





def  lowerCAmelCase_ (							UpperCamelCase_ = 1000000  )     ->		int:
       UpperCamelCase_          =  [i - 1 for i in range(limit + 1  )]

       for i in range(2					,		limit + 1  ):
              if phi[i] == i - 1:
                     for j in range(2 * i					,		limit + 1					,		UpperCamelCase_  ):
                            phi[j] -= phi[j] // i

       return sum(phi[2 : limit + 1]  )


if __name__ == "__main__":
     print(solution())








import sys




def  lowerCAmelCase_ (							UpperCamelCase_  )     ->		Union[str, Any]:
       UpperCamelCase_          =  len(UpperCamelCase_  )
       UpperCamelCase_          =  [[0 for x in range(UpperCamelCase_  )] for x in range(UpperCamelCase_  )]
       UpperCamelCase_          =  [[0 for x in range(UpperCamelCase_  )] for x in range(UpperCamelCase_  )]

       for chain_length in range(2					,		UpperCamelCase_  ):
              for a in range(1					,		n - chain_length + 1  ):
                     UpperCamelCase_          =  a + chain_length - 1

                     UpperCamelCase_          =  sys.maxsize
                     for c in range(UpperCamelCase_					,		UpperCamelCase_  ):
                            UpperCamelCase_          =  (
                                matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
                            )
                            if cost < matrix[a][b]:
                                   UpperCamelCase_          =  cost
                                   UpperCamelCase_          =  c
       return matrix, sol




def  lowerCAmelCase_ (							UpperCamelCase_					,		UpperCamelCase_					,		UpperCamelCase_  )     ->		List[str]:
       if i == j:
              print("A" + str(UpperCamelCase_  )					,		end=" "  )
       else:
              print("("					,		end=" "  )
              print_optiomal_solution(UpperCamelCase_					,		UpperCamelCase_					,		optimal_solution[i][j]  )
              print_optiomal_solution(UpperCamelCase_					,		optimal_solution[i][j] + 1					,		UpperCamelCase_  )
              print(")"					,		end=" "  )




def  lowerCAmelCase_ (							)     ->		Any:
       UpperCamelCase_          =  [30, 35, 15, 5, 10, 20, 25]
       UpperCamelCase_          =  len(UpperCamelCase_  )
       # Size of matrix created from above array will be
       # 30*35 35*15 15*5 5*10 10*20 20*25
       UpperCamelCase_       , UpperCamelCase_          =  matrix_chain_order(UpperCamelCase_  )

       print("No. of Operation required: " + str(matrix[1][n - 1]  )  )
       print_optiomal_solution(UpperCamelCase_					,		1					,		n - 1  )


if __name__ == "__main__":
     main()

