




'''simple docstring'''







from decimal import Decimal, getcontext
from math import ceil, factorial





def 						snake_case_							(_a	:							int     ):

    if not isinstance(_a    ,   _a     ):
        raise TypeError('''Undefined for non-integers'''     )
    elif precision < 1:
        raise ValueError('''Undefined for non-natural numbers'''     )

    UpperCAmelCase			       =		precision
    UpperCAmelCase			       =		ceil(precision / 1_4     )
    UpperCAmelCase			       =		4_2_6_8_8_0 * Decimal(1_0_0_0_5     ).sqrt()
    UpperCAmelCase			       =		1
    UpperCAmelCase			       =		1_3_5_9_1_4_0_9
    UpperCAmelCase			       =		Decimal(_a     )
    for k in range(1    ,   _a     ):
        UpperCAmelCase			       =		factorial(6 * k     ) // (factorial(3 * k     ) * factorial(_a     ) ** 3)
        linear_term += 5_4_5_1_4_0_1_3_4
        exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
        partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
    return str(constant_term / partial_sum     )[:-1]


if __name__ == "__main__":
   A     =50
   print(f"""The first {n} digits of pi is: {pi(n)}""")










'''simple docstring'''







class 			_a  :
       def __init__(	self						:	Any				):



           '''simple docstring'''

           UpperCAmelCase			       =		{}  # Mapping from char to TrieNode
           UpperCAmelCase			       =		False
       def     A      (	self						:	int   ,				lowercase						:	list[str]				):



           '''simple docstring'''

           for word in words:
               self.insert(lowercase				)
       def     A      (	self						:	Optional[int]   ,				lowercase						:	str				):



           '''simple docstring'''

           UpperCAmelCase			       =		self
           for char in word:
               if char not in curr.nodes:
                   UpperCAmelCase			       =		TrieNode()
               UpperCAmelCase			       =		curr.nodes[char]
           UpperCAmelCase			       =		True
       def     A      (	self						:	Optional[int]   ,				lowercase						:	str				):



           '''simple docstring'''

           UpperCAmelCase			       =		self
           for char in word:
               if char not in curr.nodes:
                   return False
               UpperCAmelCase			       =		curr.nodes[char]
           return curr.is_leaf







       def     A      (	self						:	str   ,				lowercase						:	str				):



           '''simple docstring'''

           def _delete(lowercase						:	TrieNode   ,				lowercase						:	str   ,				lowercase						:	int				) -> bool:
               if index == len(lowercase				):
                   # If word does not exist
                   if not curr.is_leaf:
                       return False
                   UpperCAmelCase			       =		False
                   return len(curr.nodes				) == 0
               UpperCAmelCase			       =		word[index]
               UpperCAmelCase			       =		curr.nodes.get(lowercase				)
               # If char not in current trie node
               if not char_node:
                   return False
               # Flag to check if node can be deleted
               UpperCAmelCase			       =		_delete(lowercase   ,				lowercase   ,				index + 1				)
               if delete_curr:
                   del curr.nodes[char]
                   return len(curr.nodes				) == 0
               return delete_curr

           _delete(self   ,				lowercase   ,				0				)






def 						snake_case_							(_a	:							TrieNode    ,   _a	:							str     ):
    if node.is_leaf:
        print(_a    ,   end=''' '''     )

    for key, value in node.nodes.items():
        print_words(_a    ,   word + key     )





def 						snake_case_							():
    UpperCAmelCase			       =		'''banana bananas bandana band apple all beast'''.split()
    UpperCAmelCase			       =		TrieNode()
    root.insert_many(_a     )
    # print_words(root, "")
    assert all(root.find(_a     ) for word in words     )
    assert root.find('''banana'''     )
    assert not root.find('''bandanas'''     )
    assert not root.find('''apps'''     )
    assert root.find('''apple'''     )
    assert root.find('''all'''     )
    root.delete('''all'''     )
    assert not root.find('''all'''     )
    root.delete('''banana'''     )
    assert not root.find('''banana'''     )
    assert root.find('''bananas'''     )
    return True





def 						snake_case_							(_a	:							str    ,   _a	:							bool     ):
    print(str(_a     )    ,   '''works!''' if passes else '''doesn\'t work :('''     )





def 						snake_case_							():
    assert test_trie()





def 						snake_case_							():
    print_results('''Testing trie functionality'''    ,   test_trie()     )


if __name__ == "__main__":
   main()




