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## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Statement

## Goal

Designers are placing shapes of different sizes and colors on the canvas of an image editor.**About Colors**

The shapes have primary colors defined in RGB color notations. Red is (255, 0, 0); Green is (0, 255, 0); Blue is (0, 0, 255). Besides these, they also use Yellow (255, 255, 0), Cyan (0, 255, 255) and Magenta (255, 0, 255).

All shapes have a very thin black border (0, 0, 0) and are on a white background (255, 255, 255).

The shapes are defined as transparent so that when one shape is overlaying another, their colors will mix to reveal a new color. When two or more colors blend together, the new color is the average of all layer's colors.

For example, when R and G blend, the mixed color is (128, 128, 0). When Y, M and G mix, the result will be ((255+255+0)/3, (255+0+255)/3, (0+255+0)/3), which is (170, 170, 85). We round the decimal results to get the nearest integers (i.e. 10.4 is regarded as 10; 10.5 is regarded as 11).

**Black and White do not have blending effects.**

In the final design, only squares and circles are used. Designers want to have a program to automatically calculate the color at any chosen point.

When a chosen point is within one or more shapes, report the color or mixed color at that point.

When a chosen point is outside the shapes, report White (255, 255, 255).

When a chosen point is on the borderline of any shape, report Black (0, 0, 0).

Input

**Line 1:**Integer

`S`and

`P`, for the number of Shapes and number of checking points.

**Next**Each line defines one Shape by seven elements, space separated:

`S`lines:`name`is either

**SQUARE**or

**CIRCLE**

`x0`

`y0`are integers. For a circle, this is the coordinates of the center. For a square, it is the coordinates of the lower-left corner. We are using the Cartesian coordinates system. All square sides are parallel to the x or y axis.

`len`is an integer. For a circle, it is the radius. For a square, it is the side length.

`R`

`G`

`B`are integers, color values of this shape.

**Next**Each line defines a point by integers

`P`lines:`x`

`y`. You have to calculate the color at each of the points.

Output

**Write**Each line is a RGB color notation in format

`P`lines**(R, G, B)**.

Constraints

1 ≤

1 ≤

0 ≤

1 ≤

0 ≤

Some shapes may be partially drawn outside the canvas. Your business is within the canvas only.

`S`≤ 501 ≤

`P`≤ 500 ≤

`x`,`y`≤ 1000 (This is the canvas size limit)1 ≤

`len`≤ 5000 ≤

`R`,`G`,`B`≤ 255Some shapes may be partially drawn outside the canvas. Your business is within the canvas only.

Example

Input

3 6 SQUARE 0 5 6 255 0 0 SQUARE 4 2 3 0 255 0 CIRCLE 4 6 3 0 0 255 0 0 4 5 2 6 5 3 5 4 3 4

Output

(255, 255, 255) (0, 0, 0) (128, 0, 128) (0, 255, 0) (0, 128, 128) (0, 0, 255)

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