B. Consecutive Points Segment
brute force; math; sortings
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.