




from __future__ import annotations

from collections.abc import Iterable
class      _UpperCamelCase :
      def __init__(     self				:List[Any]	, lowerCamelCase				:int	, lowerCamelCase				:Optional[Any] )       ->     Union[str, Any]:
       UpperCAmelCase__								=  float(lowercase_ ), float(lowercase_ )
      def __eq__(     self				:Optional[Any]	, lowerCamelCase				:Optional[Any] )       ->     Optional[Any]:
       return self.x == other.x and self.y == other.y
      def __ne__(     self				:Union[str, Any]	, lowerCamelCase				:Dict )       ->     Tuple:
       return not self == other
      def __gt__(     self				:List[Any]	, lowerCamelCase				:int )       ->     Dict:




       if self.x > other.x:
        return True
       elif self.x == other.x:
        return self.y > other.y
       return False
      def __lt__(     self				:Tuple	, lowerCamelCase				:str )       ->     Optional[Any]:
       return not self > other
      def __ge__(     self				:Union[str, Any]	, lowerCamelCase				:Any )       ->     Optional[int]:




       if self.x > other.x:
        return True
       elif self.x == other.x:
        return self.y >= other.y
       return False
      def __le__(     self				:Any	, lowerCamelCase				:str )       ->     Dict:




       if self.x < other.x:
        return True
       elif self.x == other.x:
        return self.y <= other.y
       return False
      def __repr__(     self				:str )       ->     str:
       return f'''({self.x}, {self.y})'''







      def __hash__(     self				:Dict )       ->     List[str]:
       return hash(self.x )



def   lowerCAmelCase						(						_lowerCAmelCase							:				list[Point] | list[list[float]] | Iterable[list[float]]  ,							):




 """simple docstring"""







 UpperCAmelCase__								=  []
 if list_of_tuples:
  for p in list_of_tuples:
   if isinstance(SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__		):
    points.append(SCREAMING_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   lowerCAmelCase						(						_lowerCAmelCase							:				list[Point] | list[list[float]]		):




 """simple docstring"""







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

 if not points:
  UpperCAmelCase__								=  F'''Expecting a list of points but got {points}'''
  raise ValueError(SCREAMING_SNAKE_CASE__		)

 return _construct_points(SCREAMING_SNAKE_CASE__		)



def   lowerCAmelCase						(						_lowerCAmelCase							:				Point  ,							_lowerCAmelCase							:				Point  ,							_lowerCAmelCase							:				Point		):




 """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   lowerCAmelCase						(						_lowerCAmelCase							:				list[Point]		):




 """simple docstring"""







 UpperCAmelCase__								=  sorted(_validate_input(SCREAMING_SNAKE_CASE__		)		)
 UpperCAmelCase__								=  len(SCREAMING_SNAKE_CASE__		)
 UpperCAmelCase__								=  set()

 for i in range(n - 1		):
  for j in range(i + 1  ,							SCREAMING_SNAKE_CASE__		):
   UpperCAmelCase__								=  False
   UpperCAmelCase__								=  True
   for k in range(SCREAMING_SNAKE_CASE__		):
    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(SCREAMING_SNAKE_CASE__		)



def   lowerCAmelCase						(						_lowerCAmelCase							:				list[Point]		):




 """simple docstring"""







 UpperCAmelCase__								=  sorted(_validate_input(SCREAMING_SNAKE_CASE__		)		)
 UpperCAmelCase__								=  len(SCREAMING_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

 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(SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__  ,							points[i]		)

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

 _construct_hull(SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__		)
 _construct_hull(SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__		)

 return sorted(SCREAMING_SNAKE_CASE__		)



def   lowerCAmelCase						(						_lowerCAmelCase							:				list[Point]  ,							_lowerCAmelCase							:				Point  ,							_lowerCAmelCase							:				Point  ,							_lowerCAmelCase							:				set[Point]		):




 """simple docstring"""







 if points:
  UpperCAmelCase__								=  None
  UpperCAmelCase__								=  float("-inf"		)
  UpperCAmelCase__								=  []

  for p in points:
   UpperCAmelCase__								=  _det(SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__  ,							SCREAMING_SNAKE_CASE__		)

   if det > 0:
    candidate_points.append(SCREAMING_SNAKE_CASE__		)

    if det > extreme_point_distance:
     UpperCAmelCase__								=  det
     UpperCAmelCase__								=  p

