
from __future__ import annotations

from collections.abc import Iterable







class  _lowerCamelCase			:

     def __init__(  self							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_    ):
            __snake_case       ,       __snake_case						       =   float(SCREAMING_SNAKE_CASE_    ), float(SCREAMING_SNAKE_CASE_    )

     def __eq__(  self							,       SCREAMING_SNAKE_CASE_    ):
            return self.x == other.x and self.y == other.y

     def __ne__(  self							,       SCREAMING_SNAKE_CASE_    ):
            return not self == other

     def __gt__(  self							,       SCREAMING_SNAKE_CASE_    ):
            if self.x > other.x:
                   return True
            elif self.x == other.x:
                   return self.y > other.y
            return False

     def __lt__(  self							,       SCREAMING_SNAKE_CASE_    ):
            return not self > other

     def __ge__(  self							,       SCREAMING_SNAKE_CASE_    ):
            if self.x > other.x:
                   return True
            elif self.x == other.x:
                   return self.y >= other.y
            return False

     def __le__(  self							,       SCREAMING_SNAKE_CASE_    ):
            if self.x < other.x:
                   return True
            elif self.x == other.x:
                   return self.y <= other.y
            return False

     def __repr__(  self    ):
            return f'''({self.x}, {self.y})'''

     def __hash__(  self    ):
            return hash(self.x    )





def        __lowercase(							__snake_case				:		list[Point] | list[list[float]] | Iterable[list[float]]    ,)       ->   Optional[int]:
       __snake_case						       =   []
       if list_of_tuples:
              for p in list_of_tuples:
                     if isinstance(__snake_case    ,__snake_case					):
                            points.append(__snake_case					)
                     else:
                            try:
                                   points.append(Point(p[0]    ,p[1]					)					)
                            except (IndexError, TypeError):
                                   print(
                                       f'''Ignoring deformed point {p}. All points'''
                                       ' must have at least 2 coordinates.'					)
       return points
def        __lowercase(							__snake_case				:		list[Point] | list[list[float]]					)       ->   Dict:




       if not hasattr(__snake_case    ,'__iter__'					):
              __snake_case						       =   f'''Expecting an iterable object but got an non-iterable type {points}'''
              raise ValueError(__snake_case					)

       if not points:
              __snake_case						       =   f'''Expecting a list of points but got {points}'''
              raise ValueError(__snake_case					)

       return _construct_points(__snake_case					)
def        __lowercase(							__snake_case				:		Point    ,__snake_case				:		Point    ,__snake_case				:		Point					)       ->   Optional[Any]:
       __snake_case						       =   (a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
       return det
def        __lowercase(							__snake_case				:		list[Point]					)       ->   int:
       __snake_case						       =   sorted(_validate_input(__snake_case					)					)
       __snake_case						       =   len(__snake_case					)
       __snake_case						       =   set()

       for i in range(n - 1					):
              for j in range(i + 1    ,__snake_case					):
                     __snake_case						       =   __snake_case						       =   False
                     __snake_case						       =   True
                     for k in range(__snake_case					):
                            if k != i and k != j:
                                   __snake_case						       =   _det(points[i]    ,points[j]    ,points[k]					)

                                   if det_k > 0:
                                          __snake_case						       =   True
                                   elif det_k < 0:
                                          __snake_case						       =   True
                                   else:
                                          # point[i], point[j], point[k] all lie on a straight line
                                          # if point[k] is to the left of point[i] or it's to the
                                          # right of point[j], then point[i], point[j] cannot be
                                          # part of the convex hull of A
                                          if points[k] < points[i] or points[k] > points[j]:
                                                 __snake_case						       =   False
                                                 break

                            if points_left_of_ij and points_right_of_ij:
                                   __snake_case						       =   False
                                   break

                     if ij_part_of_convex_hull:
                            convex_set.update([points[i], points[j]]					)

       return sorted(__snake_case					)
def        __lowercase(							__snake_case				:		list[Point]					)       ->   Optional[int]:
       __snake_case						       =   sorted(_validate_input(__snake_case					)					)
       __snake_case						       =   len(__snake_case					)

       # divide all the points into an upper hull and a lower hull
       # the left most point and the right most point are definitely
       # members of the convex hull by definition.
       # use these two anchors to divide all the points into two hulls,
       # an upper hull and a lower hull.

