



"""simple docstring"""






def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


  if len(str(UpperCamelCase__    )    ) == 1 or len(str(UpperCamelCase__    )    ) == 1:
    return a * b

  _SCREAMING_SNAKE_CASE        =			max(len(str(UpperCamelCase__    )    )       ,							len(str(UpperCamelCase__    )    )    )
  _SCREAMING_SNAKE_CASE        =			ma // 2

  _SCREAMING_SNAKE_CASE    ,     _SCREAMING_SNAKE_CASE        =			divmod(UpperCamelCase__       ,							10**ma    )
  _SCREAMING_SNAKE_CASE    ,     _SCREAMING_SNAKE_CASE        =			divmod(UpperCamelCase__       ,							10**ma    )

  _SCREAMING_SNAKE_CASE        =			karatsuba(UpperCamelCase__       ,							UpperCamelCase__    )
  _SCREAMING_SNAKE_CASE        =			karatsuba((aa + aa)       ,							(ba + ba)    )
  _SCREAMING_SNAKE_CASE        =			karatsuba(UpperCamelCase__       ,							UpperCamelCase__    )

  return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)


def 							A__ (     ):


  '''simple docstring'''


  print(karatsuba(15_463       ,							23_489    )    )


if __name__ == "__main__":
    main()





"""simple docstring"""






from math import gcd


def 							A__ (     UpperCamelCase__ = 12_000    ):


  '''simple docstring'''


  _SCREAMING_SNAKE_CASE        =			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() = }''')
