# 240. Square, Diamond, and Rectangle

## I'm a slow walker, but I never walk backwards.

Given four different points on the plane, determine the shape of this polygon. There are several cases.

• If the length of the four sides are the same, and the four angles are right, then it is a square. For example, the polygon by $(-1, 0), (0, 1), (1, 0), (0, -1)$ is a square.
• If the length of the four sides are the same, but the four angles are not right angle, then it is a diamond. For example, polygon by $(-2, 0), (0, 1), (2, 0), (0, -1)$ is a diamond.
• If the length of the four sides are not the same, but the four angles are right angle, then it is a rectangle. For example, polygon by $(0, 0), (0, 1), (2, 1), (2, 0)$ is a rectangle.

• 如果四邊長度相同以及角度為直角，它們即是正方形，如多邊形 $(-1, 0), (0, 1), (1, 0), (0, -1)$ 就是個正方形。
• 如果四邊長度相同但角度不是直角，它們即是菱形，如多邊形 $(-2, 0), (0, 1), (2, 0), (0, -1)$ 就是個菱形。
• 如果四邊長度不同且四個角均是直角，它們即是長方形，如 $(0, 0), (0, 1), (2, 1), (2, 0)$ 就是個長方形。
• 不屬於上述三者，請回報 other

## Input

The first line has the number of test data $n$. $n$ is at least 1 and at most 100000. Each of he next $n$ line has a test data. Each test data line has 8 integers for the four points.

The first two are the $x$ and $y$ coordinates of the first point, etc.

Since the difference between two $x$ coordinates, or two $y$ coordinates is bounded by 10000, you may assume that the computation can be safely done with int.

It is also guaranteed that there will be no three points in a straight line, and the quadrilateral is convex and unique. The four points may be given in any order.

## Output

Output the shape for each input line. You should output square, diamond, rectangle according to the definition above. If the polygon does not fit into any definition, output other.

## Sample input

4-1 0 0 -1 0 1 1 0-2 0 2 0 0 -1 0 10 1 2 1 0 0 2 00 1 0 0 2 1 2 -10


## Sample output

squarediamondrectangleother


## Hint

You can easily check whether an angle is a right angle by Pythagorean theorem - $a^2 + b^2 = c^2$.