



'''simple docstring'''





import math




def lowerCAmelCase    (__A):



     """simple docstring"""



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

     return exponent == int(__A)




def lowerCAmelCase    (__A = 1 / 12_345):



     """simple docstring"""



     _a           =    0
     _a           =    0

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


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








'''simple docstring'''





from __future__ import annotations




def lowerCAmelCase    (__A):



     """simple docstring"""



     _a           =    2
     _a           =    []
     while i * i <= n:
          if n % i:
               i += 1
          else:
               n //= i
               factors.append(__A)
     if n > 1:
          factors.append(__A)
     return factors


if __name__ == "__main__":
  import doctest

  doctest.testmod()



