


_lowerCAmelCase						:   List[str]		=   [0, 2, 4, 6, 8]
_lowerCAmelCase						:   Any		=   [1, 3, 5, 7, 9]



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int						,							_lowerCAmelCase							:   int						,							_lowerCAmelCase							:   list[int]						,							_lowerCAmelCase							:   int	):




 """simple docstring"""







 if remaining_length == 0:
  if digits[0] == 0 or digits[-1] == 0:
   return 0

  for i in range(length // 2 - 1						,							-1						,							-1	):
   remainder += digits[i] + digits[length - i - 1]

   if remainder % 2 == 0:
    return 0

   remainder //= 10

  return 1

 if remaining_length == 1:
  if remainder % 2 == 0:
   return 0

  UpperCAmelCase__							 =						0
  for digit in range(10	):
   UpperCAmelCase__							 =						digit
   result += reversible_numbers(
       0						,							(remainder + 2 * digit) // 10						,							_lowerCAmelCase						,							_lowerCAmelCase	)
  return result

 UpperCAmelCase__							 =						0
 for digita in range(10	):
  UpperCAmelCase__							 =						digita

  if (remainder + digita) % 2 == 0:
   UpperCAmelCase__							 =						ODD_DIGITS
  else:
   UpperCAmelCase__							 =						EVEN_DIGITS

  for digita in other_parity_digits:
   UpperCAmelCase__							 =						digita
   result += reversible_numbers(
       remaining_length - 2						,							(remainder + digita + digita) // 10						,							_lowerCAmelCase						,							_lowerCAmelCase						,							)
 return result



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int = 9	):




 """simple docstring"""







 UpperCAmelCase__							 =						0
 for length in range(1						,							max_power + 1	):
  result += reversible_numbers(_lowerCAmelCase						,							0						,							[0] * length						,							_lowerCAmelCase	)
 return result


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











import math



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int	):




 """simple docstring"""







 UpperCAmelCase__							 =						math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

 return exponent == int(_lowerCAmelCase	)



def 						lowerCAmelCase		(		_lowerCAmelCase							:   float = 1 / 1_2345	):




 """simple docstring"""







 UpperCAmelCase__							 =						0
 UpperCAmelCase__							 =						0

 UpperCAmelCase__							 =						3
 while True:
  UpperCAmelCase__							 =						(integer**2 - 1) / 4
  # if candidate is an integer, then there is a partition for k
  if partition_candidate == int(_lowerCAmelCase	):
   UpperCAmelCase__							 =						int(_lowerCAmelCase	)
   total_partitions += 1
   if check_partition_perfect(_lowerCAmelCase	):
    perfect_partitions += 1
  if perfect_partitions > 0:
   if perfect_partitions / total_partitions < max_proportion:
    return int(_lowerCAmelCase	)
  integer += 1


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





