






"""simple docstring"""



from __future__ import annotations

from collections.abc import Iterable


class 	_UpperCamelCase :



    '''simple docstring'''


    def __init__(      self   ,			__lowercase   ,			__lowercase			):
     UpperCAmelCase__						,	UpperCAmelCase__ 						=				float(__lowercase			), float(__lowercase			)


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


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


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


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


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


    def __le__(      self   ,			__lowercase			):
     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       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	)    ->list[Point]:
 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       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->list[Point]:

 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       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 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__		(   _SCREAMING_SNAKE_CASE			)    ->list[Point]:
 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__ 						=				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       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->list[Point]:
 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       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->None:
 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       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->list[Point]:
 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       snake_case__		(   )    ->Union[str, Any]:
 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()











"""simple docstring"""



import itertools
from pathlib import Path




def       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->int:
 UpperCAmelCase__ 						=				[tuple(_SCREAMING_SNAKE_CASE			) for login in logins]

 UpperCAmelCase__ 						=				{char for login in split_logins for char in login}

 for permutation in itertools.permutations(_SCREAMING_SNAKE_CASE			):
  UpperCAmelCase__ 						=				True
  for login in logins:
   if not (
       permutation.index(login[0]			)
       < permutation.index(login[1]			)
       < permutation.index(login[2]			)
   ):
    UpperCAmelCase__ 						=				False
    break

  if satisfied:
   return int("""""".join(_SCREAMING_SNAKE_CASE			)			)

 raise Exception("""Unable to find the secret passcode"""			)




def       snake_case__		(   _SCREAMING_SNAKE_CASE = "keylog.txt"			)    ->int:
 UpperCAmelCase__ 						=				Path(_SCREAMING_SNAKE_CASE			).parent.joinpath(_SCREAMING_SNAKE_CASE			).read_text().splitlines()

 return find_secret_passcode(_SCREAMING_SNAKE_CASE			)


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



