A15433. Playing with GCD

You are given an integer array $a$ of length $n$ .

Does there exist an array $b$ consisting of $n+1$ positive integers such that $a_i=\gcd (b_i,b_{i+1})$ for all $i$ ( $1 \leq i \leq n$ )?

Note that $\gcd(x, y)$ denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers $x$ and $y$ .

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \leq t \leq 10^5$ ). Description of the test cases follows.

The first line of each test case contains an integer $n$ ( $1 \leq n \leq 10^5$ ) — the length of the array $a$ .

The second line of each test case contains $n$ space-separated integers $a_1,a_2,\ldots,a_n$ representing the array $a$ ( $1 \leq a_i \leq 10^4$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

For each test case, output "YES" if such $b$ exists, otherwise output "NO". You can print each letter in any case (upper or lower).

In the first test case, we can take $b=[343,343]$ .

In the second test case, one possibility for $b$ is $b=[12,8,6]$ .

In the third test case, it can be proved that there does not exist any array $b$ that fulfills all the conditions.