



import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

_lowerCamelCase         =	0.2_5 + 0.0j
_lowerCamelCase         =	-0.4 + 0.6j
_lowerCamelCase         =	-0.1 + 0.651j
_lowerCamelCase         =	-2.0
_lowerCamelCase         =	56
_lowerCamelCase         =	2.0
_lowerCamelCase         =	666






def 						_lowerCAmelCase    (					__lowerCamelCase :  complex		,						__lowerCamelCase :  numpy.ndarray  ):



 """simple docstring"""





 return numpy.exp(__lowerCamelCase  ) + c_parameter






def 						_lowerCAmelCase    (					__lowerCamelCase :  complex		,						__lowerCamelCase :  numpy.ndarray  ):



 """simple docstring"""





 return z_values * z_values + c_parameter






def 						_lowerCAmelCase    (					__lowerCamelCase :  float		,						__lowerCamelCase :  int  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     List[Any]							=						numpy.linspace(-window_size		,						__lowerCamelCase		,						__lowerCamelCase  )
 __SCREAMING_SNAKE_CASE							:     List[str]							=						x.reshape((nb_pixels, 1)  )
 __SCREAMING_SNAKE_CASE							:     List[Any]							=						numpy.linspace(-window_size		,						__lowerCamelCase		,						__lowerCamelCase  )
 __SCREAMING_SNAKE_CASE							:     str							=						y.reshape((1, nb_pixels)  )
 return x + 1.0j * y






def 						_lowerCAmelCase    (					__lowerCamelCase :  Callable[[Any, numpy.ndarray], numpy.ndarray]		,						__lowerCamelCase :  Any		,						__lowerCamelCase :  int		,						__lowerCamelCase :  numpy.ndarray		,						__lowerCamelCase :  float | None = None		,						):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     Any							=						z_a.astype("complex64"  )
 for _ in range(__lowerCamelCase  ):
  __SCREAMING_SNAKE_CASE							:     List[Any]							=						eval_function(__lowerCamelCase		,						__lowerCamelCase  )
  if infinity is not None:
   numpy.nan_to_num(__lowerCamelCase		,						copy=__lowerCamelCase		,						nan=__lowerCamelCase  )
   __SCREAMING_SNAKE_CASE							:     Any							=						infinity
 return z_n






def 						_lowerCAmelCase    (					__lowerCamelCase :  str		,						__lowerCamelCase :  Any		,						__lowerCamelCase :  float		,						__lowerCamelCase :  numpy.ndarray		,						):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     List[str]							=						(abs(__lowerCamelCase  )).transpose()
 __SCREAMING_SNAKE_CASE							:     str							=						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 						_lowerCAmelCase    (					):



 """simple docstring"""





 warnings.filterwarnings(
     "ignore"		,						category=__lowerCamelCase		,						message="overflow encountered in multiply"  )
 warnings.filterwarnings(
     "ignore"		,						category=__lowerCamelCase		,						message="invalid value encountered in multiply"		,						)
 warnings.filterwarnings(
     "ignore"		,						category=__lowerCamelCase		,						message="overflow encountered in absolute"  )
 warnings.filterwarnings(
     "ignore"		,						category=__lowerCamelCase		,						message="overflow encountered in exp"  )


if __name__ == "__main__":
      _lowerCamelCase         =	prepare_grid(window_size, nb_pixels)

      ignore_overflow_warnings()  # See file header for explanations

      _lowerCamelCase         =	24
      _lowerCamelCase         =	2 * abs(c_cauliflower) + 1
      _lowerCamelCase         =	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)

      _lowerCamelCase         =	64
      _lowerCamelCase         =	2 * abs(c_polynomial_a) + 1
      _lowerCamelCase         =	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)

      _lowerCamelCase         =	161
      _lowerCamelCase         =	2 * abs(c_polynomial_a) + 1
      _lowerCamelCase         =	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)

      _lowerCamelCase         =	12
      _lowerCamelCase         =	1_0_0_0_0.0
      _lowerCamelCase         =	iterate_function(
          eval_exponential,
          c_exponential,
          nb_iterations,
          z_a + 2,
          infinity=1.0e1_0,
      )
      show_results("""e^z+c""", c_exponential, escape_radius, z_final)












def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if a < b:
										return gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)
					if a % b == 0:
										return b
					return gcd(SCREAMING_SNAKE_CASE_ , a % b	)







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if y == 0:
										return 1
					__lowerCAmelCase							  =			power(SCREAMING_SNAKE_CASE_ , y // 2 , SCREAMING_SNAKE_CASE_	) % mod
					__lowerCAmelCase							  =			(temp * temp) % mod
					if y % 2 == 1:
										__lowerCAmelCase							  =			(temp * x) % mod
					return temp







def       _a (		SCREAMING_SNAKE_CASE_				:							int	):
					__lowerCAmelCase							  =			2
					while b < n:
										if gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) == 1 and power(SCREAMING_SNAKE_CASE_ , n - 1 , SCREAMING_SNAKE_CASE_	) != 1:
															return False
										b += 1
					return True


if __name__ == "__main__":
					UpperCamelCase__            =     int(input("""Enter number: """).strip())
					if is_carmichael_number(number):
										print(f'''{number} is a Carmichael Number.''')
					else:
										print(f'''{number} is not a Carmichael Number.''')




