




def 		a_       (   __lowerCAmelCase							):
  lowerCAmelCase__								=			[True for i in range(n + 1							)]
  lowerCAmelCase__								=			[i - 1 for i in range(n + 1							)]
  lowerCAmelCase__								=			[]
  for i in range(2      ,   n + 1							):
    if is_prime[i]:
      primes.append(__lowerCAmelCase							)
    for j in range(0      ,   len(__lowerCAmelCase							)							):
      if i * primes[j] >= n:
        break
      lowerCAmelCase__								=			False

      if i % primes[j] == 0:
        lowerCAmelCase__								=			totients[i] * primes[j]
        break

      lowerCAmelCase__								=			totients[i] * (primes[j] - 1)

  return totients


if __name__ == "__main__":
      import doctest

      doctest.testmod()







def 		a_       (   __lowerCAmelCase      ,   __lowerCAmelCase							):
  assert isinstance(__lowerCAmelCase      ,   __lowerCAmelCase							), F"""The input value of [set_a={set_a}] is not a set"""
  assert isinstance(__lowerCAmelCase      ,   __lowerCAmelCase							), F"""The input value of [set_b={set_b}] is not a set"""

  return {a + b for a in set_a for b in set_b}


if __name__ == "__main__":
      from doctest import testmod

      testmod()

