code: 
  
  
  import warnings
  from collections.abc import Callable
  from typing import Any
  
  import numpy
  from matplotlib import pyplot
  
  __a   				=      0.2_5 + 0.0j
  __a   				=      -0.4 + 0.6j
  __a   				=      -0.1 + 0.651j
  __a   				=      -2.0
  __a   				=      56
  __a   				=      2.0
  __a   				=      6_66
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->numpy.ndarray:
  
  
  
  
  
  
  
        """simple docstring"""
  
        return numpy.exp(_UpperCamelCase     ) + c_parameter
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->numpy.ndarray:
  
  
  
  
  
  
  
        """simple docstring"""
  
        return z_values * z_values + c_parameter
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->numpy.ndarray:
  
  
  
  
  
  
  
        """simple docstring"""
  
        lowercase			:   List[Any]					   =		numpy.linspace(-window_size,    _UpperCamelCase,    _UpperCamelCase     )
        lowercase			:   List[Any]					   =		x.reshape((nb_pixels, 1)     )
        lowercase			:   List[str]					   =		numpy.linspace(-window_size,    _UpperCamelCase,    _UpperCamelCase     )
        lowercase			:   List[str]					   =		y.reshape((1, nb_pixels)     )
        return x + 1.0J * y
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase = None,    )    ->numpy.ndarray:
  
  
  
  
  
  
  
        """simple docstring"""
  
        lowercase			:   Optional[int]					   =		z_a.astype('''complex64'''     )
        for _ in range(_UpperCamelCase     ):
              lowercase			:   Union[str, Any]					   =		eval_function(_UpperCamelCase,    _UpperCamelCase     )
              if infinity is not None:
                    numpy.nan_to_num(_UpperCamelCase,    copy=_UpperCamelCase,    nan=_UpperCamelCase     )
                    lowercase			:   Dict					   =		infinity
        return z_n
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase,    )    ->None:
  
  
  
  
  
  
  
        """simple docstring"""
  
        lowercase			:   int					   =		(abs(_UpperCamelCase     )).transpose()
        lowercase			:   Optional[int]					   =		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 			__lowercase	(						)    ->None:
  
  
  
  
  
  
  
        """simple docstring"""
  
        warnings.filterwarnings(
            '''ignore''',    category=_UpperCamelCase,    message='''overflow encountered in multiply'''     )
        warnings.filterwarnings(
            '''ignore''',    category=_UpperCamelCase,    message='''invalid value encountered in multiply''',    )
        warnings.filterwarnings(
            '''ignore''',    category=_UpperCamelCase,    message='''overflow encountered in absolute'''     )
        warnings.filterwarnings(
            '''ignore''',    category=_UpperCamelCase,    message='''overflow encountered in exp'''     )
  
  
  if __name__ == "__main__":
    __a   				=      prepare_grid(window_size, nb_pixels)
  
    ignore_overflow_warnings()  # See file header for explanations
  
    __a   				=      24
    __a   				=      2 * abs(c_cauliflower) + 1
    __a   				=      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)
  
    __a   				=      64
    __a   				=      2 * abs(c_polynomial_a) + 1
    __a   				=      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)
  
    __a   				=      1_61
    __a   				=      2 * abs(c_polynomial_a) + 1
    __a   				=      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)
  
    __a   				=      12
    __a   				=      1_0_0_0_0.0
    __a   				=      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)
  
  
style_context: 
  
  
  import math
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase     )    ->Union[str, Any]:
  
  
  
  
  
  
  
        """simple docstring"""
  
        lowercase			:   List[Any]					   =		0
        if n % 2 == 0:
              count += 1
              while n % 2 == 0:
                    lowercase			:   Any					   =		int(n / 2     )
      # the n input value must be odd so that
      # we can skip one element (ie i += 2)
  
        lowercase			:   Optional[int]					   =		3
  
        while i <= int(math.sqrt(_UpperCamelCase     )     ):
              if n % i == 0:
                    count += 1
                    while n % i == 0:
                          lowercase			:   Optional[Any]					   =		int(n / i     )
              lowercase			:   str					   =		i + 2
  
        # this condition checks the prime
        # number n is greater than 2
  
        if n > 2:
              count += 1
        return count
  
  
  if __name__ == "__main__":
    __a   				=      51_24_21_83
    print(F'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
    print(F'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')
  
  