Serval and Mocha's Array

1000ms

262144K

Description:

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 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.

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 $$$n$$$ ($$$2\leq n\leq 100$$$) — 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 $$$a$$$.

Output:

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).

Sample Input:

6
2
3 6
3
1 2 4
3
3 6 1
3
15 35 21
4
35 10 35 14
5
1261 227821 143 4171 1941

Sample Output:

No
Yes
Yes
No
Yes
Yes

Note:

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.

Informação

Provedor Codeforces

Código CF1789A