codeforces#P1736B. Playing with GCD
Playing with GCD
Description
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) 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).
Input
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 $10^5$.
Output
For each test case, output "YES" if such $b$ exists, otherwise output "NO". You can print each letter in any case (upper or lower).
4
1
343
2
4 2
3
4 2 4
4
1 1 1 1
YES
YES
NO
YES
Note
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.