



from functools import lru_cache


@lru_cache
def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 if not isinstance(UpperCAmelCase__			,       UpperCAmelCase__       ):
  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 						UpperCAmelCase__   (   UpperCAmelCase__			:list			,       UpperCAmelCase__			:int       ):






 '''simple docstring'''

 a							=		len(UpperCAmelCase__       )
 # Find m such that F_m >= n where F_i is the i_th fibonacci number.
 a							=		0
 while True:
  if fibonacci(UpperCAmelCase__       ) >= len_list:
   a							=		i
   break
  i += 1
 a							=		0
 while fibb_k > 0:
  a							=		min(
      offset + fibonacci(fibb_k - 1       )			,       len_list - 1       )  # Prevent out of range
  a							=		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()









'''simple docstring'''


from itertools import combinations_with_replacement







def 						__magic_name__(			_A = 100       ):
						'''simple docstring'''





						UpperCamelCase__       =			[*list(range(1    ,   21       )       ), 25]
						UpperCamelCase__       =			[2 * x for x in range(1    ,   21       )] + [50]
						UpperCamelCase__       =			[3 * x for x in range(1    ,   21       )]
						UpperCamelCase__       =			singles + doubles + triples + [0]

						UpperCamelCase__       =			0
						UpperCamelCase__       =			42
						UpperCamelCase__       =			42
						UpperCamelCase__       =			42
						UpperCamelCase__       =			42

						for double in doubles:
												for throwa, throwa in combinations_with_replacement(_A    ,   2       ):
																		UpperCamelCase__       =			double + throwa + throwa
																		if checkout_total < limit:
																								num_checkouts += 1

						return num_checkouts


if __name__ == "__main__":
					print(f"""{solution() = }""")
