
"""simple docstring"""





import functools
from math import sqrt
from time import time







def       __a	(						__lowerCamelCase,						*__lowerCamelCase,						**__lowerCamelCase    ):
   UpperCAmelCase_   :   Union[str, Any]     	=       time()
   UpperCAmelCase_   :   Dict     	=       func(*__lowerCamelCase,						**__lowerCamelCase    )
   UpperCAmelCase_   :   str     	=       time()
   if int(end - start    ) > 0:
      print(f"""{func.__name__} runtime: {(end - start):0.4f} s"""    )
   else:
      print(f"""{func.__name__} runtime: {(end - start) * 1000:0.4f} ms"""    )
   return output







def       __a	(						__lowerCamelCase    ):
   if n < 0:
      raise Exception("n is negative"    )
   if n == 0:
      return [0]
   UpperCAmelCase_   :   Optional[int]     	=       [0, 1]
   for _ in range(n - 1    ):
      fib.append(fib[-1] + fib[-2]    )
   return fib







def       __a	(						__lowerCamelCase    ):

   def fib_recursive_term(__lowerCamelCase    ) -> int:
      if i < 0:
         raise Exception("n is negative"    )
      if i < 2:
         return i
      return fib_recursive_term(i - 1    ) + fib_recursive_term(i - 2    )

   if n < 0:
      raise Exception("n is negative"    )
   return [fib_recursive_term(__lowerCamelCase    ) for i in range(n + 1    )]







def       __a	(						__lowerCamelCase    ):

   @functools.cache
   def fib_recursive_term(__lowerCamelCase    ) -> int:
      if i < 0:
         raise Exception("n is negative"    )
      if i < 2:
         return i
      return fib_recursive_term(i - 1    ) + fib_recursive_term(i - 2    )

   if n < 0:
      raise Exception("n is negative"    )
   return [fib_recursive_term(__lowerCamelCase    ) for i in range(n + 1    )]







def       __a	(						__lowerCamelCase    ):
   if n < 0:
      raise Exception("n is negative"    )
   # Cache must be outside recursuive function
   # other it will reset every time it calls itself.
   UpperCAmelCase_   :   dict[int, int]     	=       {0: 0, 1: 1, 2: 1}  # Prefilled cache

   def rec_fn_memoized(__lowerCamelCase    ) -> int:
      if num in cache:
         return cache[num]

      UpperCAmelCase_   :   List[Any]     	=       rec_fn_memoized(num - 1    ) + rec_fn_memoized(num - 2    )
      UpperCAmelCase_   :   List[Any]     	=       value
      return value

   return [rec_fn_memoized(__lowerCamelCase    ) for i in range(n + 1    )]







def       __a	(						__lowerCamelCase    ):
   if n < 0:
      raise Exception("n is negative"    )
   if n >= 1475:
      raise Exception("n is too large"    )
   UpperCAmelCase_   :   Any     	=       sqrt(5    )
   UpperCAmelCase_   :   Any     	=       (1 + sqrt_a) / 2
   return [round(phi**i / sqrt_a    ) for i in range(n + 1    )]


if __name__ == "__main__":
    _a									=				30
    time_func(fib_iterative, num)
    time_func(fib_recursive, num)  # Around 3s runtime
    time_func(fib_recursive_cached, num)  # Around 0ms runtime
    time_func(fib_memoization, num)
    time_func(fib_binet, num)




'''simple docstring'''
import itertools

def     UpperCamelCase_  (						__SCREAMING_SNAKE_CASE = 1_0_0_0_0_0_0							):
    """simple docstring"""






    snake_case_			:     Optional[int]        =    [1]

    for i in itertools.count(len(__SCREAMING_SNAKE_CASE							)							):
        snake_case_			:     str        =    0
        for j in itertools.count(1							):
            snake_case_			:     List[str]        =    -1 if j % 2 == 0 else +1
            snake_case_			:     str        =    (j * j * 3 - j) // 2
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number
            index += j
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number

        if item == 0:
            return i
        partitions.append(__SCREAMING_SNAKE_CASE							)

    return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(f"""{solution() = }""")




