B. Consecutive Points Segmenttime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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).OutputFor 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.ExampleInput
5
2
1 4
3
1 2 3
4
1 2 3 7
1
1000000
3
2 5 6
Output
YES
YES
NO
YES
YES

5
2
1 4
3
1 2 3
4
1 2 3 7
1
1000000
3
2 5 6

YES YES NO YES YES 
['brute force', 'math', 'sortings', '*1000']