A. Mix Mex Maxtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output You are given an array $$$a$$$ consisting of $$$n$$$ non-negative integers. However, some elements of $$$a$$$ are missing, and they are represented by $$$−1$$$.We define that the array $$$a$$$ is good if and only if the following holds for every $$$1 \leq i \leq n-2$$$:$$$$$$ \operatorname{mex}([a_i, a_{i+1}, a_{i+2}]) = \max([a_i, a_{i+1}, a_{i+2}]) - \min([a_i, a_{i+1}, a_{i+2}]), $$$$$$where $$$\operatorname{mex}(b)$$$ denotes the minimum excluded (MEX)$$$^{\text{∗}}$$$ of the integers in $$$b$$$. You have to determine whether you can make $$$a$$$ good after replacing each $$$-1$$$ in $$$a$$$ with a non-negative integer.$$$^{\text{∗}}$$$The minimum excluded (MEX) of a collection of integers $$$b_1, b_2, \ldots, b_k$$$ is defined as the smallest non-negative integer $$$x$$$ which does not occur in the collection $$$b$$$. For example, $$$\operatorname{mex}([2,2,1])=0$$$ because $$$0$$$ does not belong to the array, and $$$\operatorname{mex}([0,3,1,2])=4$$$ because $$$0$$$, $$$1$$$, $$$2$$$, and $$$3$$$ appear in the array, but $$$4$$$ does not.InputEach test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 500$$$). The description of the test cases follows. The first line of each test case contains a single integer $$$n$$$ ($$$3 \leq n \leq 100$$$) — the length of $$$a$$$.The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$-1 \leq a_i \leq 100$$$) — the elements of $$$a$$$. $$$a_i = -1$$$ denotes that this element is missing.OutputFor each test case, output "YES" if it is possible to make $$$a$$$ good, and "NO" otherwise.You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.ExampleInput83-1 -1 -151 1 1 1 065 5 1 -1 -1 14-1 -1 0 -14-1 1 1 -133 3 -150 0 0 0 073 0 1 4 -1 2 3OutputYES
NO
NO
NO
YES
YES
NO
NO
NoteIn the first test case, we can put $$$ a_1 = a_2 = a_3 = 1 $$$. Then, $$$\operatorname{mex}([a_1, a_2, a_3]) = \operatorname{mex}([1, 1, 1]) = 0$$$; $$$\max([a_1, a_2, a_3]) = \max([1, 1, 1]) = 1$$$; $$$\min([a_1, a_2, a_3]) = \min([1, 1, 1]) = 1$$$. And $$$0 = 1 - 1$$$. Thus, the array $$$a$$$ is good.In the second test case, none of the elements in $$$a$$$ is missing. And we have $$$\operatorname{mex}([a_1, a_2, a_3]) = \max([a_1, a_2, a_3]) - \min([a_1, a_2, a_3])$$$, $$$\operatorname{mex}([a_2, a_3, a_4]) = \max([a_2, a_3, a_4]) - \min([a_2, a_3, a_4])$$$, but $$$\operatorname{mex}([a_3, a_4, a_5]) \ne \max([a_3, a_4, a_5]) - \min([a_3, a_4, a_5])$$$. Thus, the array $$$a$$$ cannot be good.In the third test case, none of $$$a_1$$$, $$$a_2$$$, or $$$a_3$$$ is missing. However, $$$\operatorname{mex}([a_1, a_2, a_3]) = \operatorname{mex}([5, 5, 1]) = 0$$$; $$$\max([a_1, a_2, a_3]) = \max([5, 5, 1]) = 5$$$; $$$\min([a_1, a_2, a_3]) = \min([5, 5, 1]) = 1$$$. And $$$0\ne 5 - 1$$$. So the array $$$a$$$ cannot be good, no matter how you replace the missing elements.