



from __future__ import annotations

from fractions import Fraction



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
 return (
     num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
 )



def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):
 __lowercase		       =			[]
 __lowercase		       =			1_1
 __lowercase		       =			int("1" + "0" * digit_len   )
 for num in range(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
  while den <= 9_9:
   if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
    if is_digit_cancelling(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
     solutions.append(F"""{num}/{den}"""   )
   den += 1
  num += 1
  __lowercase		       =			1_0
 return solutions



def    snake_case_				(    _SCREAMING_SNAKE_CASE = 2   ):
 __lowercase		       =			1.0
 for fraction in fraction_list(_SCREAMING_SNAKE_CASE   ):
  __lowercase		       =			Fraction(_SCREAMING_SNAKE_CASE   )
  result *= frac.denominator / frac.numerator
 return int(_SCREAMING_SNAKE_CASE   )


if __name__ == "__main__":
 print(solution())








def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# bit count represents no. of bits in the gray code
	if bit_count < 0:
		raise ValueError("The given input must be positive"   )

	# get the generated string sequence
	__lowercase		       =			gray_code_sequence_string(_SCREAMING_SNAKE_CASE   )
	#
	# convert them to integers
	for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
		__lowercase		       =			int(sequence[i]  ,	2   )

	return sequence



def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# The approach is a recursive one
	# Base case achieved when either n = 0 or n=1
	if bit_count == 0:
		return ["0"]

	if bit_count == 1:
		return ["0", "1"]

	__lowercase		       =			1 << bit_count  # defines the length of the sequence
	# 1<< n is equivalent to 2^n

	# recursive answer will generate answer for n-1 bits
	__lowercase		       =			gray_code_sequence_string(bit_count - 1   )

	__lowercase		       =			[]

	# append 0 to first half of the smaller sequence generated
	for i in range(seq_len // 2   ):
		__lowercase		       =			"0" + smaller_sequence[i]
		sequence.append(_SCREAMING_SNAKE_CASE   )

	# append 1 to second half ... start from the end of the list
	for i in reversed(range(seq_len // 2   )   ):
		__lowercase		       =			"1" + smaller_sequence[i]
		sequence.append(_SCREAMING_SNAKE_CASE   )

	return sequence


if __name__ == "__main__":
	import doctest

	doctest.testmod()



