
6
1 2 3 4 5 6
5
3 3 3 3 3
3
2 2 3
5
1 1 2 3 7
3
1 2 2
3
1 1 2
6
5 2 10 10 10 2
4
3 6 9 3
YES
NO
YES
NO
YES
NO
YES
NO

Note

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.