CF2127A Mix Mex Max

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.

Each 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.

For 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.

In 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.