






import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def    a__    (	A		,					A       ):
   lowercase__  ,       lowercase__    :						Dict       =			np.shape(A       )

   lowercase__    :						NDArray[floataa]       =			np.zeros((rows, 1)		,					dtype=A       )
   for row in reversed(range(A       )       ):
      lowercase__    :						Tuple       =			0
      for col in range(row + 1		,					A       ):
         total += coefficients[row, col] * x[col]

      lowercase__    :						Union[str, Any]       =			(vector[row] - total) / coefficients[row, row]

   return x
def    a__    (	A		,					A       ):
   lowercase__  ,       lowercase__    :						Any       =			np.shape(A       )
   if rows != columns:
      return np.array(()		,					dtype=A       )

   # augmented matrix
   lowercase__    :						NDArray[floataa]       =			np.concatenate((coefficients, vector)		,					axis=1       )
   lowercase__    :						Optional[Any]       =			augmented_mat.astype("""float64"""       )

   # scale the matrix leaving it triangular
   for row in range(rows - 1       ):
      lowercase__    :						Any       =			augmented_mat[row, row]
      for col in range(row + 1		,					A       ):
         lowercase__    :						Tuple       =			augmented_mat[col, row] / pivot
         augmented_mat[col, :] -= factor * augmented_mat[row, :]

   lowercase__    :						Any       =			retroactive_resolution(
       augmented_mat[:, 0:columns]		,					augmented_mat[:, columns : columns + 1]       )

   return x


if __name__ == "__main__":
 import doctest

 doctest.testmod()










from __future__ import annotations

from PIL import Image

# Define the first generation of cells
# fmt: off
a 			=							[[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    a__    (	A       ):
   return [int(A       ) for c in F'''{ruleset:08}'''[:8]]
def    a__    (	A		,					A		,					A       ):
   lowercase__    :						List[Any]       =			len(cells[0]       )  # 31
   lowercase__    :						int       =			[]
   for i in range(A       ):
      # Get the neighbors of each cell
      # Handle neighbours outside bounds by using 0 as their value
      lowercase__    :						Optional[Any]       =			0 if i == 0 else cells[time][i - 1]
      lowercase__    :						Dict       =			0 if i == population - 1 else cells[time][i + 1]
      # Define a new cell and add it to the new generation
      lowercase__    :						str       =			7 - int(F'''{left_neighbor}{cells[time][i]}{right_neighbor}'''		,					2       )
      next_generation.append(rule[situation]       )
   return next_generation
def    a__    (	A       ):
   lowercase__    :						Tuple       =			Image.new("""RGB"""		,					(len(cells[0]       ), len(A       ))       )
   lowercase__    :						Optional[Any]       =			img.load()
   # Generates image
   for w in range(img.width       ):
      for h in range(img.height       ):
         lowercase__    :						Union[str, Any]       =			255 - int(255 * cells[h][w]       )
         lowercase__    :						int       =			(color, color, color)
   return img


if __name__ == "__main__":
 a 			=							bin(int(input('Rule:\n').strip()))[2:]
 a 			=							format_ruleset(int(rule_num))
 for time in range(16):
  CELLS.append(new_generation(CELLS, rule, time))
 a 			=							generate_image(CELLS)
 # Uncomment to save the image
 # img.save(f"rule_{rule_num}.png")
 img.show()


