Consider a set of points on a line. The distance between two points $$$i$$$ and $$$j$$$ is $$$|i - j|$$$.

The point $$$i$$$ from the set is the closest to the point $$$j$$$ from the set, if there is no other point $$$k$$$ in the set such that the distance from $$$j$$$ to $$$k$$$ is strictly less than the distance from $$$j$$$ to $$$i$$$. In other words, all other points from the set have distance to $$$j$$$ greater or equal to $$$|i - j|$$$.

For example, consider a set of points $$$\{1, 3, 5, 8\}$$$:

- for the point $$$1$$$, the closest point is $$$3$$$ (other points have distance greater than $$$|1-3| = 2$$$);
- for the point $$$3$$$, there are two closest points: $$$1$$$ and $$$5$$$;
- for the point $$$5$$$, the closest point is $$$3$$$ (but not $$$8$$$, since its distance is greater than $$$|3-5|$$$);
- for the point $$$8$$$, the closest point is $$$5$$$.

You are given a set of points. You have to add an integer point into this set in such a way that it is different from every existing point in the set, and it becomes the closest point to every point in the set. Is it possible?

Input format:
The first line contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

Each test case consists of two lines:

- the first line contains one integer $$$n$$$ ($$$2 \le n \le 40$$$) — the number of points in the set;
- the second line contains $$$n$$$ integers $$$x_1, x_2, \dots, x_n$$$ ($$$1 \le x_1 < x_2 < \dots < x_n \le 100$$$) — the points from the set.
Output format:
For each test case, print YES if it is possible to add a new point according to the conditions from the statement. Otherwise, print NO.
Example Input 0:
3
2
3 8
2
5 6
6
1 2 3 4 5 10

Example Output 0:
YES
NO
NO

Notes:
In the first example, the point $$$7$$$ will be the closest to both $$$3$$$ and $$$8$$$.

In the second example, it is impossible to add an integer point so that it becomes the closest to both $$$5$$$ and $$$6$$$, and is different from both of them.

Example input:
3
2
3 8
2
5 6
6
1 2 3 4 5 10


Example output:
YES
NO
NO