Codeforces Round 825 (Div. 2) |
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Finished |

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math

number theory

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B. Playing with GCD

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$y$$$.

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).

Example

Input

4134324 234 2 441 1 1 1

Output

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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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