




from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize




class     A					(				lowerCamelCase_       ):
							_SCREAMING_SNAKE_CASE  :		Any			  =       1
							_SCREAMING_SNAKE_CASE  :		Optional[Any]			  =       2
							_SCREAMING_SNAKE_CASE  :		int			  =       3







							def __repr__(    self   :	Union[str, Any]				)		->					Optional[int]:

										"""simple docstring"""



										return f'''{self.__class__.__name__}.{self.name}'''







def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			float:

			'''simple docstring'''


			UpperCamelCase_				,   UpperCamelCase_     				= point
			return degrees(atana(y - miny     ,		x - minx					)					)




def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			Direction:

			'''simple docstring'''


			UpperCamelCase_				,   UpperCamelCase_     				= starting
			UpperCamelCase_				,   UpperCamelCase_     				= via
			UpperCamelCase_				,   UpperCamelCase_     				= target
			UpperCamelCase_     				= degrees(atana(ya - ya     ,		xa - xa					)					)
			via_angle %= 3_6_0
			UpperCamelCase_     				= degrees(atana(ya - ya     ,		xa - xa					)					)
			target_angle %= 3_6_0
			# t-
			#  \ \
			#   \ v
			#    \|
			#     s
			# via_angle is always lower than target_angle, if direction is left.
			# If they are same, it means they are on a same line of convex hull.
			if target_angle > via_angle:
						return Direction.left
			elif target_angle == via_angle:
						return Direction.straight
			else:
						return Direction.right





def  a_		(							__snake_case					)	->			list[tuple[int, int]]:

			'''simple docstring'''


			if len(__snake_case					) <= 2:
						# There is no convex hull
						raise ValueError('graham_scan: argument must contain more than 3 points.'					)
			if len(__snake_case					) == 3:
						return points
			# find the lowest and the most left point
			UpperCamelCase_     				= 0
			UpperCamelCase_				,   UpperCamelCase_     				= maxsize, maxsize
			for i, point in enumerate(__snake_case					):
						UpperCamelCase_     				= point[0]
						UpperCamelCase_     				= point[1]
						if y < miny:
									UpperCamelCase_     				= y
									UpperCamelCase_     				= x
									UpperCamelCase_     				= i
						if y == miny and x < minx:
									UpperCamelCase_     				= x
									UpperCamelCase_     				= i

    # remove the lowest and the most left point from points for preparing for sort
			points.pop(__snake_case					)

			UpperCamelCase_     				= sorted(__snake_case     ,		key=lambda __snake_case					: angle_comparer(__snake_case     ,		__snake_case     ,		__snake_case					)					)
			# This insert actually costs complexity,
			# and you should instead add (minx, miny) into stack later.
			# I'm using insert just for easy understanding.
			sorted_points.insert(0     ,		(minx, miny)					)

			UpperCamelCase_     				= deque()
			stack.append(sorted_points[0]					)
			stack.append(sorted_points[1]					)
			stack.append(sorted_points[2]					)
			# In any ways, the first 3 points line are towards left.
			# Because we sort them the angle from minx, miny.
			UpperCamelCase_     				= Direction.left

			for i in range(3     ,		len(__snake_case					)					):
						while True:
									UpperCamelCase_     				= stack[-2]
									UpperCamelCase_     				= stack[-1]
									UpperCamelCase_     				= sorted_points[i]
									UpperCamelCase_     				= check_direction(__snake_case     ,		__snake_case     ,		__snake_case					)

									if next_direction == Direction.left:
												UpperCamelCase_     				= Direction.left
												break
									if next_direction == Direction.straight:
												if current_direction == Direction.left:
															# We keep current_direction as left.
															# Because if the straight line keeps as straight,
															# we want to know if this straight line is towards left.
															break
												elif current_direction == Direction.right:
															# If the straight line is towards right,
															# every previous points on those straigh line is not convex hull.
															stack.pop()
									if next_direction == Direction.right:
												stack.pop()
						stack.append(sorted_points[i]					)
			return list(__snake_case					)






from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types




def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			torch.Tensor:

			'''simple docstring'''


			if not inplace:
						UpperCamelCase_     				= ma + ma
			else:
						ma += ma

			return ma




def  a_		(							__snake_case     ,		__snake_case					)	->			torch.Tensor:

			'''simple docstring'''


			UpperCamelCase_     				= -1 * len(__snake_case					)
			UpperCamelCase_     				= list(range(len(tensor.shape[:zero_index]					)					)					)
			return tensor.permute(first_inds + [zero_index + i for i in inds]					)




def  a_		(							__snake_case     ,		__snake_case					)	->			torch.Tensor:

