"""simple docstring"""


def       UpperCAmelCase					(	UpperCAmelCase      )       ->   int:
     return n * (2 * n - 1)







def       UpperCAmelCase					(	UpperCAmelCase      )       ->   bool:
     snake_case_       =      (1 + 24 * n) ** 0.5
     return ((1 + root) / 6) % 1 == 0







def       UpperCAmelCase					(	UpperCAmelCase = 144      )       ->   int:
     snake_case_       =      start
     snake_case_       =      hexagonal_num(UpperCAmelCase      )
     while not is_pentagonal(UpperCAmelCase      ):
          n += 1
          snake_case_       =      hexagonal_num(UpperCAmelCase      )
     return num


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


"""simple docstring"""


import math







def       UpperCAmelCase					(	UpperCAmelCase      )       ->   float:
     snake_case_       =      math.log(2		,      10      ) * number
     snake_case_       =      round((log_number - int(UpperCAmelCase      ))		,      15      )

     return difference







def       UpperCAmelCase					(	UpperCAmelCase = 678910      )       ->   int:
     snake_case_       =      90
     snake_case_       =      0

     snake_case_       =      math.log(1.23		,      10      )
     snake_case_       =      math.log(1.24		,      10      )
     snake_case_       =      0

     while position < number:
          snake_case_       =      log_difference(UpperCAmelCase      )

          if difference >= upper_limit:
               power_iterator += 93

          elif difference < lower_limit:
               power_iterator += 196

          else:
               snake_case_       =      power_iterator
               power_iterator += 196
               position += 1

     return previous_power


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    print(F"""{solution() = }""")

