


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)





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}''')

