




"""simple docstring"""







from __future__ import annotations

from collections.abc import Iterable

class 							snake_case_ :







   """simple docstring"""




   def __init__(		self					,				lowerCamelCase_					,				lowerCamelCase_)							->      Optional[int]:
       UpperCamelCase					,  UpperCamelCase										=  float(lowerCamelCase_), float(lowerCamelCase_)







   def __eq__(		self					,				lowerCamelCase_)							->      Tuple:
       return self.x == other.x and self.y == other.y







   def __ne__(		self					,				lowerCamelCase_)							->      Dict:
       return not self == other







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







   def __lt__(		self					,				lowerCamelCase_)							->      Dict:
       return not self > other







   def __ge__(		self					,				lowerCamelCase_)							->      Optional[Any]:
       if self.x > other.x:
           return True
       elif self.x == other.x:
           return self.y >= other.y
       return False







   def __le__(		self					,				lowerCamelCase_)							->      Optional[int]:
       if self.x < other.x:
           return True
       elif self.x == other.x:
           return self.y <= other.y
       return False







   def __repr__(		self)							->      Union[str, Any]:
       return F'({self.x}, {self.y})'







   def __hash__(		self)							->      Optional[Any]:
       return hash(self.x)





def     __snake_case   (							_lowercase     :   Dict ,):


    """simple docstring"""







    UpperCamelCase										=  []
    if list_of_tuples:
        for p in list_of_tuples:
            if isinstance(_lowercase ,_lowercase						):
                points.append(_lowercase						)
            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     __snake_case   (							_lowercase     :   Tuple						):


    """simple docstring"""







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

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

    return _construct_points(_lowercase						)





def     __snake_case   (							_lowercase     :   List[str] ,_lowercase     :   Optional[Any] ,_lowercase     :   str						):


    """simple docstring"""







    UpperCamelCase										=  (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     __snake_case   (							_lowercase     :   Optional[int]						):


    """simple docstring"""







    UpperCamelCase										=  sorted(_validate_input(_lowercase						)						)
    UpperCamelCase										=  len(_lowercase						)
    UpperCamelCase										=  set()

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

                    if det_k > 0:
                        UpperCamelCase										=  True
                    elif det_k < 0:
                        UpperCamelCase										=  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]:
                            UpperCamelCase										=  False
                            break

                if points_left_of_ij and points_right_of_ij:
                    UpperCamelCase										=  False
                    break

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

    return sorted(_lowercase						)





def     __snake_case   (							_lowercase     :   Tuple						):


    """simple docstring"""







    UpperCamelCase										=  sorted(_validate_input(_lowercase						)						)
    UpperCamelCase										=  len(_lowercase						)

    # 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

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

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

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

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

    _construct_hull(_lowercase ,_lowercase ,_lowercase ,_lowercase						)
    _construct_hull(_lowercase ,_lowercase ,_lowercase ,_lowercase						)

    return sorted(_lowercase						)





def     __snake_case   (							_lowercase     :   Tuple ,_lowercase     :   List[str] ,_lowercase     :   str ,_lowercase     :   Union[str, Any]						):


    """simple docstring"""







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

        for p in points:
            UpperCamelCase										=  _det(_lowercase ,_lowercase ,_lowercase						)

            if det > 0:
                candidate_points.append(_lowercase						)

                if det > extreme_point_distance:
                    UpperCamelCase										=  det
                    UpperCamelCase										=  p

        if extreme_point:
            _construct_hull(_lowercase ,_lowercase ,_lowercase ,_lowercase						)
            convex_set.add(_lowercase						)
            _construct_hull(_lowercase ,_lowercase ,_lowercase ,_lowercase						)





def     __snake_case   (							_lowercase     :   Union[str, Any]						):


    """simple docstring"""







    UpperCamelCase										=  sorted(_validate_input(_lowercase						)						)
    UpperCamelCase										=  len(_lowercase						)

    UpperCamelCase										=  points[:2]
    for i in range(2 ,_lowercase						):
        UpperCamelCase										=  _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:
            UpperCamelCase										=  points[i]
    i += 1

    for j in range(_lowercase ,_lowercase						):
        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(_lowercase						) > 3 else convex_hull						)





def     __snake_case   (							):


    """simple docstring"""







    UpperCamelCase										=  [
        (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)]
    UpperCamelCase										=  convex_hull_bf(_lowercase						)

    UpperCamelCase										=  convex_hull_recursive(_lowercase						)
    assert results_bf == results_recursive

    UpperCamelCase										=  convex_hull_melkman(_lowercase						)
    assert results_bf == results_melkman

    print(_lowercase						)


if __name__ == "__main__":
  main()





"""simple docstring"""







from math import pi





def     __snake_case   (							_lowercase						):


    """simple docstring"""







    return degree / (180 / pi)


if __name__ == "__main__":
  from doctest import testmod

  testmod()