code: 
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  import functools
  from math import sqrt
  from time import time
  
  
  def 				UpperCamelCase	(  snake_case	,     *snake_case	,     **snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     SCREAMING_SNAKE_CASE__			:				Optional[int]       						= time()
     SCREAMING_SNAKE_CASE__			:				str       						= func(*snake_case	,     **snake_case   )
     SCREAMING_SNAKE_CASE__			:				Optional[int]       						= time()
     if int(end - start   ) > 0:
        print(f"""{func.__name__} runtime: {(end - start):0.4f} s"""   )
     else:
        print(f"""{func.__name__} runtime: {(end - start) * 10_00:0.4f} ms"""   )
     return output
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     if n < 0:
        raise Exception('''n is negative'''   )
     if n == 0:
        return [0]
     SCREAMING_SNAKE_CASE__			:				Tuple       						= [0, 1]
     for _ in range(n - 1   ):
        fib.append(fib[-1] + fib[-2]   )
     return fib
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     def fib_recursive_term(snake_case   ) -> 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(snake_case   ) for i in range(n + 1   )]
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     @functools.cache
     def fib_recursive_term(snake_case   ) -> 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(snake_case   ) for i in range(n + 1   )]
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     if n < 0:
        raise Exception('''n is negative'''   )
     # Cache must be outside recursuive function
     # other it will reset every time it calls itself.
     SCREAMING_SNAKE_CASE__			:				dict[int, int]       						= {0: 0, 1: 1, 2: 1}  # Prefilled cache
  
     def rec_fn_memoized(snake_case   ) -> int:
        if num in cache:
           return cache[num]
  
        SCREAMING_SNAKE_CASE__			:				Tuple       						= rec_fn_memoized(num - 1   ) + rec_fn_memoized(num - 2   )
        SCREAMING_SNAKE_CASE__			:				int       						= value
        return value
  
     return [rec_fn_memoized(snake_case   ) for i in range(n + 1   )]
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     if n < 0:
        raise Exception('''n is negative'''   )
     if n >= 14_75:
        raise Exception('''n is too large'''   )
     SCREAMING_SNAKE_CASE__			:				int       						= sqrt(5   )
     SCREAMING_SNAKE_CASE__			:				List[Any]       						= (1 + sqrt_a) / 2
     return [round(phi**i / sqrt_a   ) for i in range(n + 1   )]
  
  
  if __name__ == "__main__":
         lowercase__				=	3_0
         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)
  
  
style_context: 
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  def 				UpperCamelCase	(  snake_case = 99_80_01   ):
  
  
  
  
     '''simple docstring'''
  
     for number in range(n - 1	,     99_99	,     -1   ):
        SCREAMING_SNAKE_CASE__			:				int       						= str(snake_case   )
  
        # checks whether 'str_number' is a palindrome.
        if str_number == str_number[::-1]:
           SCREAMING_SNAKE_CASE__			:				Any       						= 9_99
  
           # if 'number' is a product of two 3-digit numbers
           # then number is the answer otherwise fetch next number.
           while divisor != 99:
              if (number % divisor == 0) and (len(str(number // divisor   )   ) == 3.0):
                 return number
              divisor -= 1
     raise ValueError('''That number is larger than our acceptable range.'''   )
  
  
  if __name__ == "__main__":
         print(F"{solution() = }")
  
  