CF1671B Consecutive Points Segment

You are given $ n $ points with integer coordinates on a coordinate axis $ OX $ . The coordinate of the $ i $ -th point is $ x_i $ . All points' coordinates are distinct and given in strictly increasing order. For each point $ i $ , you can do the following operation no more than once: take this point and move it by $ 1 $ to the left or to the right (i..e., you can change its coordinate $ x_i $ to $ x_i - 1 $ or to $ x_i + 1 $ ). In other words, for each point, you choose (separately) its new coordinate. For the $ i $ -th point, it can be either $ x_i - 1 $ , $ x_i $ or $ x_i + 1 $ . Your task is to determine if you can move some points as described above in such a way that the new set of points forms a consecutive segment of integers, i. e. for some integer $ l $ the coordinates of points should be equal to $ l, l + 1, \ldots, l + n - 1 $ . Note that the resulting points should have distinct coordinates. You have to answer $ t $ independent test cases.

The first line of the input contains one integer $ t $ ( $ 1 \le t \le 2 \cdot 10^4 $ ) — the number of test cases. Then $ t $ test cases follow. The first line of the test case contains one integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of points in the set $ x $ . The second line of the test case contains $ n $ integers $ x_1 < x_2 < \ldots < x_n $ ( $ 1 \le x_i \le 10^6 $ ), where $ x_i $ is the coordinate of the $ i $ -th point. It is guaranteed that the points are given in strictly increasing order (this also means that all coordinates are distinct). It is also guaranteed that the sum of $ n $ does not exceed $ 2 \cdot 10^5 $ ( $ \sum n \le 2 \cdot 10^5 $ ).

For each test case, print the answer — if the set of points from the test case can be moved to form a consecutive segment of integers, print YES, otherwise print NO.