


'''simple docstring'''
from math import gcd



def 				lowerCAmelCase__	(       UpperCAmelCase = 1_2000     ):






       """simple docstring"""





       snake_case__					:	Tuple          =					0
       for d in range(max_d + 1     ):
              for n in range(d // 3 + 1    ,       (d + 1) // 2     ):
                     if gcd(UpperCAmelCase    ,       UpperCAmelCase     ) == 1:
                            fractions_number += 1
       return fractions_number


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








'''simple docstring'''
import math



def 				lowerCAmelCase__	(       UpperCAmelCase     ):






       """simple docstring"""





       snake_case__					:	Tuple          =					math.log(2    ,       10     ) * number
       snake_case__					:	int          =					round((log_number - int(UpperCAmelCase     ))    ,       15     )

       return difference



def 				lowerCAmelCase__	(       UpperCAmelCase = 67_8910     ):






       """simple docstring"""





       snake_case__					:	str          =					90
       snake_case__					:	Dict          =					0

       snake_case__					:	List[str]          =					math.log(1.2_3    ,       10     )
       snake_case__					:	Optional[Any]          =					math.log(1.2_4    ,       10     )
       snake_case__					:	Any          =					0

       while position < number:
              snake_case__					:	Tuple          =					log_difference(UpperCAmelCase     )

              if difference >= upper_limit:
                     power_iterator += 93

              elif difference < lower_limit:
                     power_iterator += 196

              else:
                     snake_case__					:	Union[str, Any]          =					power_iterator
                     power_iterator += 196
                     position += 1

       return previous_power


if __name__ == "__main__":
     import doctest

     doctest.testmod()

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




