"""simple docstring"""







def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Union[str, Any]     ,			__SCREAMING_SNAKE_CASE							:     List[str]      ):
     return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Optional[Any]     ,			__SCREAMING_SNAKE_CASE							:     Optional[Any]=0      ):
     return sorted(lowerCAmelCase_     ,			key=lambda __SCREAMING_SNAKE_CASE      : x[column]      )



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     str     ,			__SCREAMING_SNAKE_CASE							:     Optional[Any]     ,			__SCREAMING_SNAKE_CASE							:     List[Any]=float('inf'      )      ):


     for i in range(points_counts - 1      ):
          for j in range(i + 1     ,			lowerCAmelCase_      ):
               lowercase_	:				Any													=	euclidean_distance_sqr(points[i]     ,			points[j]      )
               if current_dis < min_dis:
                    lowercase_	:				Dict													=	current_dis
     return min_dis



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Optional[Any]     ,			__SCREAMING_SNAKE_CASE							:     Union[str, Any]     ,			__SCREAMING_SNAKE_CASE							:     int=float('inf'      )      ):


     for i in range(min(6     ,			points_counts - 1      )     ,			lowerCAmelCase_      ):
          for j in range(max(0     ,			i - 6      )     ,			lowerCAmelCase_      ):
               lowercase_	:				str													=	euclidean_distance_sqr(points[i]     ,			points[j]      )
               if current_dis < min_dis:
                    lowercase_	:				str													=	current_dis
     return min_dis



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Tuple     ,			__SCREAMING_SNAKE_CASE							:     List[Any]     ,			__SCREAMING_SNAKE_CASE							:     Optional[Any]      ):


     if points_counts <= 3:
          return dis_between_closest_pair(lowerCAmelCase_     ,			lowerCAmelCase_      )

     # recursion
     lowercase_	:				str													=	points_counts // 2
     lowercase_	:				Optional[Any]													=	closest_pair_of_points_sqr(
         lowerCAmelCase_     ,			points_sorted_on_y[:mid]     ,			lowerCAmelCase_      )
     lowercase_	:				Optional[int]													=	closest_pair_of_points_sqr(
         lowerCAmelCase_     ,			points_sorted_on_y[mid:]     ,			points_counts - mid      )
     lowercase_	:				Optional[int]													=	min(lowerCAmelCase_     ,			lowerCAmelCase_      )
     lowercase_	:				Optional[Any]													=	[]
     for point in points_sorted_on_x:
          if abs(point[0] - points_sorted_on_x[mid][0]      ) < closest_pair_dis:
               cross_strip.append(lowerCAmelCase_      )

     lowercase_	:				str													=	dis_between_closest_in_strip(
         lowerCAmelCase_     ,			len(lowerCAmelCase_      )     ,			lowerCAmelCase_      )
     return min(lowerCAmelCase_     ,			lowerCAmelCase_      )



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Dict     ,			__SCREAMING_SNAKE_CASE							:     List[str]      ):
     lowercase_	:				Union[str, Any]													=	column_based_sort(lowerCAmelCase_     ,			column=0      )
     lowercase_	:				Dict													=	column_based_sort(lowerCAmelCase_     ,			column=1      )
     return (
         closest_pair_of_points_sqr(
             lowerCAmelCase_     ,			lowerCAmelCase_     ,			lowerCAmelCase_      )
     ) ** 0.5


if __name__ == "__main__":
       __SCREAMING_SNAKE_CASE    	=[(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
       print("Distance:", closest_pair_of_points(points, len(points)))





"""simple docstring"""







def    UpperCAmelCase__       (lowerCAmelCase_ = 100_0000   ):




					'''simple docstring'''


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

					__SCREAMING_SNAKE_CASE						   =				[float(lowerCAmelCase_   ) for n in range(limit + 1   )]

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

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


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