

def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     Tuple  ,  SCREAMING_SNAKE_CASE_					:     List[str] = 1_0_0_0   )							->       str:
      """simple docstring"""

      if (not isinstance(_SCREAMING_SNAKE_CASE  ,  _SCREAMING_SNAKE_CASE   )) or (digit_position <= 0):
            raise ValueError("Digit position must be a positive integer"   )
      elif (not isinstance(_SCREAMING_SNAKE_CASE  ,  _SCREAMING_SNAKE_CASE   )) or (precision < 0):
            raise ValueError("Precision must be a nonnegative integer"   )

      # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
      # accurate
      SCREAMING_SNAKE_CASE_				:      List[str]					=	(
          4 * _subsum(_SCREAMING_SNAKE_CASE  ,  1  ,  _SCREAMING_SNAKE_CASE   )
          - 2 * _subsum(_SCREAMING_SNAKE_CASE  ,  4  ,  _SCREAMING_SNAKE_CASE   )
          - _subsum(_SCREAMING_SNAKE_CASE  ,  5  ,  _SCREAMING_SNAKE_CASE   )
          - _subsum(_SCREAMING_SNAKE_CASE  ,  6  ,  _SCREAMING_SNAKE_CASE   )
      )

      # return the first hex digit of the fractional part of the result
      return hex(int((sum_result % 1) * 1_6   )   )[2:]


def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     List[str]  ,  SCREAMING_SNAKE_CASE_					:     Tuple  ,  SCREAMING_SNAKE_CASE_					:     Optional[int]   )							->       float:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_				:      Tuple					=	0.0
      for sum_index in range(digit_pos_to_extract + precision   ):
            SCREAMING_SNAKE_CASE_				:      List[Any]					=	8 * sum_index + denominator_addend
            if sum_index < digit_pos_to_extract:
                  # if the exponential term is an integer and we mod it by the denominator
                  # before dividing, only the integer part of the sum will change;
                  # the fractional part will not
                  SCREAMING_SNAKE_CASE_				:      Dict					=	pow(
                      1_6  ,  digit_pos_to_extract - 1 - sum_index  ,  _SCREAMING_SNAKE_CASE   )
            else:
                  SCREAMING_SNAKE_CASE_				:      Union[str, Any]					=	pow(1_6  ,  digit_pos_to_extract - 1 - sum_index   )
            total += exponential_term / denominator
      return total


if __name__ == "__main__":
      import doctest

      doctest.testmod()




'''simple docstring'''






from __future__ import annotations

from PIL import Image

# Define the first generation of cells
# fmt: off
snake_case_					  =	[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]


def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     int   )							->       list[int]:
      """simple docstring"""

      return [int(SCREAMING_SNAKE_CASE_   ) for c in F"{ruleset:08}"[:8]]


def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     list[list[int]]  ,  SCREAMING_SNAKE_CASE_					:     list[int]  ,  SCREAMING_SNAKE_CASE_					:     int   )							->       list[int]:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_				:      Optional[Any]					=	len(cells[0]   )  # 31
      SCREAMING_SNAKE_CASE_				:      Dict					=	[]
      for i in range(SCREAMING_SNAKE_CASE_   ):
            # Get the neighbors of each cell
            # Handle neighbours outside bounds by using 0 as their value
            SCREAMING_SNAKE_CASE_				:      Any					=	0 if i == 0 else cells[time][i - 1]
            SCREAMING_SNAKE_CASE_				:      Dict					=	0 if i == population - 1 else cells[time][i + 1]
            # Define a new cell and add it to the new generation
            SCREAMING_SNAKE_CASE_				:      List[Any]					=	7 - int(F"{left_neighbor}{cells[time][i]}{right_neighbor}"  ,  2   )
            next_generation.append(rule[situation]   )
      return next_generation


def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     list[list[int]]   )							->       Image.Image:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_				:      Tuple					=	Image.new("RGB"  ,  (len(cells[0]   ), len(SCREAMING_SNAKE_CASE_   ))   )
      SCREAMING_SNAKE_CASE_				:      Optional[int]					=	img.load()
      # Generates image
      for w in range(img.width   ):
            for h in range(img.height   ):
                  SCREAMING_SNAKE_CASE_				:      List[Any]					=	2_5_5 - int(2_5_5 * cells[h][w]   )
                  SCREAMING_SNAKE_CASE_				:      Optional[int]					=	(color, color, color)
      return img


if __name__ == "__main__":
      snake_case_					  =	bin(int(input('Rule:\n').strip()))[2:]
      snake_case_					  =	format_ruleset(int(rule_num))
      for time in range(1_6):
            CELLS.append(new_generation(CELLS, rule, time))
      snake_case_					  =	generate_image(CELLS)
      # Uncomment to save the image
      # img.save(f"rule_{rule_num}.png")
      img.show()

