


from __future__ import annotations
def 				__lowerCamelCase						( UpperCAmelCase_						:		dict ,  UpperCAmelCase_						:		str						):




      """simple docstring"""





      a							,				a						:Optional[Any] 							=       set(UpperCAmelCase_						), [start]

      while stack:
            a						:Optional[int] 							=       stack.pop()
            explored.add(UpperCAmelCase_						)
            # Differences from BFS:
            # 1) pop last element instead of first one
            # 2) add adjacent elements to stack without exploring them
            for adj in reversed(graph[v]						):
                  if adj not in explored:
                        stack.append(UpperCAmelCase_						)
      return explored


snake_case				:    Optional[int]       				=     {
    '''A''': ['''B''', '''C''', '''D'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F'''],
    '''D''': ['''B''', '''D'''],
    '''E''': ['''B''', '''F'''],
    '''F''': ['''C''', '''E''', '''G'''],
    '''G''': ['''F'''],
}

if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(depth_first_search(G, '''A'''))









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() = }""")





