

def 	UpperCAmelCase__   (				A__ = 100_0000   )      ->      int:




   """simple docstring"""
   lowerCamelCase__						=			set(range(3	,    lowercase_	,    2   )   )
   primes.add(2   )
   for p in range(3	,    lowercase_	,    2   ):
      if p not in primes:
         continue
      primes.difference_update(set(range(p * p	,    lowercase_	,    lowercase_   )   )   )

   lowerCamelCase__						=			[float(lowercase_   ) for n in range(limit + 1   )]

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

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


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







"""simple docstring"""




# Algorithm for the pigeonhole sorting





def 	UpperCAmelCase__   (				A__   )      ->      Dict:




   """simple docstring"""
   lowerCamelCase__						=			min(A__   )  # min() finds the minimum value
   lowerCamelCase__						=			max(A__   )  # max() finds the maximum value

   lowerCamelCase__						=			max_val - min_val + 1  # size is difference of max and min values plus one

   # list of pigeonholes of size equal to the variable size
   lowerCamelCase__						=			[0] * size

   # Populate the pigeonholes.
   for x in a:
      assert isinstance(A__	,    A__   ), "integers only please"
      holes[x - min_val] += 1

   # Putting the elements back into the array in an order.
   lowerCamelCase__						=			0
   for count in range(A__   ):
      while holes[count] > 0:
         holes[count] -= 1
         lowerCamelCase__						=			count + min_val
         i += 1



def 	UpperCAmelCase__   (				)      ->      Optional[int]:




   """simple docstring"""
   lowerCamelCase__						=			[8, 3, 2, 7, 4, 6, 8]
   pigeonhole_sort(A__   )
   print("Sorted order is:"	,    " ".join(A__   )   )


if __name__ == "__main__":
     main()




