
from __future__ import annotations

from collections.abc import Iterator



class 		UpperCamelCase__  :
   def __init__(self			: Any ,    snake_case_			: int       ):
    __a			:  int		    =  value
    __a			:  Node | None		    =  None
    __a			:  Node | None		    =  None





class 		UpperCamelCase__  :
   def __init__(self			: List[str] ,    snake_case_			: Node       ):
    __a			:  Dict		    =  tree
   def 				lowerCAmelCase      (self			: Optional[Any] ,    snake_case_			: Node | None       ):
    if node is None:
     return 0
    return node.value + (
        self.depth_first_search(node.left       ) + self.depth_first_search(node.right       )
    )







   def __iter__(self			: Optional[Any]       ):
    yield self.depth_first_search(self.tree       )


if __name__ == "__main__":
      import doctest

      doctest.testmod()


from math import pi, sqrt




def        __UpperCamelCase					(    lowerCAmelCase__							:    float  ):
 if num <= 0:
  raise ValueError('''math domain error'''  )
 if num > 1_71.5:
  raise OverflowError('''math range error'''  )
 elif num - int(lowerCAmelCase__  ) not in (0, 0.5):
  raise NotImplementedError('''num must be an integer or a half-integer'''  )
 elif num == 0.5:
  return sqrt(lowerCAmelCase__  )
 else:
  return 1.0 if num == 1 else (num - 1) * gamma(num - 1  )




def        __UpperCamelCase					(    ):
 assert gamma(0.5  ) == sqrt(lowerCAmelCase__  )
 assert gamma(1  ) == 1.0
 assert gamma(2  ) == 1.0


if __name__ == "__main__":
      from doctest import testmod

      testmod()
      lowercase__          =1.0
      while num:
            lowercase__          =float(input('Gamma of: '))
            print(F"""gamma({num}) = {gamma(num)}""")
            print('\nEnter 0 to exit...')
