code: 
  
  
  from __future__ import annotations
  
  import math
  import random
  
  
  
  
  
  
  def 		_A		(		_lowercase				,     _lowercase				,     _lowercase   )				->   list[int]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = d * e - 1
       __UpperCamelCase   = 0
       __UpperCamelCase   = 0
       while p == 0:
            __UpperCamelCase   = random.randint(2				,     n - 1   )
            __UpperCamelCase   = k
            while True:
                 if t % 2 == 0:
                      __UpperCamelCase   = t // 2
                      __UpperCamelCase   = (g**t) % n
                      __UpperCamelCase   = math.gcd(x - 1				,     _lowercase   )
                      if x > 1 and y > 1:
                           __UpperCamelCase   = y
                           __UpperCamelCase   = n // y
                           break  # find the correct factors
                 else:
                      break  # t is not divisible by 2, break and choose another g
       return sorted([p, q]   )
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()
  
  
  
style_context: 
  
  
  import warnings
  from collections.abc import Callable
  from typing import Any
  
  import numpy
  from matplotlib import pyplot
  
  __snake_case             =	0.25 + 0.0j
  __snake_case             =	-0.4 + 0.6j
  __snake_case             =	-0.1 + 0.6_51j
  __snake_case             =	-2.0
  __snake_case             =	5_6
  __snake_case             =	2.0
  __snake_case             =	6_6_6
  
  
  
  
  
  
  def 		_A		(		_lowercase				,     _lowercase   )				->   numpy.ndarray:
  
  
       """simple docstring"""
  
  
       return numpy.exp(_lowercase   ) + c_parameter
  
  
  
  
  
  
  def 		_A		(		_lowercase				,     _lowercase   )				->   numpy.ndarray:
  
  
       """simple docstring"""
  
  
       return z_values * z_values + c_parameter
  
  
  
  
  
  
  def 		_A		(		_lowercase				,     _lowercase   )				->   numpy.ndarray:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = numpy.linspace(-window_size				,     _lowercase				,     _lowercase   )
       __UpperCamelCase   = x.reshape((nb_pixels, 1)   )
       __UpperCamelCase   = numpy.linspace(-window_size				,     _lowercase				,     _lowercase   )
       __UpperCamelCase   = y.reshape((1, nb_pixels)   )
       return x + 1.0J * y
  
  
  
  
  
  
  def 		_A		(		_lowercase				,     _lowercase				,     _lowercase				,     _lowercase				,     _lowercase = None				,     )				->   numpy.ndarray:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = z_a.astype('complex64'   )
       for _ in range(_lowercase   ):
            __UpperCamelCase   = eval_function(_lowercase				,     _lowercase   )
            if infinity is not None:
                 numpy.nan_to_num(_lowercase				,     copy=_lowercase				,     nan=_lowercase   )
                 __UpperCamelCase   = infinity
       return z_n
  
  
  
  
  
  
  def 		_A		(		_lowercase				,     _lowercase				,     _lowercase				,     _lowercase				,     )				->   None:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = (abs(_lowercase   )).transpose()
       __UpperCamelCase   = abs_z_final[::-1, :]
       pyplot.matshow(abs_z_final < escape_radius   )
       pyplot.title(f'''Julia set of ${function_label}$, $c={function_params}$'''   )
       pyplot.show()
  
  
  
  
  
  
  def 		_A		(		)				->   None:
  
  
       """simple docstring"""
  
  
       warnings.filterwarnings(
           'ignore'				,     category=_lowercase				,     message='overflow encountered in multiply'   )
       warnings.filterwarnings(
           'ignore'				,     category=_lowercase				,     message='invalid value encountered in multiply'				,     )
       warnings.filterwarnings(
           'ignore'				,     category=_lowercase				,     message='overflow encountered in absolute'   )
       warnings.filterwarnings(
           'ignore'				,     category=_lowercase				,     message='overflow encountered in exp'   )
  
  
  if __name__ == "__main__":
      __snake_case             =	prepare_grid(window_size, nb_pixels)
  
      ignore_overflow_warnings()  # See file header for explanations
  
      __snake_case             =	2_4
      __snake_case             =	2 * abs(c_cauliflower) + 1
      __snake_case             =	iterate_function(
          eval_quadratic_polynomial,
          c_cauliflower,
          nb_iterations,
          z_a,
          infinity=1.1 * escape_radius,
      )
      show_results('''z^2+c''', c_cauliflower, escape_radius, z_final)
  
      __snake_case             =	6_4
      __snake_case             =	2 * abs(c_polynomial_a) + 1
      __snake_case             =	iterate_function(
          eval_quadratic_polynomial,
          c_polynomial_a,
          nb_iterations,
          z_a,
          infinity=1.1 * escape_radius,
      )
      show_results('''z^2+c''', c_polynomial_a, escape_radius, z_final)
  
      __snake_case             =	1_6_1
      __snake_case             =	2 * abs(c_polynomial_a) + 1
      __snake_case             =	iterate_function(
          eval_quadratic_polynomial,
          c_polynomial_a,
          nb_iterations,
          z_a,
          infinity=1.1 * escape_radius,
      )
      show_results('''z^2+c''', c_polynomial_a, escape_radius, z_final)
  
      __snake_case             =	1_2
      __snake_case             =	10_000.0
      __snake_case             =	iterate_function(
          eval_exponential,
          c_exponential,
          nb_iterations,
          z_a + 2,
          infinity=1.0e10,
      )
      show_results('''e^z+c''', c_exponential, escape_radius, z_final)
  
  
  