





"""simple docstring"""




class  _a						:






				def __init__( self		:    Tuple							)	->      Optional[Any]:




										'''simple docstring'''



										_UpperCamelCase			:					List[str]     =    []
										_UpperCamelCase			:					Optional[int]     =    0
										_UpperCamelCase			:					Tuple     =    0






				def __str__( self		:    Tuple							)	->      List[str]:




										'''simple docstring'''



										_UpperCamelCase			:					List[str]     =    '''<''' + str(self.entries							)[1:-1] + '''>'''
										return printed






				def 				snake_case	( self		:    Tuple, lowerCAmelCase__		:    Union[str, Any]							)	->      str:




										'''simple docstring'''



										self.entries.append(lowerCAmelCase__							)
										_UpperCamelCase			:					Dict     =    self.length + 1






				def 				snake_case	( self		:    Tuple							)	->      Dict:




										'''simple docstring'''



										_UpperCamelCase			:					str     =    self.length - 1
										_UpperCamelCase			:					int     =    self.entries[self.front]
										# self.front-=1
										# self.entries = self.entries[self.front:]
										_UpperCamelCase			:					List[str]     =    self.entries[1:]
										return dequeued






				def 				snake_case	( self		:    List[str], lowerCAmelCase__		:    Dict							)	->      Optional[Any]:




										'''simple docstring'''



										for _ in range(lowerCAmelCase__							):
																self.put(self.get()							)






				def 				snake_case	( self		:    Optional[Any]							)	->      Tuple:




										'''simple docstring'''



										return self.entries[0]






				def 				snake_case	( self		:    str							)	->      Dict:




										'''simple docstring'''



										return self.length










"""simple docstring"""




from functools import lru_cache





@lru_cache
def        a_				(							_lowercase   ):
						if not isinstance(_lowercase       ,						_lowercase   ):
												raise TypeError('''k must be an integer.'''   )
						if k < 0:
												raise ValueError('''k integer must be greater or equal to zero.'''   )
						if k == 0:
												return 0
						elif k == 1:
												return 1
						else:
												return fibonacci(k - 1   ) + fibonacci(k - 2   )





def        a_				(							_lowercase       ,						_lowercase   ):
						_UpperCamelCase			:					Any     =    len(_lowercase   )
						# Find m such that F_m >= n where F_i is the i_th fibonacci number.
						_UpperCamelCase			:					Optional[int]     =    0
						while True:
												if fibonacci(_lowercase   ) >= len_list:
																		_UpperCamelCase			:					List[Any]     =    i
																		break
												i += 1
						_UpperCamelCase			:					Tuple     =    0
						while fibb_k > 0:
												_UpperCamelCase			:					Union[str, Any]     =    min(
												    offset + fibonacci(fibb_k - 1   )       ,						len_list - 1   )  # Prevent out of range
												_UpperCamelCase			:					Any     =    arr[index_k]
												if item_k_1 == val:
																		return index_k
												elif val < item_k_1:
																		fibb_k -= 1
												elif val > item_k_1:
																		offset += fibonacci(fibb_k - 1   )
																		fibb_k -= 2
						else:
												return -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()