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



def   lowerCAmelCase						(						_lowerCAmelCase							:				list[Point]		):




 """simple docstring"""







 UpperCAmelCase__								=  sorted(_validate_input(SCREAMING_SNAKE_CASE__		)		)
 UpperCAmelCase__								=  len(SCREAMING_SNAKE_CASE__		)

 UpperCAmelCase__								=  points[:2]
 for i in range(2  ,							SCREAMING_SNAKE_CASE__		):
  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(SCREAMING_SNAKE_CASE__  ,							SCREAMING_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(SCREAMING_SNAKE_CASE__		) > 3 else convex_hull		)



def   lowerCAmelCase						(						):




 """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(SCREAMING_SNAKE_CASE__		)

 UpperCAmelCase__								=  convex_hull_recursive(SCREAMING_SNAKE_CASE__		)
 assert results_bf == results_recursive

 UpperCAmelCase__								=  convex_hull_melkman(SCREAMING_SNAKE_CASE__		)
 assert results_bf == results_melkman

 print(SCREAMING_SNAKE_CASE__		)


if __name__ == "__main__":
  main()











from __future__ import annotations

from string import ascii_letters



def   lowerCAmelCase						(						_lowerCAmelCase							:				str  ,							_lowerCAmelCase							:				int  ,							_lowerCAmelCase							:				str | None = None		):




 """simple docstring"""







 UpperCAmelCase__								=  alphabet or ascii_letters

 # The final result string
 UpperCAmelCase__								=  ""

 for character in input_string:
  if character not in alpha:
   # Append without encryption if character is not in the alphabet
   result += character
  else:
   # Get the index of the new key and make sure it isn't too large
   UpperCAmelCase__								=  (alpha.index(_lowerCAmelCase		) + key) % len(_lowerCAmelCase		)

   # Append the encoded character to the alphabet
   result += alpha[new_key]

 return result



def   lowerCAmelCase						(						_lowerCAmelCase							:				str  ,							_lowerCAmelCase							:				int  ,							_lowerCAmelCase							:				str | None = None		):




 """simple docstring"""







 key *= -1

 return encrypt(_lowerCAmelCase  ,							_lowerCAmelCase  ,							_lowerCAmelCase		)



def   lowerCAmelCase						(						_lowerCAmelCase							:				str  ,							_lowerCAmelCase							:				str | None = None		):




 """simple docstring"""







 UpperCAmelCase__								=  alphabet or ascii_letters

 # To store data on all the combinations
 UpperCAmelCase__								=  {}

 # Cycle through each combination
 for key in range(1  ,							len(_lowerCAmelCase		) + 1		):
  # Decrypt the message and store the result in the data
  UpperCAmelCase__								=  decrypt(_lowerCAmelCase  ,							_lowerCAmelCase  ,							_lowerCAmelCase		)

 return brute_force_data


if __name__ == "__main__":
  while True:
    print(F'''\n{"-" * 1_0}\n Menu\n{"-" * 1_0}''')
    print(*["1.Encrypt", "2.Decrypt", "3.BruteForce", "4.Quit"], sep="\n")

    # get user input
    _lowerCAmelCase  :				List[Any]						=				input("\nWhat would you like to do?: ").strip() or "4"

    # run functions based on what the user chose
    if choice not in ("1", "2", "3", "4"):
      print("Invalid choice, please enter a valid choice")
    elif choice == "1":
      _lowerCAmelCase  :				Any						=				input("Please enter the string to be encrypted: ")
      _lowerCAmelCase  :				str						=				int(input("Please enter off-set: ").strip())

      print(encrypt(input_string, key))
    elif choice == "2":
      _lowerCAmelCase  :				Optional[Any]						=				input("Please enter the string to be decrypted: ")
      _lowerCAmelCase  :				Any						=				int(input("Please enter off-set: ").strip())

      print(decrypt(input_string, key))
    elif choice == "3":
      _lowerCAmelCase  :				int						=				input("Please enter the string to be decrypted: ")
      _lowerCAmelCase  :				Dict						=				brute_force(input_string)

      for key, value in brute_force_data.items():
        print(F'''Key: {key} | Message: {value}''')

    elif choice == "4":
      print("Goodbye.")
      break





