codeforces#P1975B. 378QAQ and Mocha's Array
378QAQ and Mocha's Array
Description
Mocha likes arrays, so before her departure, 378QAQ gave her an array $a$ consisting of $n$ positive integers as a gift.
Mocha thinks that $a$ is beautiful if there exist two numbers $i$ and $j$ ($1\leq i,j\leq n$, $i\neq j$) such that for all $k$ ($1 \leq k \leq n$), $a_k$ is divisible$^\dagger$ by either $a_i$ or $a_j$.
Determine whether $a$ is beautiful.
$^\dagger$ $x$ is divisible by $y$ if there exists an integer $z$ such that $x = y \cdot z$.
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($3\leq n\leq 10^5$) — the length of the array $a$.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
For each test case, output "Yes" if array $a$ is beautiful, and output "No" otherwise.
You can output "Yes" and "No" in any case (for example, strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive response).
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($3\leq n\leq 10^5$) — the length of the array $a$.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
Output
For each test case, output "Yes" if array $a$ is beautiful, and output "No" otherwise.
You can output "Yes" and "No" in any case (for example, strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive response).
4
3
7 3 8
5
7 1 9 3 5
5
4 12 2 6 3
5
7 49 9 3 1000000000
No
Yes
Yes
No
Note
In the first test case, any two numbers in the array are coprime, so the answer is "No".
In the second test case, we can pick $i=2$ and $j=1$. Since every number in the array is divisible by $a_i = 1$, the answer is "Yes".
In the third test case, we can pick $i=3$ and $j=5$. $2$ and $4$ is divisible by $a_i = 2$ while $3$, $6$ and $12$ is divisible by $a_j = 3$, so the answer is "Yes".