A15722. Serval and Mocha's Array

Mocha likes arrays, and Serval gave her an array consisting of positive integers as a gift.

Mocha thinks that for an array of positive integers $a$ , it is good iff the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of all the elements in $a$ is no more than its length. And for an array of at least $2$ positive integers, it is beautiful iff all of its prefixes whose length is no less than $2$ are good.

For example:

- $[3,6]$ is not good, because $\gcd(3,6)=3$ is greater than its length $2$ .
- $[1,2,4]$ is both good and beautiful, because all of its prefixes whose length is no less than $2$ , which are $[1,2]$ and $[1,2,4]$ , are both good.
- $[3,6,1]$ is good but not beautiful, because $[3,6]$ is not good.

Now Mocha gives you the gift array $a$ of $n$ positive integers, and she wants to know whether array $a$ could become beautiful by reordering the elements in $a$ . It is allowed to keep the array $a$ unchanged.

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 $n$ ( $2\leq n\leq 100$ ) — the length of array $a$ .

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $1\leq a_1,a_2,\ldots,a_n\leq 10^6$ ) — the elements of array $a$ .

For each test case, print Yes if it is possible to reorder the elements in $a$ to make it beautiful, and print No if not.

You can output Yes and No in any case (for example, strings yEs, yes, Yes and YES will be recognized as a positive response).

In the first test case, neither $[3,6]$ nor $[6,3]$ are beautiful, so it's impossible to obtain a beautiful array by reordering the elements in $a$ .

In the second test case, $[1,2,4]$ is already beautiful. Keeping the array $a$ unchanged can obtain a beautiful array.