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.

给你 $n$ 个位于坐标轴 $OX$ 上、具有整数坐标的点。第 $i$ 个点的坐标为 $x_i$。所有点的坐标互不相同，且严格递增地给出。

对于每个点 $i$，你最多可执行以下操作一次：将该点向左或向右移动 $1$ 个单位（即，可将其坐标 $x_i$ 改为 $x_i - 1$ 或 $x_i + 1$）。换言之，对每个点，你（独立地）选择其新坐标；对第 $i$ 个点，其新坐标可以是 $x_i - 1$、$x_i$ 或 $x_i + 1$ 中的任意一个。

你的任务是判断：能否按上述方式移动某些点，使得新得到的点集构成一段连续的整数区间，即存在某个整数 $l$，使得各点坐标恰好为 $l, l + 1, \ldots, l + n - 1$。

注意：最终得到的点的坐标必须互不相同。

你需要回答 $t$ 个相互独立的测试用例。

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 $x_1 \lt x_2 \lt \ldots \lt x_n$ ($1 \le x_i \le 10^6$), 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 $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).

输入的第一行包含一个整数 $t$（$1 \le t \le 2 \cdot 10^4$），表示测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$），表示集合 $x$ 中点的个数。

每个测试用例的第二行包含 $n$ 个整数 $x_1 \lt x_2 \lt \ldots \lt x_n$（$1 \le x_i \le 10^6$），其中 $x_i$ 表示第 $i$ 个点的坐标。

保证所给点的坐标严格递增（这也意味着所有坐标互不相同）。同时保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$（即 $\sum n \le 2 \cdot 10^5$）。

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.

对于每个测试用例，输出答案：如果测试用例中的点集能够通过移动形成一个连续的整数区间，则输出 YES，否则输出 NO。