


def 				__lowerCamelCase						( UpperCAmelCase_						:		int = 100_0000						):




      """simple docstring"""





      a						:Any 							=       set(range(3 ,  UpperCAmelCase_ ,  2						)						)
      primes.add(2						)
      for p in range(3 ,  UpperCAmelCase_ ,  2						):
            if p not in primes:
                  continue
            primes.difference_update(set(range(p * p ,  UpperCAmelCase_ ,  UpperCAmelCase_						)						)						)

      a						:Union[str, Any] 							=       [float(UpperCAmelCase_						) for n in range(limit + 1						)]

      for p in primes:
            for n in range(UpperCAmelCase_ ,  limit + 1 ,  UpperCAmelCase_						):
                  phi[n] *= 1 - 1 / p

      return int(sum(phi[2:]						)						)


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









def 				__lowerCamelCase						( UpperCAmelCase_						:		int ,  UpperCAmelCase_						:		int						):




      """simple docstring"""





      while b:
            a							,				a						:Optional[Any] 							=       b, a % b
      return a
def 				__lowerCamelCase						( UpperCAmelCase_						:		int ,  UpperCAmelCase_						:		int						):




      """simple docstring"""





      return a if b == 0 else euclidean_gcd_recursive(UpperCAmelCase_ ,  a % b						)
def 				__lowerCamelCase						( ):




      """simple docstring"""





      print(F'''euclidean_gcd(3, 5) = {euclidean_gcd(3 ,  5						)}'''						)
      print(F'''euclidean_gcd(5, 3) = {euclidean_gcd(5 ,  3						)}'''						)
      print(F'''euclidean_gcd(1, 3) = {euclidean_gcd(1 ,  3						)}'''						)
      print(F'''euclidean_gcd(3, 6) = {euclidean_gcd(3 ,  6						)}'''						)
      print(F'''euclidean_gcd(6, 3) = {euclidean_gcd(6 ,  3						)}'''						)

      print(F'''euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3 ,  5						)}'''						)
      print(F'''euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5 ,  3						)}'''						)
      print(F'''euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1 ,  3						)}'''						)
      print(F'''euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3 ,  6						)}'''						)
      print(F'''euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6 ,  3						)}'''						)


if __name__ == "__main__":
     main()