       # all points to the left (above) the line joining the extreme points belong to the
       # upper hull
       # all points to the right (below) the line joining the extreme points below to the
       # lower hull
       # ignore all points on the line joining the extreme points since they cannot be
       # part of the convex hull

       __snake_case						       =   points[0]
       __snake_case						       =   points[n - 1]

       __snake_case						       =   {left_most_point, right_most_point}
       __snake_case						       =   []
       __snake_case						       =   []

       for i in range(1    ,n - 1					):
              __snake_case						       =   _det(__snake_case    ,__snake_case    ,points[i]					)

              if det > 0:
                     upper_hull.append(points[i]					)
              elif det < 0:
                     lower_hull.append(points[i]					)

       _construct_hull(__snake_case    ,__snake_case    ,__snake_case    ,__snake_case					)
       _construct_hull(__snake_case    ,__snake_case    ,__snake_case    ,__snake_case					)

       return sorted(__snake_case					)
def        __lowercase(							__snake_case				:		list[Point]    ,__snake_case				:		Point    ,__snake_case				:		Point    ,__snake_case				:		set[Point]					)       ->   List[Any]:




       if points:
              __snake_case						       =   None
              __snake_case						       =   float('-inf'					)
              __snake_case						       =   []

              for p in points:
                     __snake_case						       =   _det(__snake_case    ,__snake_case    ,__snake_case					)

                     if det > 0:
                            candidate_points.append(__snake_case					)

                            if det > extreme_point_distance:
                                   __snake_case						       =   det
                                   __snake_case						       =   p

              if extreme_point:
                     _construct_hull(__snake_case    ,__snake_case    ,__snake_case    ,__snake_case					)
                     convex_set.add(__snake_case					)
                     _construct_hull(__snake_case    ,__snake_case    ,__snake_case    ,__snake_case					)
def        __lowercase(							__snake_case				:		list[Point]					)       ->   List[Any]:
       __snake_case						       =   sorted(_validate_input(__snake_case					)					)
       __snake_case						       =   len(__snake_case					)

       __snake_case						       =   points[:2]
       for i in range(2    ,__snake_case					):
              __snake_case						       =   _det(convex_hull[1]    ,convex_hull[0]    ,points[i]					)
              if det > 0:
                     convex_hull.insert(0    ,points[i]					)
                     break
              elif det < 0:
                     convex_hull.append(points[i]					)
                     break
              else:
                     __snake_case						       =   points[i]
       i += 1

       for j in range(__snake_case    ,__snake_case					):
              if (
                  _det(convex_hull[0]    ,convex_hull[-1]    ,points[j]					) > 0
                  and _det(convex_hull[-1]    ,convex_hull[0]    ,points[1]					) < 0
              ):
                     # The point lies within the convex hull
                     continue

              convex_hull.insert(0    ,points[j]					)
              convex_hull.append(points[j]					)
              while _det(convex_hull[0]    ,convex_hull[1]    ,convex_hull[2]					) >= 0:
                     del convex_hull[1]
              while _det(convex_hull[-1]    ,convex_hull[-2]    ,convex_hull[-3]					) <= 0:
                     del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
       return sorted(convex_hull[1:] if len(__snake_case					) > 3 else convex_hull					)
def        __lowercase(							)       ->   List[Any]:
       __snake_case						       =   [
           (0, 3),
           (2, 2),
           (1, 1),
           (2, 1),
           (3, 0),
           (0, 0),
           (3, 3),
           (2, -1),
           (2, -4),
           (1, -3),
       ]
       # the convex set of points is
       # [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
       __snake_case						       =   convex_hull_bf(__snake_case					)

       __snake_case						       =   convex_hull_recursive(__snake_case					)
       assert results_bf == results_recursive

       __snake_case						       =   convex_hull_melkman(__snake_case					)
       assert results_bf == results_melkman

       print(__snake_case					)


if __name__ == "__main__":
 main()





'''simple docstring'''



def 	__lowerCAmelCase       (				lowerCamelCase :    float					,		lowerCamelCase :    float       ):






	'''simple docstring'''




	__lowerCAmelCase       				=	float()
	try:
		__lowerCAmelCase       				=	mass * acceleration
	except Exception:
		return -0.0
	return force


if __name__ == "__main__":
	import doctest

	# run doctest
	doctest.testmod()

	# demo
	lowerCAmelCase						:		List[Any]						      = 12.5
	lowerCAmelCase						:		Optional[Any]						      = 1_0
	lowerCAmelCase						:		str						      = newtons_second_law_of_motion(mass, acceleration)
	print('''The force is ''', force, '''N''')