


def 						lowerCAmelCase		(		_lowerCAmelCase							:   int						,							_lowerCAmelCase							:   int	):




 """simple docstring"""







 return x if y == 0 else greatest_common_divisor(_lowerCAmelCase						,							x % y	)



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int						,							_lowerCAmelCase							:   int	):




 """simple docstring"""







 return (x * y) // greatest_common_divisor(_lowerCAmelCase						,							_lowerCAmelCase	)



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int = 20	):




 """simple docstring"""







 UpperCAmelCase__							 =						1
 for i in range(1						,							n + 1	):
  UpperCAmelCase__							 =						lcm(_lowerCAmelCase						,							_lowerCAmelCase	)
 return g


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() = }''')





