1980D · GCD-sequence

Problem: GCD (Greatest Common Divisor) of two integers $x$ and $y$ is the maximum integer $z$ by which both $x$ and $y$ are divisible. For example, $GCD(36, 48) = 12$, $GCD(5, 10) = 5$, and $GCD(7,11) = 1$.

Kristina has an array $a$ consisting of exactly $n$ positive integers. She wants to count the GCD of each neighbouring pair of numbers to get a new array $b$, called GCD-sequence.

So, the elements of the GCD-sequence $b$ will be calculated using the formula $b_i = GCD(a_i, a_{i + 1})$ for $1 \le i \le n - 1$.

Determine whether it is possible to remove exactly one number from the array $a$ so that the GCD sequence $b$ is non-decreasing (i.e., $b_i \le b_{i+1}$ is always true).

For example, let Khristina had an array $a$ = [$20, 6, 12, 3, 48, 36$]. If she removes $a_4 = 3$ from it and counts the GCD-sequence of $b$, she gets:

• $b_1 = GCD(20, 6) = 2$
• $b_2 = GCD(6, 12) = 6$
• $b_3 = GCD(12, 48) = 12$
• $b_4 = GCD(48, 36) = 12$

Input Format: The first line of input data contains a single number $t$ ($1 \le t \le 10^4$) — he number of test cases in the test.

This is followed by the descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the number of elements in the array $a$.

The second line of each test case contains exactly $n$ integers $a_i$ ($1 \le a_i \le 10^9$) — the elements of array $a$.

It is guaranteed that the sum of $n$ over all test case does not exceed $2 \cdot 10^5$.

Output Format: For each test case, output a single line:

• "YES" if you can remove exactly one number from the array $a$ so that the GCD-sequence of $b$ is non-decreasing;
• "NO" otherwise.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will all be recognized as a positive answer).

Note: The first test case is explained in the problem statement.