#P1671B. Consecutive Points Segment
Consecutive Points Segment
Description
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.
Input
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 $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).
Output
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.
Samples
5
2
1 4
3
1 2 3
4
1 2 3 7
1
1000000
3
2 5 6
YES
YES
NO
YES
YES