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.