## Goal

You have to print the nature of the quadrilaterals whose verticesâ€™ coordinates are given.

The nature can be:

* nothing, in which case you should write "quadrilateral",

* parallelogram (opposite sides are parallel to each other),

* rhombus (all four sides are equal),

* rectangle (all four angles are right) or

* square (it is a rectangle and a rhombus).
Input

**Line 1**: The number of quadrilaterals (`n`)

**Next **`n` lines: Each vertex followed by its coordinates, one quadrilateral per line. In the format:

`A` `xA` `yA` `B` `xB` `yB` `C` `xC` `yC` `D` `xD` `yD`

Output

The name of the quadrilateral followed by its nature. For example:

ABCD is a rhombus.

DEFA is a quadrilateral.

The vertices are printed in the given order. Note that ABCD, ABDC and ACBD are three distinct quadrilaterals. Just follow the order of the vertices.

Constraints

The coordinates are integers between -20 and 20, you have no more than 3 quadrilaterals.

You wonâ€™t have to test if a quadrilateral is degenerate or convex.

Example

Input

1
A -14 -3 B 5 -9 C 11 4 D -7 13

Output

ABCD is a quadrilateral.