



from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean





def 		a__      (		_UpperCamelCase      :			int				):

   # A local function to see if a dot lands in the circle.
   def is_in_circle(_UpperCamelCase      :			float			,_UpperCamelCase      :			float				) -> bool:
      __lowerCamelCase    				=     sqrt((x**2) + (y**2)				)
      # Our circle has a radius of 1, so a distance
      # greater than 1 would land outside the circle.
      return distance_from_centre <= 1

   # The proportion of guesses that landed in the circle
   __lowerCamelCase    				=     mean(
       int(is_in_circle(uniform(-1.0			,1.0				)			,uniform(-1.0			,1.0				)				)				)
       for _ in range(_UpperCamelCase				)				)
   # The ratio of the area for circle to square is pi/4.
   __lowerCamelCase    				=     proportion * 4
   print(F"""The estimated value of pi is {pi_estimate}"""				)
   print(F"""The numpy value of pi is {pi}"""				)
   print(F"""The total error is {abs(pi - pi_estimate				)}"""				)





def 		a__      (		_UpperCamelCase      :			int			,_UpperCamelCase      :			Callable[[float], float]			,_UpperCamelCase      :			float = 0.0			,_UpperCamelCase      :			float = 1.0			,):
   return mean(
       function_to_integrate(uniform(_UpperCamelCase			,_UpperCamelCase				)				) for _ in range(_UpperCamelCase				)				) * (max_value - min_value)





def 		a__      (		_UpperCamelCase      :			int			,_UpperCamelCase      :			float = 0.0			,_UpperCamelCase      :			float = 1.0				):

   def identity_function(_UpperCamelCase      :			float				) -> float:
      return x

   __lowerCamelCase    				=     area_under_curve_estimator(
       _UpperCamelCase			,_UpperCamelCase			,_UpperCamelCase			,_UpperCamelCase				)
   __lowerCamelCase    				=     (max_value * max_value - min_value * min_value) / 2

   print('''******************'''				)
   print(F"""Estimating area under y=x where x varies from {min_value} to {max_value}"""				)
   print(F"""Estimated value is {estimated_value}"""				)
   print(F"""Expected value is {expected_value}"""				)
   print(F"""Total error is {abs(estimated_value - expected_value				)}"""				)
   print('''******************'''				)





def 		a__      (		_UpperCamelCase      :			int				):

   def function_to_integrate(_UpperCamelCase      :			float				) -> float:
      return sqrt(4.0 - x * x				)

   __lowerCamelCase    				=     area_under_curve_estimator(
       _UpperCamelCase			,_UpperCamelCase			,0.0			,2.0				)

   print('''******************'''				)
   print('''Estimating pi using area_under_curve_estimator'''				)
   print(F"""Estimated value is {estimated_value}"""				)
   print(F"""Expected value is {pi}"""				)
   print(F"""Total error is {abs(estimated_value - pi				)}"""				)
   print('''******************'''				)


if __name__ == "__main__":
  import doctest

  doctest.testmod()











def 		a__      (		_UpperCamelCase      :			str				):
   if not all(x.isalpha() for x in string				):
      raise ValueError('''String must only contain alphabetic characters.'''				)

   __lowerCamelCase    				=     sorted(string.lower()				)
   return len(_UpperCamelCase				) == len(set(_UpperCamelCase				)				)


if __name__ == "__main__":
  a_								=       input("""Enter a string """).strip()

  a_								=       is_isogram(input_str)
  print(f"{input_str} is {'an' if isogram else 'not an'} isogram.")