			'''simple docstring'''


			return t.reshape(t.shape[:-no_dims] + (-1,)					)




def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case     ,		__snake_case = 1E-4					)	->			torch.Tensor:

			'''simple docstring'''


			UpperCamelCase_     				= mask.expand(*value.shape					)
			return torch.sum(mask * value     ,		dim=__snake_case					) / (eps + torch.sum(__snake_case     ,		dim=__snake_case					))




def  a_		(							__snake_case     ,		__snake_case = 2.31_25     ,		__snake_case = 21.68_75     ,		__snake_case = 6_4					)	->			torch.Tensor:

			'''simple docstring'''


			UpperCamelCase_     				= torch.linspace(__snake_case     ,		__snake_case     ,		no_bins - 1     ,		device=pts.device					)
			UpperCamelCase_     				= torch.sqrt(torch.sum((pts.unsqueeze(-2					) - pts.unsqueeze(-3					)) ** 2     ,		dim=-1					)					)
			return torch.bucketize(__snake_case     ,		__snake_case					)




def  a_		(							__snake_case     ,		__snake_case					)	->			dict:

			'''simple docstring'''


			UpperCamelCase_     				= dicts[0]
			UpperCamelCase_     				= {}
			for k, v in first.items():
						UpperCamelCase_     				= [d[k] for d in dicts]
						if isinstance(__snake_case     ,		__snake_case					):
									UpperCamelCase_     				= dict_multimap(__snake_case     ,		__snake_case					)
						else:
									UpperCamelCase_     				= fn(__snake_case					)

			return new_dict




def  a_		(							__snake_case     ,		__snake_case					)	->			torch.Tensor:

			'''simple docstring'''


			UpperCamelCase_     				= v_bins.view(((1,) * len(x.shape					)) + (len(__snake_case					),)					)
			UpperCamelCase_     				= x[..., None] - reshaped_bins
			UpperCamelCase_     				= torch.argmin(torch.abs(__snake_case					)     ,		dim=-1					)
			return nn.functional.one_hot(__snake_case     ,		num_classes=len(__snake_case					)					).float()




def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case = 0     ,		__snake_case = 0					)	->			torch.Tensor:

			'''simple docstring'''


			UpperCamelCase_     				= []
			for i, s in enumerate(data.shape[:no_batch_dims]					):
						UpperCamelCase_     				= torch.arange(__snake_case					)
						UpperCamelCase_     				= r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape					) - i - 1)))					)
						ranges.append(__snake_case					)

			UpperCamelCase_     				= [slice(__snake_case					) for _ in range(len(data.shape					) - no_batch_dims					)]
			UpperCamelCase_     				= inds
			ranges.extend(__snake_case					)
			# Matt note: Editing this to get around the behaviour of using a list as an array index changing
			# in recent Numpy versions
			return data[tuple(__snake_case					)]


__a			:	List[Any]							     =		TypeVar("""T""")




def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			Dict[Any, Union[dict, list, tuple, Any]]:

			'''simple docstring'''


			UpperCamelCase_     				= {}
			for k, v in dic.items():
						if isinstance(__snake_case     ,		__snake_case					):
									UpperCamelCase_     				= dict_map(__snake_case     ,		__snake_case     ,		__snake_case					)
						else:
									UpperCamelCase_     				= tree_map(__snake_case     ,		__snake_case     ,		__snake_case					)

			return new_dict




@overload
def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			Any:

			'''simple docstring'''


			...




@overload
def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			dict:

			'''simple docstring'''


			...




@overload
def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			list:

			'''simple docstring'''


			...




@overload
def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			tuple:

			'''simple docstring'''


			...




def  a_		(							__snake_case     ,		__snake_case     ,		__snake_case					)	->			Any:

			'''simple docstring'''


			if isinstance(__snake_case     ,		__snake_case					):
						return dict_map(__snake_case     ,		__snake_case     ,		__snake_case					)
			elif isinstance(__snake_case     ,		__snake_case					):
						return [tree_map(__snake_case     ,		__snake_case     ,		__snake_case					) for x in tree]
			elif isinstance(__snake_case     ,		__snake_case					):
						return tuple(tree_map(__snake_case     ,		__snake_case     ,		__snake_case					) for x in tree					)
			elif isinstance(__snake_case     ,		__snake_case					):
						return fn(__snake_case					)
			else:
						print(type(__snake_case					)					)
						raise ValueError('Not supported'					)





__a			:	Tuple							     =		partial(tree_map, leaf_type=torch.Tensor)
