Codeforces Round 950 (Div. 3) |
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Finished |

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greedy

implementation

math

number theory

*1400

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D. GCD-sequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGCD (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

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

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).

Example

Input

12620 6 12 3 48 36412 6 3 4310 12 3532 16 8 4 25100 50 2 10 2042 4 8 1107 4 6 2 4 5 1 4 2 875 9 6 8 5 9 2611 14 8 12 9 395 7 3 10 6 3 12 6 334 2 481 6 11 12 6 12 3 6

Output

YES NO YES NO YES YES NO YES YES YES YES YES

Note

The first test case is explained in the problem statement.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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