Color Class Operations

You are required to implement a Color class which represents a color in RGB format and supports several operations including conversion to hexadecimal, conversion to HSL, and darkening the color by a given percentage.

The class must support the following methods:

• to_hex(): Returns the hexadecimal string representation of the color in the format #RRGGBB.
• to_hsl(): Returns the HSL (Hue, Saturation, Lightness) representation as a tuple where Hue is an integer (in degrees) and Saturation and Lightness are floats rounded to two decimals. Use the standard formulas:</p>

  \( L = \frac{\max(r,g,b) + \min(r,g,b)}{2} \)

  \( \text{if } \Delta = \max(r,g,b)-\min(r,g,b)=0 \text{ then } H = S = 0 \)

  \( \text{otherwise, } S = \begin{cases} \frac{\Delta}{\max(r,g,b)+\min(r,g,b)} & L\leq0.5\\ \frac{\Delta}{2.0-\max(r,g,b)-\min(r,g,b)} & L>0.5 \end{cases} \)

  and Hue is determined based on which of RGB is maximum.

• darker(percentage): Returns a new Color instance that is a darker shade by reducing each RGB component by a factor of \( (1-\text{percentage}) \). Here, percentage is a float between 0 and 1.

Input/Output Interaction:

The program will process multiple queries. Each query begins with an integer indicating the type of operation, followed by the corresponding parameters:

• Type 1: Convert to hexadecimal. Input: 1 r g b
• Type 2: Convert to HSL. Input: 2 r g b
• Type 3: Darken the color. Input: 3 r g b percentage

For each query, output the corresponding result on a new line. For HSL, output the three components separated by a space (Hue as an integer, Saturation and Lightness as floats rounded to 2 decimals).

inputFormat

The first line of input contains an integer Q (Q ≥ 3) representing the number of queries. Each of the following Q lines contains a query. The queries are in one of the following formats:

• 1 r g b - where r, g, b are integers (0-255) for converting to hexadecimal.
• 2 r g b - where r, g, b are integers (0-255) for converting to HSL.
• 3 r g b percentage - where r, g, b are integers (0-255) and percentage is a float between 0 and 1 for darkening the color.

outputFormat

For each query, output the result on a new line:

• For type 1 queries, output the hexadecimal color as a string in the format #RRGGBB.
• For type 2 queries, output the HSL values separated by a space. Hue must be an integer and Saturation and Lightness rounded to two decimals.
• For type 3 queries, output the hexadecimal representation of the darkened color.

## sample

3
1 255 0 0
2 0 255 0
3 0 0 255 1.0

#FF0000
120 1.00 0.50
#000000

</p>