B. Playing with GCD
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$y$$$.

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
4
1
343
2
4 2
3
4 2 4
4
1 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.