






"""simple docstring"""



def 						lowercase    (				__snake_case				: int		,					__snake_case				: int	):
		return x if y == 0 else greatest_common_divisor(__snake_case		,					x % y	)



def 						lowercase    (				__snake_case				: int		,					__snake_case				: int	):
		return (x * y) // greatest_common_divisor(__snake_case		,					__snake_case	)



def 						lowercase    (				__snake_case				: int = 2_0	):
		lowercase_ : List[str]							       =   1
		for i in range(1		,					n + 1	):
				lowercase_ : Optional[int]							       =   lcm(__snake_case		,					__snake_case	)
		return g


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






def 		_lowercase (     lowercase__   ,	lowercase__						):
      return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2







def 		_lowercase (     lowercase__   ,	lowercase__=0						):
      return sorted(lowercase__   ,	key=lambda lowercase__						: x[column]						)







def 		_lowercase (     lowercase__   ,	lowercase__   ,	lowercase__=float('''inf'''						)						):

      for i in range(points_counts - 1						):
            for j in range(i + 1   ,	lowercase__						):
                  __lowerCAmelCase					:						List[str]					=					euclidean_distance_sqr(points[i]   ,	points[j]						)
                  if current_dis < min_dis:
                        __lowerCAmelCase					:						Tuple					=					current_dis
      return min_dis







def 		_lowercase (     lowercase__   ,	lowercase__   ,	lowercase__=float('''inf'''						)						):

      for i in range(min(6   ,	points_counts - 1						)   ,	lowercase__						):
            for j in range(max(0   ,	i - 6						)   ,	lowercase__						):
                  __lowerCAmelCase					:						Union[str, Any]					=					euclidean_distance_sqr(points[i]   ,	points[j]						)
                  if current_dis < min_dis:
                        __lowerCAmelCase					:						int					=					current_dis
      return min_dis







def 		_lowercase (     lowercase__   ,	lowercase__   ,	lowercase__						):

      # base case
      if points_counts <= 3:
            return dis_between_closest_pair(lowercase__   ,	lowercase__						)

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

      __lowerCAmelCase					:						List[Any]					=					dis_between_closest_in_strip(
          lowercase__   ,	len(lowercase__						)   ,	lowercase__						)
      return min(lowercase__   ,	lowercase__						)







def 		_lowercase (     lowercase__   ,	lowercase__						):
      __lowerCAmelCase					:						Union[str, Any]					=					column_based_sort(lowercase__   ,	column=0						)
      __lowerCAmelCase					:						Any					=					column_based_sort(lowercase__   ,	column=1						)
      return (
          closest_pair_of_points_sqr(
              lowercase__   ,	lowercase__   ,	lowercase__						)
      ) ** 0.5


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


