




from __future__ import annotations

from collections.abc import Iterable




class 	UpperCamelCase__			:

    '''simple docstring'''



    def __init__(					self  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   str:
           lowerCamelCase				,   lowerCamelCase     :   Union[str, Any]    				=      float(UpperCamelCase__  ), float(UpperCamelCase__  )







    def __eq__(					self  ,						UpperCamelCase__  )  ->   List[Any]:
           return self.x == other.x and self.y == other.y







    def __ne__(					self  ,						UpperCamelCase__  )  ->   Tuple:
           return not self == other







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







    def __lt__(					self  ,						UpperCamelCase__  )  ->   List[str]:
           return not self > other







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







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







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







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




def   A   (   _SCREAMING_SNAKE_CASE				,)			->				list[Point]:
       lowerCamelCase     :   list[Point]    				=      []
       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   A   (   _SCREAMING_SNAKE_CASE					)			->				list[Point]:

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

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

       return _construct_points(_SCREAMING_SNAKE_CASE					)

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				float:
       lowerCamelCase     :   Any    				=      (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   A   (   _SCREAMING_SNAKE_CASE					)			->				list[Point]:
       lowerCamelCase     :   Dict    				=      sorted(_validate_input(_SCREAMING_SNAKE_CASE					)					)
       lowerCamelCase     :   Optional[Any]    				=      len(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Dict    				=      set()

       for i in range(n - 1					):
              for j in range(i + 1				,_SCREAMING_SNAKE_CASE					):
                     lowerCamelCase     :   Optional[int]    				=      False
                     lowerCamelCase     :   Optional[int]    				=      True
                     for k in range(_SCREAMING_SNAKE_CASE					):
                            if k != i and k != j:
                                   lowerCamelCase     :   List[str]    				=      _det(points[i]				,points[j]				,points[k]					)

                                   if det_k > 0:
                                          lowerCamelCase     :   Union[str, Any]    				=      True
                                   elif det_k < 0:
                                          lowerCamelCase     :   str    				=      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]:
                                                 lowerCamelCase     :   str    				=      False
                                                 break

                            if points_left_of_ij and points_right_of_ij:
                                   lowerCamelCase     :   List[str]    				=      False
                                   break

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

       return sorted(_SCREAMING_SNAKE_CASE					)

def   A   (   _SCREAMING_SNAKE_CASE					)			->				list[Point]:
       lowerCamelCase     :   Any    				=      sorted(_validate_input(_SCREAMING_SNAKE_CASE					)					)
       lowerCamelCase     :   List[str]    				=      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

       lowerCamelCase     :   int    				=      points[0]
       lowerCamelCase     :   List[str]    				=      points[n - 1]

       lowerCamelCase     :   List[str]    				=      {left_most_point, right_most_point}
       lowerCamelCase     :   Union[str, Any]    				=      []
       lowerCamelCase     :   Optional[int]    				=      []

       for i in range(1				,n - 1					):
              lowerCamelCase     :   List[Any]    				=      _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   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				None:
       if points:
              lowerCamelCase     :   List[str]    				=      None
              lowerCamelCase     :   Union[str, Any]    				=      float("-inf"					)
              lowerCamelCase     :   int    				=      []

              for p in points:
                     lowerCamelCase     :   List[str]    				=      _det(_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)

                     if det > 0:
                            candidate_points.append(_SCREAMING_SNAKE_CASE					)

                            if det > extreme_point_distance:
                                   lowerCamelCase     :   str    				=      det
                                   lowerCamelCase     :   List[str]    				=      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   A   (   _SCREAMING_SNAKE_CASE					)			->				list[Point]:
       lowerCamelCase     :   str    				=      sorted(_validate_input(_SCREAMING_SNAKE_CASE					)					)
       lowerCamelCase     :   Union[str, Any]    				=      len(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   int    				=      points[:2]
       for i in range(2				,_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   List[str]    				=      _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:
                     lowerCamelCase     :   Any    				=      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   A   (   )			->				int:
       lowerCamelCase     :   Dict    				=      [
           (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)]
       lowerCamelCase     :   Optional[Any]    				=      convex_hull_bf(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   Optional[Any]    				=      convex_hull_recursive(_SCREAMING_SNAKE_CASE					)
       assert results_bf == results_recursive

       lowerCamelCase     :   Optional[Any]    				=      convex_hull_melkman(_SCREAMING_SNAKE_CASE					)
       assert results_bf == results_melkman

       print(_SCREAMING_SNAKE_CASE					)


if __name__ == "__main__":
       main()












import os
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
       import torch

       from transformers import GPTaLMHeadModel




@require_torch
@require_sentencepiece
@require_tokenizers
class 	UpperCamelCase__			(unittest.TestCase  ):

    '''simple docstring'''



    @slow
    @unittest.skip("Model is not available."  )
    def 					_lowercase  (					self  )  ->   List[Any]:
           lowerCamelCase     :   List[Any]    				=      "nvidia/megatron-gpt2-345m/"
           if "MYDIR" in os.environ:
                  lowerCamelCase     :   Union[str, Any]    				=      os.path.join(os.environ["MYDIR"]  ,						UpperCamelCase__  )
           lowerCamelCase     :   Any    				=      GPTaLMHeadModel.from_pretrained(UpperCamelCase__  )
           model.to(UpperCamelCase__  )
           model.half()

           lowerCamelCase     :   Dict    				=      torch.tensor(
               [[101, 7110, 1005, 1056, 2023, 1_1333, 1_7413, 1029, 102]]  ,						device=UpperCamelCase__  ,						dtype=torch.long  ,						)

           with torch.no_grad():
                  lowerCamelCase     :   Any    				=      model(UpperCamelCase__  ).logits

           lowerCamelCase     :   Union[str, Any]    				=      torch.Size((1, 9, 5_0257)  )
           self.assertEqual(output.shape  ,						UpperCamelCase__  )

           lowerCamelCase     :   List[str]    				=      torch.tensor(
               [
                   4.9414,
                   -0.2920,
                   -1.2148,
                   -4.0273,
                   -0.5161,
                   -5.2109,
                   -1.2412,
                   -1.8301,
                   -1.7734,
                   -4.7148,
                   -0.2317,
                   -1.0811,
                   -2.1777,
                   0.4141,
                   -3.7969,
                   -4.0586,
                   -2.5332,
                   -3.3809,
                   4.3867,
               ]  ,						device=UpperCamelCase__  ,						dtype=torch.half  ,						)

           for i in range(19  ):
                  lowerCamelCase				,   lowerCamelCase     :   Optional[int]    				=      8 * i // 17, 2792 * i  # along the diagonal
                  lowerCamelCase				,   lowerCamelCase     :   Tuple    				=      output[0, r, c], expected_diag[i]
                  lowerCamelCase     :   List[str]    				=      F'''row={r} col={c} computed={computed} expected={expected}'''
                  self.assertAlmostEqual(UpperCamelCase__  ,						UpperCamelCase__  ,						delta=1e-4  ,						msg=UpperCamelCase__  )






