Description:
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.