"""simple docstring"""




import math







def 				_UpperCAmelCase		(							lowerCamelCase__  ):





		"""simple docstring"""




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

		return exponent == int(lowerCamelCase__  )







def 				_UpperCAmelCase		(							lowerCamelCase__ = 1 / 1_2345  ):





		"""simple docstring"""




		lowerCAmelCase__   = 0
		lowerCAmelCase__   = 0

		lowerCAmelCase__   = 3
		while True:
				lowerCAmelCase__   = (integer**2 - 1) / 4
				# if candidate is an integer, then there is a partition for k
				if partition_candidate == int(lowerCamelCase__  ):
						lowerCAmelCase__   = 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() = }")





"""simple docstring"""




from itertools import permutations







def 				_UpperCAmelCase		(							lowerCamelCase__  ):





		"""simple docstring"""




		if num[3] % 2 != 0:
				return False

		if (num[2] + num[3] + num[4]) % 3 != 0:
				return False

		if num[5] % 5 != 0:
				return False

		lowerCAmelCase__   = [7, 11, 13, 17]
		for i, test in enumerate(lowerCamelCase__  ):
				if (num[i + 4] * 100 + num[i + 5] * 10 + num[i + 6]) % test != 0:
						return False
		return True







def 				_UpperCAmelCase		(							lowerCamelCase__ = 10  ):





		"""simple docstring"""




		return sum(
		    int("""""".join(map(lowerCamelCase__      ,	lowerCamelCase__  )  )  )
		    for num in permutations(range(lowerCamelCase__  )  )
		    if is_substring_divisible(lowerCamelCase__  )  )


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




